The Nature of Creativity in Fractal Art, Part 2: Mutationism

In the first posting I made the argument that fractal art is a variety of automatism. Automatism being imagery that is created by an automatic, self-operating device. One doesn’t draw fractals, the fractal program draws them. The fractal program is the self-operating device or automaton (ie. automatic thing).

Being an automatic thing, a fractal program is a machine. A machine is merely something that does something that isn’t a human being. So the distinction here is really between mechanical things and human things. Human things are conscious, have “life” and they think, are intelligent and imagine things. Machines are just assemblies of parts that work together – a system of active parts.

The active parts of a fractal “machine” are the parameter settings and the rest of the program that can’t be adjusted. We only need to look at the adjustable parts because that’s all we have to work with and it’s what we work with –the medium– that involves our creativity. This whole posting series is about creativity in fractal art. (In the next part I deal with the non-mechanical, “manualist vs. automatist” extended, non-core features that some fractal programs offer.)

To the user, a fractal program is parameter settings; variables that can be variously set. A fractal image is literally defined by its parameter settings. Reproduce the parameter settings and you reproduce, right down to the exact location and zoom level, the same image. So if you think about it, what can you, as a fractal artist, do but change the variable settings?

Since a fractal image is defined by the values that go with it’s variables (parameters), a new fractal image is nothing more than a new combination and permutation of those preexisting variables. In fact, it is impossible to create anything with the fractal program that is not a permutation of the parameter values. Of course, there’s an awful lot of permutations possible with even a simple fractal program that has only ten or so parameter settings, so it’s not really a limitation from an artistic perspective. You can produce a lot of variety of imagery with even just a simple fractal program using just one formula and rendering option. This is of course what attracts artists like ourselves to fractal programs: they’re very creative.

So you have a set of variables which together form the image we see. Altering any one of the variables can have unpredictable results on the appearance of the image although small changes to just a single variable tend to have progressive, and proportional effects that we can anticipate to some degree. Nevertheless, you can never be absolutely sure what a parameter change will do until you see the image that results.

Parameter produces picture…

This is analogous to a biological organism’s appearance. An organism’s appearance, form, is determined by it’s genetic code.  Variations between organisms of the same species are solely the result of alterations to the information contained in one or more genes. There are a distinct number of genes and each one has a value, so to speak, and so they’re just like the parameters of a fractal image. We could call the genes of an organism it’s parameters and the resulting “image” the appearance (state) of the organism.

So when a fractal artist works with a fractal program, the altering of parameter settings is exactly analogous to the altering of genetic information in a biological organism. I said “exactly” analogous because it is exactly equivalent: both actions are performing the function of mutation. They are both “mutational” actions and activities.  If I was Archimedes, I would jump up out of my bathtub and shout, “Eureka!”  Mutation is the central function and core skill of what we all do.  It’s the unifying thing.

Anyhow.  We say an organism has mutated, or been mutated, when a change occurs in it’s appearance (or physiological function) that is genetic. Biological researchers can actually make alterations to the genetic code for some genes for some organisms deliberately. They then develop the organism (render it) to see if it does anything worthwhile (or dies). In the same way fractalists change the setting for a single parameter in a fractal program and render the image to see what it does. Some parameter changes result in no image at all. The image “died” so to speak. So you can have non-viable mutations in biological organisms and in fractal images, as well.

The essence of “mutation” as opposed to “creation” is in what you start with. Creation starts with nothing at all or with just common raw materials while mutation always (always, always) starts with a preexisting “creature” (something created). Biological researchers don’t spend their time creating new organisms and hoping that they live and do something useful; they alter a preexisting one to improve it’s appearance or function. Fractal artists also don’t create new fractal images, they alter a preexisting one in hopes of improving it’s function; it’s function being it’s aesthetic appearance.  We ought to wear lab coats when using a fractal program.

When have you ever made a fractal image from nothing? Even if you wrote your own formula, that is merely the mutation of the “formula gene”.  Ultra Fractal is probably the most complex fractal program so it’s the best example to use to cover all the possibilities; one always has to load a formula as well as a rendering method, although the start up screen will load a basic one by default. But the automaton is not the formula, it’s the whole program and the formula is just another parameter to be set to initiate the automaton. You have to see that even with UF, the user just works with a long list of variables and alters their settings. Like I said, that’s all that’s in the parameter file and the parameter file is literally the DNA of the fractal image.

I’m not the first person to make this observation or even this sort of analysis; maybe with fractals but not with automatic imagery. A number of computer artists arrived at the realization that their “creative” work was merely generating permutations of their programs of which all existed ahead of time as “potential images”. But what got me really excited about this mutationist concept for fractal art was that it linked another form of automatism to it by the same principle of mutation, or medium of mutation. Mutation is ultimately the medium.

Photoshop filter “creations” also start with a preexisting image, a bitmap (jpg, photo) and through a series of transformations (gauntlet of visual virtual beatings) arrive at something viable or dead. The only difference with “filtering” (as I call it) is that the artist seems to have a great deal of discretion with regards to what effect to apply next as well as what settings to give it and whether to repeat it again or try something else. In short, it doesn’t look like an algorithm or a machine even, in the way that a fractal program with it’s nice neat set of menus and options does. However, I have often found myself arranging “syndromes” of filters to get a single effect in the same way a fractal program arranges “syndromes” of parameters to arrive at a single type of fractal imagery. Photoshop filter combinations are just modular algorithms and actually repeatable just like a fractal parameter file will “repeat” a previously produced image precisely.

So a series of photoshop filter combinations is not conceptually any different than a series of fractal parameter combinations and both become an organism with a discrete genetic makeup which can then be mutated in a series of permutations of the “genetic information” to produce a variety of new images. Both kinds of artists, the filterist and the fractalist, work by mutating a preexisting image and not by creating anything substantially new. The function of the mutationist is characterized by trial and error alterations which can’t be predicted ahead of time but whose steps can be retraced afterwards to arrive at the exact same result. This retracing shows that the creativity is in the mechanism, the automaton and not in the artist’s personal style or method of using the machine. The artist “discovers” new things, and doesn’t create them. The program creates them.

Place is a parameter

It’s like Columbus discovering the New World. We don’t credit Columbus with making the New World, just with discovering it. Thinking in terms of parameters, the surface of the Earth is a combination and permutation of spherical coordinates: latitude and longitude; East/West value and North/South value. I guess you could say that exploring the Earth is a binomial function. If anyone else sailed to the coordinates of the Bahamas (the first landfall) they too would have “discovered” it. All any explorer can do is summed up in all the permutations of latitude and longitude. Geometrically, all an explorer can do is visit a coordinate on the sphere of the Earth. Once all the coordinates have been visited then there’s nothing left to discover.

Bear with me; Columbus was a mutationist. What he did was to speculate at the possibility of venturing to a new coordinate setting and then “rendered” it.  Furthermore, Columbus was dissatisfied with the “rendered” results because it wasn’t India.  However, he came to accept the arbitrariness of the “program” and worked with the Americas in  a plan B sort of way to achieve his original goals of fame and fortune.  But was Columbus creative? Is discovery a creative act?

Is it creative to make “new” fractal images? that is, to render permutations of the parameters that haven’t been rendered yet? This is what this series of postings is all about. My answer is that it is creative, but that the creativity is entirely from the automaton, the fractal program. Discovery is a different kind of creative act just as in the sciences we speak of great discoveries and not great inventions. Dr. Mandelbrot discovered fractal geometry, he didn’t create it or invent it. That discovery was an awesome thing even though as we now know all about it, many people can retrace Mandelbrot’s steps just as many retraced Columbus’ steps and explored the rest of the New World.

I don’t know if it helps fractal artists to see themselves as mutationists rather than artists. That is, artists in the sense of being imaginative and manually skillful like a painter or sculptor is. Those kind of artists create artwork and don’t perform the function of a mutationist. Frankly, I find the mutationist works of most fractal artists to be more interesting than the creative works of most painters and sculptors.  (That’s why I spend my time doing things like this.) Fractal art doesn’t need to prop itself up with myths about creative artists using “drawing tools”. The world of mechanical creativity, automatism, is a very creative one and also one that is conceptually just as interesting.

The next part, Part 3, deals with the issue of image editing and the mixing of manual creativity with automatic. Does layering, masking, image importing and other hand-directed interventions make the fractal art created with it substantially different, and more like the traditional plastic arts (hand formed) or are those additions just trivial or at best secondary embellishments to what is still primarily an art form that revolves around mechanical creativity?  Is personal style relevant?  Is it even possible?  Style is the critical thing.

The Nature of Creativity in Fractal Art, Part 1: Automatism

Six months ago… I decided to summarize… and bring to completion… all my thoughts…

…about whatever it is my computer hobby is all about.

I didn’t even have a good label for it.

But nothing helps you think deeper and deeper than trying to write more and more precisely about something. It wasn’t about fractals really, it was about (what I came to call) “Picture Machines”. Anyhow, every rewrite spawned another rewrite, a better rewrite than the rewrite before. With the passing of each month I changed the date at the end of my preface chapter and changed what my preface was prefacing.  Here I am, facing another preface.

Eventually I came to the bottom of it all: fractals; cellular automata; IFS things; other programs that make neat pictures but are hard to label. I finally stumbled on what I casually call my Unified Field Theory of …whatever it is my computer hobby is all about. But now I have a name for it: automatism.

But that’s not the really big thing. While plumbing the deep concepts of automatism my mind wandered and I got hung up on authorship and creativity in fractal art. You see, automatism, the computerized type, is mostly fractal art. Fractals are the most developed and the most sophisticated species of automatism. That’s not the big thing. The real big thing is that I came to understand the nature of creativity in fractal art and that it brings together and explains as a single art form all the little weird programs I’ve used including that seemingly unrelated, and quite eclectic category of them called photoshop filters: automatism à la carte.

Four-part series

I need to explain what “automatism” is. Then I’ll explain “mutationism”. And then I’ll talk about image editing and after that I think there’ll be another part that takes all those things and then puts it all together and zaps it with lightning in a thunderstorm and screams, “It’s alive!”.  I’m expecting it to be a four part series of postings, but I’ve come to expect the unexpected.

If you don’t know automatism, you don’t know fractal art

It’s all about automatism. Fractals, and the fractal art form that comes from them, is automatic, all the time. Automatism is imagery that is created by a self-operating device. Automatic, in this context, means “self-operating” or “self-moving”. Obviously, this describes a machine, and since it’s self-this and self-that and implies a high degree of independence it doesn’t have the same category of function as that of a mere “tool”. In automatism, or we could say, in automatic art, the machine does everything because it doesn’t leave anything else for anyone to do; it works selfishly and in a self-contained way; the machine monopolizes everything and like a temperamental painter, won’t let you look until it’s finished. Such a machine, since it’s automatic, is called an automaton. The plural is automata, although one can say “automatons” if they prefer. Automatism is the art form, or the medium, or the method of automatic image creation.

Calling a fractal program an automaton and saying it “does everything” ought to sound extreme and possibly even mean and insulting in the context of fractal art. I know, I’ve been here a while, too. But that’s okay, I wouldn’t be writing such extreme things if I didn’t think they were true and that I could explain them and counter all objections. I don’t say these things lightly; I’ve been countering all my own objections to these ideas over the last six months. It’s all been proven, but let me show you the proof, the argument.

“Follow the creativity…”

Remember my comments about my mind wandering off following the idea of authorship? I know this issue has been dealt with years ago, but it was dealt with wrongly. Where does the creativity come from in fractal art? I read something on the Wikipedia on a page dealing with Algorithmic Art or some automatic art category like that, and it stated that the user is the creative agent because although the program draws everything, it merely carries out the directions and instructions that the “artist” gives it. The artist directs the machine.

You should find that to be a reasonable statement if you’re a healthy and well adjusted member of the fractal art world, that is: the fractal artist is the creative agent because they actually direct the automaton and configure it. The artist tells the machine what to do. The artist leads the creation of algorithmic art and is therefore, obviously, the author of it. Have you ever seen a fractal program make art all on it’s own? That is, have you ever seen a fractal program set it’s own parameters? Can a fractal program operate without a user?  Totally autonomously?

Well of course it can. In fact, the program is the leader and the “artist” is always the follower. The artist is not even in the position to direct the creation of imagery that they can’t even imagine beforehand. Fractal artists work by guessing at new parameters and reacting by trial and error at what the program draws from those guesses. Fractal artist always start with a preexisting image and mutate the parameter settings, guessing and then refining their guessing.  First big guesses and then smaller and smaller ones.  Self-similar guessing at multiple scales. They guess because they have absolutely no idea what any parameter change will look like ahead of time. Does that sound like the user giving the machine direction or the machine giving the user direction?

I’m not saying fractal artist don’t own the copyrights to “their images” or that we should all stop putting our names on “our own work” or treating it as “original” or “personal expression”. But you know, there has always been an equally valid argument for the machine being the originator of all fractal art. In fact, if the machine were a person, copyright would be a real problem in fractal art. They have this problem with operas: who’s more important, the composer of the music or the composer of the lyrics? So who should have the copyrights to fractals? The composer of the image or the composer of the title?

A little clarification of automatism

  • Automatism is a principle: self-operation (there’s nothing else to it)
  • Operation refers to the actual formation (drawing) of the imagery and not the peripheral actions of a user (or random number generator) making parameter settings that merely “initialize” the drawing process
  • Self-operation means mechanical operation instead of manual operation (they’re the only two options)
  • No manual operation means no personal involvement because, simply put, you’re not personally involved in the formation (drawing) of the imagery; it’s independent of, and doesn’t reflect the thoughts, ideas, imagination or intentions of the user
  • The concept of personal style is a mistake and is actually impossible.  When it occurs, it’s merely an association that is made with the first person to render that particular combination and permutation of settings with the program.  One “adopts” a style from the automaton rather than “fathering” their own.
  • One’s contribution to the whole image making process consists entirely of adjusting the variables of the automaton, in this case, the parameters in the fractal program, something that can be automated as well (eg. random batches). There is nothing else a user can do than “variate” the variables.
  • Creatively, one browses along a linear series of permutations, hopping or stepping from value to value, all of which were possible before they were actually rendered by individual users because they are just the permutations and combinations of the program’s variables; each image is a “condition” of the program and can be “activated” by anyone using it, even another machine like a random parameter generator.
  • The only way to create something personal and unique is to somehow involve one’s hands in the formation of the image, that is, draw on the image or alter it manually and selectively at the micro-scale.
  • The hands connect one’s conscious mind and imagination to the image because that is the only way our thoughts can be visually expressed and thereby introduces the medium of manualism to the medium of automatism (this will be dealt with in a later posting)
  • All these points are characteristics shared by all forms of automatism, not just fractal programs. Fractal programs are just “fractal-based” automata and as automatic as cellular automata, kaleidoscopes, transformation filters, and all the other varieties of genetic art programming. They’re all “picture machines” drawing a different style of picture, automatically.

What does a fractalist do?

Let’s take a closer look at how a user works with a fractal program. If you’re a fractal artist you know all this but you’ve probably forgotten what is really happening because everybody looks at a fractal program these days as a tool used by a fractal artist when in fact the fractal artist is a tool used by a fractal program.

Let’s take the most creative of all fractal artists:

  • He makes his own formulas!
  • He makes his own rendering methods!
  • He even invents his own gradients!

The program, Ultra Fractal, is the automaton. A mere shell of a thing, it is ultra programmable and not only waiting for UF Man’s directions, it’s waiting for a formula, and a rendering method, and a coloring thing… Can you imagine such a minimal automaton and such a maximal user as this? If anyone can be called The Stallion of Fractal Art, it’s such a user as this.

But even this user is a eunuch, a creative eunuch. Eunuchs are interesting legal entities because they can never be accused of fathering an heir to the throne or other stuff. Google defines it like this: “a man who has been castrated, especially (in the past) one employed to guard the women’s living areas at an oriental court.” So you see, a eunuch is never the author because a eunuch can’t be an author. In fractal art women can be eunuchs, too.

To understand how all fractal program users are followers instead of leaders, and guessers instead of directors, you need to look just a little more closely as what the fractal artist does and when. It’s like a court case, “What did you know and when did you know it?” Firstly, even the author of a fractal formula has no idea what it’s going to look like until it’s rendered. As for the rendering method, it’s just a set of instructions until the program combines it with the formula. The coloring gradient is the same. They’re all configuration settings even in UF where they can be written separately and aren’t just a menu item to be clicked on. But one loads a formula the same way they input any other configuration setting like iteration number or whatever. Writing a formula is just a longer and more elaborate configuration input.  More complex, but not categorically different.

In other programs, Tierazon, for instance; they have simple formula parsers which allow for trigonometric functions (sin, tan, cos…) as well as bracketed sections and the usual numbers and variables like “x”, “c”, etc… The formula parser is just another menu option or input field for variables that the algorithm permits. And no one knows what they’re going to look like until the program displays it. The big point though, is that the program always starts the creative process and not the user. The user then reacts to what the program produces. Like upping the iterations or lowering them, or zooming-in to a deeper location or whatever. It’s the machine making an image and the user fine-tuning it -afterwards. That’s the nature of (the user’s) creativity in fractal art: mutation.

Mutation is the name of the game

Mutation is the rearrangement or alteration of a preexisting system. Just as in Biology, a mutation is the changing of a gene’s function. A gene is like a variable of which the organism is the expression and the form that derives from all the genes in it. A parameter setting in a fractal program is like a gene and the altered value that goes with it is like a mutation to that gene. The image is the result of all the parameter settings’ expression, which would be the equivalent of the reproduced organism. What is there in the rendering of a fractal image that is not a variable? And what variables are there that do not have some sort of option as to what they can be set? Even a formula in UF is just a very elaborate parameter setting which forms part of the machine, the fractal program. The entire fractal program is the automaton, not just the fractal algorithm itself. Fractalists don’t draw the fractal images, they configure them. This is why a fractal image can be stored in a very small text file called a parameter file because it’s not the image, it’s the configuration settings for the automaton.

Artists don’t work by editing parameter files because they wouldn’t know what they were making until it was rendered. It might not even produce anything when edited as a text file in text editor. The user saves the parameter file after the user knows what their parameter changes look like. The user needs the program to guide it in changing parameter settings. The parameter settings are the DNA of the image and the user works by changing them one at a time, one gene at a time, on a preexisting image. They make art by mutation and not creation and certainly not with their imagination.

Mandelbrot said it first

Nothing I’ve said here changes how fractal art works or what it’s value is; it’s just a clarification of what’s been going on ever since Dr Mandelbrot made the first fractals on a computer. Even he said it changed the rules in art back in 1989 in his article, Fractals and an Art for the Sake of Science, in the computer art journal, Leonardo.

A new form of art redefines the boundary between ‘invention’ and ‘discovery’ as understood in the sciences and ‘creativity’ as understood in the plastic arts.

And how about this humdinger…

They [fractals] lend themselves to ‘painting by numbers’ that is surprisingly effective, even in the hands of the rank amateur.

Fractals and an Art for the Sake of Science, Benoit B. Mandelbrot, Leonardo. Supplemental Issue, Vol. 2, Computer Art in Context: SIGGRAPH ’89 Art Show Catalog (1989), pp. 21-24

Has anyone in the fractal art world read Mandelbrot’s article from way back in 1989? It doesn’t seem to have had any influence on them if they have. But I don’t fault anyone for not grasping the brilliant analysis Mandelbrot made back then about fractals and art. The article is very concise and unless you’re familiar with the terminology that accompanies the study of automatism, you would not immediately notice the careful nuances and implications of the words he uses. Mandelbrot understood automatism and for that reason he understood creativity in fractal art very well. I think most fractal artists understand better what Mandelbrot said about geometry than they do what he said about art.  More about that later, as well.

Coming soon, Part 2, which will be all about mutation; our favorite pastime.

Postscript: get an education, visit the new Fractovia

In particular, check out the “READ” section.  I found the article by Dr. Mandelbrot I quoted in Juan Luis Martinez’ most recent blog posting: “Defining fractal art: A “history” (kind of)“.  Juan Luis has been doing a lot of reading and a lot of thinking, too.  From my experience, it’s  the thinking that takes the most time and effort but that’s what yields the most progress.  I’m sure Dr. Mandelbrot spent most of his life thinking.  I was surprised to read how much he thought about art.  I don’t think anyone has contributed as much to both the science of fractals, as well as the art of fractals, as he has.

Galleries of the Gods

Aztec double-headed serpent, British Museum

Aztec double-headed serpent, British Museum

As I said in my last post, there’s something captivating about the Buddhist artworks in the Mogao caves in northwestern China and, strangely enough, I find it to be reminiscent of things I’ve seen in fractal programs.  I’ve come up with a term for this electrifying visual genre: “Divine Diagrams.”  “Divine” because they’re mostly, but not exclusively, religious artworks, and “Diagrams” because they have a highly ordered composition to them that makes them function like elaborate and very ornate diagrams; one almost feels like they should “read” them.  Furthermore, the term is generic because I’ve found that the kind of images in the Mogao caves are universal, occurring in almost every religion and culture and not exclusively Buddhist or Chinese.  Although the actual subject matter and purpose of Divine Diagrams differs depending on the religion or culture they’re from, the basic visual characteristics are the same and form a single, universal style spanning the entire world and even extending into the realm of fractals.

Geometry unites and defines the Divine Diagram genre and gives them also what I think is their artistic appeal.  Otherwise imagery made in such a mechanical medium as a fractal program would be irrelevant and completely unrelated.  But the reason fractal programs are able to produce similar types of imagery is because the medium fractal artists work with, the computer rendering of complex geometry, produces imagery with the same highly ordered visual characteristics.  Different mediums but pursuing the same goal of geometric composition.  In fact, it’s the hand-made artists of the non-computerized media who are attempting to imitate and follow geometric rules while fractal programs are merely doing what is natural to them and for this reason actually have an edge over their manual colleagues.

Geometry is the primary “visual ingredient” that flavours them all –hand-made or computerized.  Geometry is the connection and since geometry is also the source of their artistic appeal, as I personally suggested, fractal programs are not a second-rate source of these Divine Diagrams but simply a fresh variation on this very old artistic theme.

Fractal programs differ in only one substantial way and that’s with respect to the hand-made or hand-painted elements.  But although the faces, hands, trees and other realistic imagery found in the hand-made artworks do not exist in the fractal medium, fractal programs more than make up for this abstract-only limitation with their exhaustive output of complex and intense imagery.  As a result, fractals and other computerized algorithms ought to have a lot of potential for making “Divine Diagrams” if their own specialized abstract medium consisting of color, shape and pattern can fill the obvious aesthetic gaps left by a lack of hand-made artistic content.  Is fractal imagery too plain for such things?

Divine Diagrams

What characterizes this genre of imagery is what it attempts to depict or express:

  • power
  • hierarchy and status
  • divine order
  • revelatory declaration
  • iconic abstraction; simplified, purified essence

The visual characteristics of the genre are:

  • symmetry
  • geometric composition and elements (unifying patterns and simple shapes)
  • symbolic abstraction to the point of being stylish
  • multi-functional imagery (beautiful diagram, ideological map, useful ornament)

Heraldry is an example of the Divine Diagram

Most religious or sacred artwork is a variation of what is best exemplified by a coat of arms.  Heraldic imagery contains all the essential aspects of a Divine Diagram:  they’re symmetrical; symbolic; abstracted; and perform the function of illustrating ideologies or cosmologies (world views) as well as being artistically attractive (ornate, decorative).  Just as form follows function in architecture, the visual characteristics of Divine Diagrams take the form of abstract geometric shapes and patterns which symbolize order, hierarchy, and corporate identity (generic vs. personal).  “Geometric” practically describes the fractal medium so it’s no wonder fractal artists have been stumbling across images that look like coats of arms: it’s a natural product of the fractal medium.

Typical heraldic imagery (from Wikipedia)

Typical, generic heraldic imagery (from Wikipedia)

Notice the symmetry first of all.  And foremost too.  Symmetry is the strongest visual attribute of Divine Diagrams.  But also note the stylized lions on each side.  They could be dragons they look so abstracted and stylized.  The shield in the center is a simple geometric element, as are the little scrolls at the top and bottom (also centered).

For years fractal artists have been posting images with titles like “fractal coat of arms”.  Here’s the first page from a Google search on fractal coat of arms:

Click to go to search page results on Google

Click to reproduce search results on Google


I’m sure there’s been a lot of anthropological studies done on the symbols and styles of the various religious art forms because the similar look, on the surface, and dissimilar ideologies, underneath, make for a startling contrast.  I think the common link uniting all these religious artworks is the human mind and how it intuitively attempts to portray power, authority, order, supreme truth, as well as something a little more vague which I would call “cosmic wonders;” the supernatural has nothing to do with it.  The ideologies associated with the artworks conflict with each other but the pictures, ironically, all fit nicely into one unending cosmic exhibition. Fractals however, lacking any ideological association offer a treasure trove of divine templates for any religion or ideological movement that currently finds itself a little short on visual inspiration.

Divine Diagrams from across the world

Aztec double-headed serpent, British Museum

Aztec double-headed serpent, British Museum

It’s not a huge painting like the ones in the Mogao caves; in fact it’s a sculpture.  This thing is so abstracted and stylized as to be a company logo.  Maybe it will be one day, the interest in this sort of iconic imagery is timeless.  The loops in the center are so seriously geometric that it’s hard to see how its construction wasn’t planned out in a formulaic way with center points, angles and curves.  Although it was carved from wood and covered with turquoise and pine resin (adhesive) it has a very modern, mechanical look to it because of geometric accuracy with which it was made.  It hardly seems necessary to point out the mirror image symmetry.

Virgin of Guadalupe, 1531, Mexico

Virgin of Guadalupe, 1531, Mexico

Still in Mexico but jumping to a different religious world, the famous Virgin of Guadalupe, the New World’s version of the Shroud of Turin.  It displays the traditional Christian Madonna icon geometric layout: semi-symmetrical, encircling rays of a halo.  The human form is naturally symmetrical so it’s presence immediately adds that quality without the artists intention.  The round or oval encircling halo is common to most venerated religious figures.  The use of gold to decorate it is also a universal characteristic of religious art.

Here’s a reinterpretation of the Virgin of Guadalupe.  Notice how it’s been made more symmetrical and more orderly –more official and authoritative:


The prize for madonna images goes to the shrine in Walsingham, England, if you can believe that.  It’s actually 20th century, which explains the heavy art noveau look to it.  Originally I thought it was medieval but it’s just too artistically wild for that.  Note, again, the same geometric composition: symmetry; abstraction; simple formulaic shapes, etc…

Our Lady of Walsingham Shrine, England, 1938

Our Lady of Walsingham Shrine, England, 1938

How could British protestants produce such a fine example of iconic artwork?  I would have guessed this was Russian or even something more eastern.  But the answer to the question is simple: when you follow the simple style guidelines of all Divine Diagrams the resemblance to others is automatic.

Here’s a larger image of the shrine:

Holy House, Walsingham England

Holy House, Walsingham England

Compare it, visually, not ideologically, with this Buddhist shrine:

Buddhist Shrine

Buddhist Shrine

The visual style is universal; it’s only the ideologies behind them –behind the imagery– that is contrasting.

Gold Pectoral Plaque of a Shaman Wearing a Saurian Costume 8th - 12th century AD, Central America

Gold Pectoral Plaque of a Shaman Wearing a Saurian Costume 8th – 12th century AD, Central America

Pay attention to the head and the stylized body in general and compare it with this fractal image from Sterling:

Fractal image from Sterling

Fractal image from Sterling

Of course it’s not a perfect match or anything like that, but what I want to suggest here is that the stylized human form is similar and that fractals so easily make these similar kinds of images because the imagery is more geometric than realistic and therefore fractals naturally lend themselves to this genre of geometric abstraction.

Here’s two other pre-columbian Mayan or Incan figurines to consider.  Note the heavy non-human, geometric alterations to the basic human form.

mayan gold figurine 250ad

Apart from the eye/nose/mouth combination of elements, what is human to this figurine? Isn't it mostly geometic?

Apart from the eye/nose/mouth combination of elements, what is human to this figurine? Isn’t it mostly geometric?  The Sterling fractal “man” is just an eye/mouth/ear variation –just like this.

Ultimately the connection is the entire category of Applied Arts since most of this religious stuff falls just as easily into the category of jewelry, a class of artwork that is clearly an applied art rather fine art and has a different function and performs a different function than works of the fine arts.

This one below makes the jewelry connection case well, but there’s thousands of other examples of fractal-like jewelry —  or jewelry-like fractals?  They seem to both come from the same place.

Item from the Waddeston Bequest, British Museum, from Wikipedia

Item from the Waddeston Bequest, British Museum, from Wikipedia

The above item is practically the Mandelbrot set although, again, not an exact match.  The resemblance suggests that many of the shapes formed by fractal programs have already been envisaged by artists and artisans over the centuries as they’ve tried to come up with variations on the theme of geometric ornamentation.

Mandelbrot man variation made in Xaos

Mandelbrot man variation made in Xaos


Navaho sand painting, modern origin from traditional design

Navaho sand painting, modern origin from traditional design

Another geometric design; almost with a digital, pixelated look.  Color, shape and pattern with the added hand-made touch of realistic, representational imagery (people).  This divine diagram really is intended to be read and contains a whole bunch of symbolic statements.  Compare it with this one:

Photoshop filter painting

Photoshop filter “digital sand painting”

This isn’t a fractal, but it’s still algorithmic in origin.  I like it better than the authentic Navajo works and I’d like to see how well it sells at the souvenir stands in New Mexico compared to prints of the genuine sand paintings.  I made it with a variety of chopping effects and finally a symmetry effect that mirror images anything you let it get its hands on.  The style of divine diagrams is simple and geometric and so it’s easy to imitate with simple geometric algorithms.  I can make up a colorful legend to go on the back of the postcard, too.  Tourists love that sort of thing.

Double red-ship palepai ceremonial textile, Paminggir peoples, Kalianda peninsula, Lampung, south Sumatra, Indonesia, radiocarbon-dated to the period 1652–1806. Click to go to larger version at

Double red-ship palepai ceremonial textile, Paminggir peoples, Kalianda peninsula, Lampung, south Sumatra, Indonesia, radiocarbon-dated to the period 1652–1806. Click to go to larger version at

So we’re now in Indonesia and yet the same geometric type imagery is present.  I don’t know if this one is strictly speaking “religious” or not, but “ceremonial” still has the same power and authority theme as its function.  This has a real computer art look with it’s squarey-ness.  The margin on the right side almost looks like an old dot matrix printer report border.  They had some sort of chevron pattern to them if I remember correctly.  Is there some kind of ancient computing connection with the cultures of the world?  Adds a whole new dimension to Erich Von Daniken’s, Chariots of the Gods theories:  Computer Graphics of the Gods.

Here’s something but I’m not sure what it is.  I found it on the Wikipedia on the Waddeston Bequest page:

Jupiter, flanked by reading clerics with asses ears, rear of WB.30

Jupiter, flanked by reading clerics with asses ears, rear of WB.30

Remember, the content is irrelevant, we’re just looking at the pictures:

The Third International - Miniature on a round lacquered plate

The Third International – Miniature on a round lacquered plate.  Click to view larger version.

Different geometric shapes and patterns but the same ideological/religious type of message and therefore the same geometric style to the artwork.  This one, incidentally, was located under the heading of “propaganda” on the Wikipedia page for the Comintern (“Communist International”, also known as the Third International).  I like how both contain the same gesturing, pointing hands and arms.

The leafy border of the Jupiter one with the stylized, coat of arms like composition in the center compares nicely with this soviet era coat of arms for the Ukraine:

Ukraine SSR Coat Of Arms 1949-1992 Soviet Union

Ukraine SSR Coat Of Arms 1949-1992 Soviet Union

Note the common scrolled background/frame element in both the coat of arms and the Jupiter thing.  Their common form follows their common function.  The abstracted wheat that forms the border of the coat of arms is a good example of abstracted imagery; it’s become a pattern and the kind of pattern which fractal programs often spontaneously generate:

Fractal from Sterling

Fractal from Sterling

I could go on with more examples but I think by now you’re either connecting the dots in the same way I am or you never will.  I admit there is something of a “gestalt” here that one needs to “perceive” before they “see it.”  A lot of stuff in art is like that and that’s why I think tastes can vary so much: we don’t understand what others are thinking when they look at “that.”

There’s much more I hope to write about with respect to the “divine diagram” genre because it’s one that I’ve personally made a lot of examples of while experimenting with photoshop filters and other algorithms besides fractals.  It’s really an algorithmic thing and not exclusively fractal.  Fractals just make the most elegant examples, but as you can see now how important the element of symmetry is, almost any image takes on a divine diagram look when it’s mirror imaged or kaleidescoped.  It’s a very easy thing to do digitally but requires much more effort and skill for a hand made artist to imitate.  Algorithmic artists have the edge here, surprisingly and the hand made artists have to struggle to imitate us.

Ultimately my hope is to show that the scope and artistic “reach” of fractals is a function of their medium and not the artists who work with it.  Fractals easily make coats of arms and “divine diagrams” because the geometric essence of those two applied arts genres is geometry.  Add in jewelry and you’ve got just about everything that fractals are capable of making.  They’re in their natural element when they produce works of the applied arts and out of it when the artist tries to fit them into the fine arts category.  That requires a change in the medium because it’s the medium that restricts them to the applied arts.  Changing the medium means adding other software (post-processing) or adding other kinds of imagery like photographs or hand made enhancements (mixed media).  Fractals are simple but fun.

Fractals are the Mogao Caves of our times

One of the many illustrated caves

One of the many illustrated Mogao Caves in northwestern China

Alright, maybe it’s just me but the image above and just about everything else in the Mogao Caves bears a strong visual resemblance to what I see in fractal programs.

What I see in fractal programs:  That might be a new way of defining the term but I believe it’s the most relevant in the context of visual art. This is because fractal formulas when rendered exhibit a discernible style to them just like the work of a painter like Van Gogh or Gustav Klimt or an architect like Frank Lloyd Wright does.  Think of all fractal images as the work of just one artist: would you not suspect he was possibly inspired by the type of artworks we see in the Mogao Caves?

Fractal made in Sterlingware 1.7

So, what are the visual similarities?  What’s the family resemblance between the Buddhist cave and the fractal image?

Visual similarities

  • Symmetry (left/right mirror image)
  • Hierarchical structure (the details support the “macro-tails”)
  • Geometric (circles, squares, parabolas, shapes that are formulaic)
  • Abstracted/Symbolic (simplified and stylized but retaining a resemblance to real things, mainly natural: hills, sky, clouds, flowers,)

It’s not just the visual style resemblance; illustrated caves seems to work like fractal programs too.

Viewing environment similarities (caves and fractal programs, in general)

  • Immersive (walk into a cave; zoom into a fractal)
  • No frame (the whole image is uncontained and unconfined)
  • Interactive (your head’s the frame; turn the head, change the composition; focus on a detail in a corner or the main structure in the center, or something you never noticed before)
  • Variations on a theme (we see repeating shapes and structures; visual deja vu)
  • No distractions (related to immersive; one can easily lose track of time, and space, in fractals because there is no real beginning or end; same for an illustrated cave)

Notice the little, tiny buddha-circles on the side walls in the photo and the little red, dot-balls in the central area of the fractal, one the “walls” of the fractal?  Obviously there’s no close fractal equivalent to the human form so all we can compare the statue of the Buddha in the center of the cave with is the prominent central shape that occurs very often in fractal images (especially in Sterling).  In this fractal it appears to be breaking out of a clearing in the clouds which frame it’s “head” like a garland of flowers or crown of brilliant clouds.

Another of the Mogao Caves

Another of the Mogao Caves


Another of the Sterlingware Caves

Another of the Sterling Caves

The similarity comes from more than just the three niche elements; although you will notice that the fractal niches are all proportional and complimentary to each other like they are in the cave example.  This is what I mean when I’ve said in previous postings that certain kinds of imagery are natural for fractal formulas to make.  Symmetry, hierarchical order, and profuse detail and ornamentation come naturally to fractal images.  The Buddhist art in the Mogao Caves (and elsewhere) exemplifies these same visual aspects for religious reasons to convey and express religious ideology.  The are, in a sense, what I would call “Divine Diagrams” and it should come as no surprise to anyone familiar with fractals that fractal images often bear the same elements but, naturally, in a generic way.  Fractal images could easily be used for symbolic purposes in a number of religious contexts.

One interesting bit: notice in the fractal, below each of the niches, there are similar “stains” just as one sees below the niches in the cave photo.  Perhaps it’s from burning candles or food offerings or some sort of weathering?  In the fractal, of course, it’s just part of the formula rendering.

A couple other similarities to point out:

  • there is a vertical line structure/feature extending up above the central niche in both the photo and the fractal
  • all three niches have a framing element to them including a large, expanded framing element overtop of them in both images
  • extending up from the two minor niches in the fractal are two obvious lines which meet a horizontal line just above them.  This corresponds, to some extent, to the wall corners and the border of the edge of the ceiling in the cave image.  It’s just a fluke that the fractal should look like it’s got walls and a ceiling but it’s expected that one should find such geometric elements in a fractal; in the cave they’re just ornamentation of the room’s structure which in this cave is square, rather than round.
  • Notice what could pass as doorways on either side of the fractal on the edge of the image in line with the niches and real doorways in the photo.
  • The geometrical, architectural element of the ledge in front of the cave’s niches is also found below the fractal’s niches.  Again, geometric shapes occur naturally and frequently in fractals which cause them to easily support an architectural analogy because architecture is almost always geometrical.


Mogao Cave painting

Mogao Cave painting


Fractal Cave painting

Fractal Cave painting


Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist (or Hindu?)

Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist or Hindu or both.

Some of the same similarities occur here with respect to shapes, frames, borders, hierarchy; I think you get the idea now.  I added the last one, a statue from somewhere, because it really emphasizes the design similarities between fractal imagery and these Buddhist paintings and statues.  The last one looks so much like the fractal image that it’s hard to believe it came first.  But this is my big point: the type of imagery that fractal programs produce has existed for centuries in the form of Buddhist religious imagery.  And, if you’re familiar with religious art in general, many forms of religious art and symbolism have this fractal program resemblance .  In fact, it has no particular correlation with any one religion, I just happened to notice it for the first time while browsing the Mogao Caves on the Wikipedia.

I’m sure I’m not the first person to notice this fractal art / religious art connection.  In my next post I expand the comparison of fractal imagery with the whole spectrum of religious art showing that the elements and style of religious art are in fact inherently fractal and therefore the sort of visual art that fractals produce easily, prolifically and to perfection.

Everything you need to know about Fractals and Art in one blog post


Fractals are many things to many people but as an art form they’re really very simple:  Fractals are a visual medium.

Do not be fooled by such simple language and such a simple statement,  “medium” is the thin edge of the wedge that splits fractal art apart and reveals all it’s inner workings!  If you’ve ever wanted to get to the bottom of what fractal art is, this is it.

First, let’s define things more precisely: An art medium is the material an artist works with and creates their art from.  More importantly, the medium is what an artist “works in.”  Think of it as a workshop that contains all their tools and all the raw materials they have to construct with and also contains, within its walls, all the ways they can interact or work with those tools and materials.  Whatever can be done in that workshop is what constitutes and defines “the medium.”  To understand a medium is to know how it works: what’s possible and what isn’t.

Fractals are perhaps one of the simplest of all art mediums and therefore ought to be one of the easiest to understand.  Let’s ask the question, “What can be done with fractals?”  The answer to this question ought to be a definition or description of the medium.  This will in turn define the scope of fractal art and explain why certain artistic goals are not possible with fractals as well as explain why others are so very, very easy.

Although there’s no limit to the formulas that can be discovered and the rendering techniques that can be written for a fractal program, this apparent “unlimitedness” is actually quite limited: fractal artists can only work with formulas and rendering methods.

How is this “limited?” especially considering the endless array of options that populate most fractal programs?  You have to understand that I’m trying to relate fractal art to the rest of what is called “art.”  You need to step back and look at the whole world of art and all the many other mediums that there are.  You need to consider the “workshops” of other artists and compare those to that of a fractal artist.  This is why I say fractals are a very simple medium –compared to all the others.

Fractals are artificial, mechanical imagery that lacks both the real world imagery of photography and the imaginary imagery that artists create when working directly on the canvas with their hands.  Fractal artists work by remote control adjusting whatever parameters the formulas and rendering methods allow while the program fulfills the traditional role of the artist by drawing the actual imagery.

Photographers can capture anything they can see and painters can depict anything their imagination can conceive but fractal artists can’t do either of these two things and so their “workshop” lacks the two most common sources of artistic imagery: the real world and the human mind.

How far would Salvador Dali have gotten with a fractal program?  I think he would have found it rather limiting although somewhat interesting in its own limited way.  Yousuf Karsh, the great portrait photographer: how can fractals do what he does?  Which brings us to the real essence of what an artistic medium means: The medium isn’t the message; the medium is the vocabulary of the message.

The fractal medium is the vocabulary that fractal artists work with: it creates and therefore limits what artists can speak with and depict in their art work.  It’s a vocabulary of color, shape and pattern.  That’s the workshop of the fractal artist.  It’s abstract, organic and geometric.  But there’s one other important element to the fractal workshop: it’s computational.  The same thing that creates the artificial and mechanical nature to fractal imagery also gives it a prolific level of output, intensity of detail, and rendering perfection that no other medium can match.

The fractal medium has weaknesses but it also has some strengths.  As an artist, whether you find it engaging or frustrating really depends on what kind of artistry you’re pursuing.  If we can divide the art world into the two categories of Fine Arts and Applied Arts, then fractals clearly fall into the Applied Arts variety.  This is a direct result of the simple color, shape and pattern vocabulary of fractals: they don’t convey complex themes and subtle commentary that photographic or hand-made artworks do.  On the other hand, fractals naturally portray complex graphical designs with unwavering perfection in every single detail.  What graphic designer will ever create imagery that matches even the humble Mandelbrot Set in terms of detail and complexity?  This is what fractals do best.  Actually, it’s the only thing they do:  Abstract, organic imagery that is variations on the three basic visual elements of color, shape and pattern.

There will be no fractal da Vincis (or Dalis), but there will be fractal coats of arms and other works of computational heraldry.  You won’t find fractals in the fine arts category but you will find them rivaling the best works in the decorative arts and even redefining and extending what can be conceived in that genre.  Fractal artists regularly look at the impossible in their fractal programs and I think have grown a little complacent to the sort of visionary imagery that would be a masterpiece on the wall of almost any religious temple.

In fact, that’s how I came to write this blog post and why it took me so long.  While viewing photos of the Buddhist Mogao Caves on the Wikipedia I found myself nagged by this persistent question: “Why does this look fractal?”  Here’s an outline of my odyssey that took me, backwards, to what fractals are as an art form:

-mogao caves: what is fractal about this? – religious art, icons
-religious art: what is fractal? symmetry, geometric, abstracted, symbolic, hierarchical –heraldry
-heraldry: coats of arms, noticed for a long time by fractal artists, natural for fractals, –part of applied arts
-applied arts: what is fractal? the medium, not fine arts, small vocabulary of color, shape, pattern,
-medium: fractals are an applied art medium, they make that kind of imagery because they are limited to color, shape and pattern –separated from photography because realistic imagery isn’t part of the medium

This blog post is just the conclusion of that odyssey.  I will cover the other parts in future posts because this all happened backwards and they’re practically already written.  I’m sure it will be even more convincing because nothing describes art better than the art itself.  You can judge for yourself then if my conclusions seem correct.  The Bermuda Triangle may never get solved but I believe I’ve finally “solved” fractal art.


The Art Dimension: turning fractals into art

In my previous series of postings (first, second) on how to separate the art from the fractals, I basically say that the only way to do more with fractals than simply create computer crafts is to focus on producing works of abstract expressionism or landscape/place.  These are the only two existing art genres where fractals seem to gain any traction.  This is where the artistic talent of fractal algorithms really start to shine.  Everywhere else fractal programs function as nothing more than The Kaleidoscope of the Computer Age, a magical toy that makes everyone feel they’ve captured the genie in Aladdin’s lamp and become rich.

On a side note, I was recently contacted by Paul Griffitts, a fractal artist whose work fits in well with the Benoit Mandelbrot Fractal Art Exhibitions that occurred several years ago in Spain..  Paul’s vision of fractal art is dramatically different than mine as can be easily seen by the work he produces.  But Paul’s work, despite being made in the 3D fractal program, Mandelbulb3d, doesn’t exploit the landscape or “depiction of place” potential that this new fractal programming presents and for that reason is a good teaching example of why fractals so often fall short of becoming more than just colorful imagery.  However, another of Paul’s images that I will present is something that shows real potential in a way that startled even me.  Fractal art is full of surprises.

~ Click on images to view full size on original site ~

A Festive 3D Encounter by Crike49 on

A Festive 3D Encounter by Crike49 on

Folks, don’t be fooled by the homey Christmas theme here, I cried out, “Son of Dali!” when I saw this one just a few weeks ago.  It’s full of the “window-worlds” of micro imagery that often pour forth and drain back into the limitless panoramas of Salvador Dali’s fragmented surrealist symphonies.

The ornate spiderweb fractal thing is not terribly important; it’s the three dimensional landscape and places to be discovered in the web holes and and room dividers of the image.  The simple blue palette is almost “anti-fractal” in its muted appearance but the strong reflective light on the snow (ice?) in the left foreground pours a strange kind of life into the image’s deserted panorama.  It’s “full” of emptiness.  As well as additional rendering in Twisted Brush, if I’m reading the gallery page notes correctly.

This is the kind of mental dimension that I’ve been saying marks the difference between artistic imagery and the purely “nice to look at” imagery that is craft or decoration or ornament.  They function differently and as such the two types of imagery get different receptions.  Not everyone will get the same sort of mental thrill out of this image by Crike49 that I do, but I have enough confidence in my perception of art to say that it’s not just all in my own head.  People argue all the time about the relative merits of artworks.  Click on it and view it full size on Fractalforums to get a heaping eye-full.

Untitled (June 18, 2016) by Holocene (Paul Griffitts)

Untitled (June 18, 2016) by Holocene (Paul Griffitts)

Believe it or not, this was made with a 3d fractal program and not Ultra Fractal.  I find it intriguing how Paul would pursue a type of traditional fractal imagery, ornamentalism, with a program that has been blowing the doors off business as usual in the fractal art world.  This is what I mean when I said Paul has a different vision for fractal art: he’s not afraid of sticking with the conventional 2d style of fractal art that could almost be labeled retro (note the spirals).  The 3d capabilities of the Mandelbulb3d are utilized in a muted way here just to provide a bas-relief or embossed effect rather than the deep panoramic landscapes that Crike49 presents.

Paul’s work is oriented around a very different aesthetic and naturally that’s his prerogative as a creative artist; what I’m arguing is that the elegant design approach to fractal art is actually rather limited because it speaks a much simpler language than landscape and place does and for that reason all one can say is “beautiful” over and over again as variations on a theme.  It’s a niche, and not a very deep one despite it’s prevalence in the fractal art scene for decades.  There was a time when that’s we all had to work with.  It’s ironic that the new software is being used to make the old art.

And now for something completely different

Untitled May 18 2016 by Holocene (Paul Griffitts)

Untitled May 18 2016 by Holocene (Paul Griffitts)

If you remember what I wrote about fractals and portraits you will know that I basically said that fractals can’t make portraits because the human form and especially human facial expressions just don’t happen with fractal algorithms in the same way that landscapes and wild abstract expressionism does.  So the guy I just labeled as “retro,” and using the same program as before, created this “impossible” fractal portrait: he broke the fractal portrait sound barrier.

If you don’t see the portrait that’s okay.  I don’t think Paul saw it either, but that’s what art criticism is here for: to sharpen your perception.

A picture says a thousand words and this one should do it:

The Son of Man by Rene Magritte, 1946

The Son of Man by Rene Magritte, 1946

Son of Magritte!  Notice how well Magritte avoids the human face in his portrait.  It’s almost become a sub-genre in surrealist art, putting an apple or anything else in front of a human face to obscure the expression in a startlingly expressive way.  I think the most widely accepted interpretation of Magritte’s floating apple in front of the face is that people hide behind things and so a more accurate portrayal of people is actually what obscures them rather than the “real” person behind the apple.  If the existentialist quote is true: “man invents himself” then this portrait by Magritte would say: “man becomes his deception”: we are what he hide behind: our choice of masks betrays our identity.  Ironic, iconoclastic and well worth the effort it takes to produce a painting; not to mention the numerous art discussions it has spawned.  Perhaps Magritte just like painting stuff that was startling and it was his audience that invented the “man hides his true face” explanation.  The paint never dries on a surrealist artwork.

Back to Paul’s image: surely you must see the portrait now: there’s a suit jacket, a shirt collar, a tie; and the clothing pattern reiterates itself into the face which appears, like Magritte’s in basic shape only, a sort of “your face here” portrait template that could fit as the (male) avatar for our age.  Paul made a piece of “art”.  Compare how it functions with this extremely famous one:

Figure with Meat by Francis Bacon, 1954

Figure with Meat by Francis Bacon, 1954

Nobody worth his gallery coffee shop latte argues that this isn’t “art”  And what does it mean?  What is it saying?  Many artists are silent on what they’re work “means” or “says” and I think one reason is that they themselves aren’t completely sure about what it’s saying or meaning and they don’t want to appear ignorant.  Art is not always deliberate or intentional and just as I said the paint never dries on surrealist art, it’s pretty slow to dry on many other kinds, too.

One of the things the study of psychology brings to art is the understanding that we don’t always know why we do things and therefore an artist may not fully understand what it is that creates the impression they get from their own work.  How much less the impression their audience gets.  Or doesn’t get?  Furthermore, in different cultural contexts and even different generation contexts I’m sure “the” message of almost any artwork can change.  I’ll bet no one looks at Paul’s, Untitled May 18 2016 the same way anymore, now that I’ve reinterpreted it.  That doesn’t mean I’ve made them like it or not like it, art is too complicated for such crude words; a useful interpretation is one that helps people decode their own impression of an artwork.  At its best, a useful interpretation allows the viewer to see greatness in an artwork that they’d previously passed over.  It’s the same with movies, books and music, too.  Art isn’t always obvious but beauty is.

Where art grows on trees

fractal-7792 by Jock Cooper

fractal-7792 by Jock Cooper

Looks pretty “fractal” doesn’t it?  Not in the usual way but in the sense that it’s very geometric and detailed.  What transforms this image from just an example of freaky fractal feedback into art is the expression of an idea: art factory.  The little mondrian frames are each quite unique and the medium sized one in the right bottom edge ground (bottom second column from the right) with it’s yellow color scheme has an almost deliberate artistic touch. Move up two frames to the little louvered thing and the impression of sunlight and the outdoors is a sharp contrast to the factory, although it might represent the final installation of a factory made ventilator outlet.  Could this be the raw artwork for a sales brochure?

But the strongest of all themes and ideas represented here is the recursion of the frames in several places that clearly suggests mass production all over the place.  So much everywhere and leading back into an endless supply of more.  It’s almost a comment on fractals: cheap and perfect.  I doubt Jock was thinking of that, but I’m sure the theme of recursion is what caught his eye when he made this one and picked it out from his explorations.

This one is an example of both place as well as abstract expressionism.  Notice how in the top right corner of the largest recursion example, in the top mid-ground, the pattern becomes just squares on a black background in an Escher-esque dissolving into simple shapes way: substance becomes symbol.

Then there’s the simple blue frame triplet in the top right corner.  It looks like the view out of a window overlooking the sea, and again in contrast to the darkened factory imagery this outdoor and minimalist view suggests the intervention of human artistry, but I’m guessing it’s just one of those fractal accidents that one has to keep their eyes peeled for when browsing raw fractal imagery.

Fractals are a different kind of medium and I guess in the end that’s what makes fractal art so hard to explain, as well as so hard to make.  We think we’re the artists but we’re really the audience.  Our role is different and it’s more about looking and sensing than it is about making and doing.

Place: Where Art and Fractals Overlap

As I concluded in my previous posting, there are only two art genres which fractals are capable of contributing to: Abstract Expressionism and Landscape/Place. Everything else created with the fractal medium is what I would call snapshots: interesting, even fascinating imagery but lacking in expressiveness or the portrayal of a tangible “place”. If it doesn’t go with Pollock or look like a place you could step into then it goes into the photo album. Most fractal imagery is of the photo album variety because most fractal “artists” are really craft and decoration makers and so they pursue pretty things rather than artistic things. That’s who they are and so that’s what they do. Art has a deeper dimension to it, a mental resonance, and fractal art can have a deeper dimension to it also but it only seems to achieve this when it creates works that fit into the categories of Abstract Expressionism and Place. That’s where the fractal medium has it’s artistic application; that’s where art and fractals overlap.

Mandelbrot is the founder of fractal science, but Pollock is the founder of fractal art

Mandelbrot is the founder of fractal science, but Pollock is the founder of fractal art

I guess you’re thinking along the lines of the old argument that it all depends on how you choose to define what “art” is? Let me propose this simple, practical definition: we recognize art because it’s the stuff that’s harder to forget. Art makes a stronger impression on us and that’s what separates the “art from the toys”, if you will forgive me for making such an attempt at humour. I agree with the opinion that art is subjective, but I would also add that art is collective, and not because it rhymes. Purely personal, exclusive tastes in art are simply the eccentricities of one’s personality; art is a social thing because it’s communication/expression/conversation and that requires something in common, a interaction between people, a sharing of experience/ideas/revelation/perception. If no one else sees what you see then it’s all in your head.

One of the things that has always distinguished fractals as an art form is how hard it is to define in terms of artistry because it’s made in such a different way and bends and breaks all the normal definitions of “artist” and “medium”. Fractal imagery is incredibly easy to make and but it often has more detail and “workmanship” in it than almost any great painting. And yet, after more than several decades of existence there isn’t a single great “standard” or influential masterpiece of fractal artwork to point to that has any sort of widespread acceptance in the art world or even within the fractal art world itself. There have been many prizes awarded over the years in the fractal art world but there has been very little artwork that deserved them.  The “great” fractal art of the past seems to have been easily forgotten: the hallmark of “not-art” because it hasn’t left a lasting impression on the minds of its audience.  Fractals are dramatic but art is traumatic.  Memory is a like a mental dent.

A word about art sales

I think the easiest form of art to sell is not really art at all but rather something I would more precisely label as “craft”. Craft differs from art in that it’s something pretty and visually soothing to look at rather than mentally provocative. Craft is like visual air freshener or decoration or a comfy graphical couch to rest our eyes on. Craft is something that most people always like to look at, while art is something you have to be in the right frame of mind for. As a result people will more likely buy a big piece of craft to decorate their living room than they will buy an art print.

Living room, dining room or front hall?

Living room, dining room or front hall?

While art is something we will often stare at we don’t really like it staring at us –all the time. And so we like to have art, like Picasso’s Guernica, or just about anything made by Salvador Dali, –in a book on a shelf– so we can take it out and put it away when we’ve had enough of those ideas and things. Art satisfies a mental appetite rather than a purely visual one and so the hunger for art is much more unpredictable and has a wider range of intensities. Art is often not beautiful in the common sense but possesses a mental beauty which at times is unappropriate. Craft is fun and much more marketable. Art is highly respected and honored by generations to come but Craft makes more money and drives a nice car right now.

Most fractal artists confuse craft with art because craft is what they like and the only kind of imagery that achieves consensus in online social groups, the primary venue for presenting fractal art (ie. “Fractalbook“).

Back to art…

What’s been separating fractals from art for so long is the inability of artists to capitalize on the few artistic themes that the fractal medium is capable of reproducing. Instead of looking for fresh examples of abstract expressionism, fractal artists have been collecting wispy pinwheels, or, as I said a few years ago in another post, Sheets in the Wind and Rings of Gold. Eyecatching but shallow stuff that makes the question, Is it art? not worth asking. I came to the conclusion years ago that artists just don’t find the fractal medium to be very exciting and for that reason there are very few of them getting involved with it.

However, the 3d fractal revolution has changed that. Art has become an easy thing for 3d fractal artists to pursue because the 3d fractal medium makes it easy to capitalize on another artistic theme, other than abstract expressionism, that fractals are capable of: the theme of “place”. Place is a room, building, landscape; any location or spatial situation you can find yourself in. Place is any “place” you can be; It’s the physical context of “being”. Place is where you “are” or where you could be. It’s a rich fertile artistic theme and one which 3d fractal algorithms have a natural talent for. Abstract expressionism benefited greatly from the use of post-processing methods like photoshop filters which meant 2d fractal artists had to expand their skill set and incorporate non-fractal tools, not to mention a more traditional artistic sensibility, in order to make innovative work; something which rubbed most members of the fractal art “herd” the wrong way. But place is the natural domain of 3d fractal programming and the herd is taking to it quite well.

Place: the portrait without a face

Portrait (from Wikipedia)
A portrait is a painting, photograph, sculpture, or other artistic representation of a person, in which the face and its expression is predominant. The intent is to display the likeness, personality, and even the mood of the person.

The portrait is the most potent form of realistic art. Nothing is more expressive and conveys more information, subtle and nuanced, than a human face. People can easily relate to other people because we know them like we know ourselves. Art is colossally human-centric and facial imagery and the human form attract the majority of artistic activity and attention. Here’s where fractals (but not photography) get cut off, alienated and exiled from the world of art. Without the ability to create facial imagery or the human form, fractal artists are practically castrated when it comes to creating art.

Next to the portrait in artistic powers is the landscape. One could even call a landscape painting a landscape portrait. Once again, we can easily relate to landscape imagery because we live in landscapes ourselves. Landscape is the environment we live in and portraits are the people. Between those two themes is most of what is called realistic art –realism. One is either looking at a person’s face or the environment they live in. Art is about ideas: thought, ruminations, commentary, criticism, speculation, analysis, life, enjoyment, beauty. It’s not surprising then that most artwork literally reflects the people who make it and the things that surround them because the human mind is what art comes from and revolves around. This is a problem for mechanically made imagery like fractals because it lacks relevance and connection to the ongoing human soap opera called life. Art is cognitive, not simply what is visual. Art is about thinking, not merely seeing. The mind is the audience, not the eyes and so it’s the impression of art that counts, not really the imagery, particularly the quality of the imagery that creates the impression.

Godzilla vs The Mona Lisa


This doesn’t need a caption

Whenever I feel in a balloon-popping, iconoclastic mood about art, I like to belittle the Mona Lisa. This usually provokes people into becoming more interesting as they attempt to either fight back and defend that great masterpiece or join in with the attack on it which then quickly spreads to everything that has ever gained any respect in the art world. Often, later on, while reflecting on my Mona Listic insults in private, I sometimes felt I had actually stumbled onto something intelligent and not merely a conversational toy: pry off the face of the Mona Lisa and something genuinely intriguing is revealed.

That intriguing thing is the landscape in the background; that mysterious road through the bare, desolate mountains that looks both pristine and ancient; that wispy world of “both shadow and substance”.  It’s my favorite part of the painting (here I go again), perhaps not even painted by da Vinci himself who probably delegated such peripheral elements to his students while concentrating his own artistic efforts on the serious part of the painting, that of Mona’s face. Fractals are more likely to come up with a better “landscape in the background” than they are a “face in the foreground”.

We can see as much emotion and feeling in a place as we do a face although place is more subtle and not as direct. We can convey a mood with an environment as well as a human face. It’s not as powerful as an actual portrait of a person. When it comes to artistic expression, you can’t beat the human face! Look how ridiculously famous the Mona Lisa is. And for what? Is she really about to smile, or to grimace at having to sit still for so long?  And for that matter, isn’t that famous “smile” thing just an example of mental suggestion? Now no one can look at the painting objectively.

All the feeling of a portrait without a human representation

Place represents the subtle smile or the much more subtle facial expressions, or even the so subtle it’s not possible to portray them as facial phenomenon expressions that are faceless yet deep and moving. Like the feeling associated with the imagery from a dream, that has no logical connection with that feeling, and is as if it has been merely painted with it, like an ordinary rock bearing the fragrance of a strange perfume. One of the most easily recognizable surrealist painters is Giorgio de Chirico.  In his simple and minimalistic paintings, de Chirico has, like most surrealist painters, captured the “fragrance” of a dream –feeling or sensation.  The effect often comes as much from the place and the non-human elements in the painting than it does from the secondary roles played by the human forms or faces.

The Anguish of Departure, Giorgio de Chirico, 1914

The Anguish of Departure, Giorgio de Chirico, 1914

Place is more than landscape: place is location and is any spatial situation one can find themself in. In short, anywhere you can be. Place is context. Place is as primordial as the human face. Somewhere in my first year Psychology course it was mentioned that all human beings can relate to the simple imagery of trees with grass around them because that’s the primordial nursery our race was born into: the African Savannah.

Fractal imagery can’t compete in the portrait category because faces are an unlikely outcome for geometric or organic algorithms. Faces are too unique, specialized and complicated. But fractals, especially 3d fractals, are quite good at creating environments, landscapes and places. 3d fractals lend themselves to architectural imagery and often surpass the creativity of the hand made arts in this respect. Place is becoming the most successful niche of fractal art thanks to the development of 3d fractals. You could go so far as to say it’s the only thing they do consistently well.

I think it’s because architecture as well as landscape is much more geometric and textural than portraits are. A smile is a complicated thing and composed more of impression than design. It’s extremely nuanced and involves all of the other facial elements like the eyes, cheeks, complexion and so on. Fractal algorithms have been used for a long time in computer generated landscape creation because it uses their natural abilities. Landscapes are very fractal while faces are not. In fact, landscapes are fractal. 3d fractals have brought fractal art back full circle to where the concept of fractals originated: describing natural phenomena like coastlines, clouds and frosty window panes. That’s where Benoit Mandelbrot got his ideas from.

In the next posting, Part 3, I’ll focus on some examples of fractal art that lay in that shared artistic space where art and fractals overlap.  Finally, some examples of real fractal art –after all these years!

Why can’t fractals do what art does?

Over the years I’ve come to see this as the perennial problem in fractal art. Naturally there are many other perspectives regarding the “art-worthiness” of fractals, among which the most common seems to be that they’re essentially no different than any other medium that artists work with. But this doesn’t explain why the enormous creative powers of fractal formulas hasn’t resulted in enormous amounts of creative art. Fractals ought to be artistic powerhouses but instead they’re merely fractal powerhouses.


There’s a killer on the road…

There seems to be something deceptively enticing about fractals with respect to their artistic potential: they look like they can do almost anything and yet after a couple of decades what has resulted is almost nothing except for works of mere technological interest. There are no great works of fractal art, only a great number of little fascinating things.

The fractal medium is deceptive. Part of the deception of fractals is that the creative thrill of using a fractal program and zooming through the incredible fractal vistas that it magically generates is lost when we stop the “fractal experience” and try to capture it as a still image. It’s like looking at vacation photos or, for your audience, looking at someone else’s vacation photos; they’re just not anything like the real thing, the vacation is missing from the vacation photos. But then a picture taken on a roller coaster isn’t anything like riding that roller coaster and fractals are a graphical roller coaster. To use yet another analogy: fractal art pulled out of its interactive fractal environment is like a fish out of water. We don’t understand the art form and so we don’t understand why it dies when we move it to the art gallery.


The other deceptive thing about fractals I’ve come to recognize is that they speak a completely different visual language than most everything else in the art world. Fractals are not just abstract, they’re an almost empty kind of abstraction; full of fractal style and “infinite detail” but lacking anything that the average person can connect with, relate to.  Monet’s water lillies are full of feeling although being, just like most examples of impressionism are, semi-abstracted. Fractal programs can create all sorts of freaky things but they just can’t do what simple water lillies do. It sounds ridiculous to say that but that’s what is deceptive about fractals: they contain all the ingredients for an explosion of art but seem to be missing that ridiculous little spark.

And that would be an artist, right?  What about the artist? How about adding the creative talents and direction of a feeling, human mind to the mix? A fractal program is just a tool. An artist will use that software tool to make art just like a photographer uses a camera to make their art.

Yeah, how come that doesn’t work either?

One of the biggest surprises of the Ultrafractal phenomenon where the artist was placed right in the middle of the rendering process where they could layer, mask, import, add, substract, multiply, etc… with full artistic control, was that it didn’t make for fractal art that was any better than the old single layer fractal programs. It just allowed everyone to boast about how hard they’d worked to make it. In fact, I came to the conclusion that the more an “artist” was allowed to get their hands on the imagery and alter the simple processing of a fractal program, the more likely they were to degrade the image rather than improve it. Becoming an “Ultrafractalist” allowed everyone to say they were artists and not simple button pushers but the lack of good artwork just emphasized how incredibly defeating the medium was because those “artists” were no better than button pushers when it came to making fractal art. Just look at all the award winning stuff the Benoit Mandelbrot Fractal Art Contests exhibited: who remembers any of them now that the social effervescence that attracted their audience is gone? Fractals programs were more interesting when they were soulless mechanical things than when they received a human heart from their well intentioned Wizard of Oz artist who was now directing them by hand: manual and mechanical methods don’t mix.


There are only two strategies for making art with fractals. What I mean is there are only two areas of fractal graphics that overlap with areas in the world of art. Maybe there are more, but I’ve noticed only two after my brief fifteen years with the medium. There are only two artistic genres that fractals have any natural talent to function in and that’s Abstract Expressionism and Landscape. Outside of those two themes fractal programs are just an amusement park to stroll around in.

And I’ll tell you, I love to go on those fractal roller coasters more than anyone. I just don’t expect any art to come from them anymore, just vacation photos: warm memories of the past that no one understands but me.

Stay tuned.  Part II won’t be quite as grumpy.

Only …the Awesome!

There are many ways to judge fractal artworks; you could look for beauty, whatever that is, or you could look for expression, or artistic merit, or something else too profound for words.  I look for “Awesome!”.  Call it the Awesome School of Fractal Art Criticism, or Awesome-ism for short.  The exclamation mark is optional.

~ Click on images to view full-size on original site ~

The Congregation by Madman

The Congregation by Madman

Isn’t that awesome!  It’s even better full-size;  the “painterly” quality is more evident.  The composition and variety in this one really shows the potential for 3D fractals: play with the parameters enough and look around long enough and you’ll find readymade paintings like this one.  The lighting looks natural and with the repeated pattern of attending pillars there appear to be surreal sub-congregations tucked in beside uber-members who tower with architectural prominence.  If a painter set out to paint a scene like this the hard way, would it turn out better than this?

Landscape by alexl

Landscape by alexl

This one is just too real.  It looks like the perfect photograph of an imaginary place.  I think that’s a mausoleum in the background and though that might not sound too exciting, the whole place is begging to be explored.  Fractals are virtual places and we explore them in computer programs but I think they’re more real than the photos of real world places we’ve never been and never will visit.  A good 3d fractal image leaves you with the feeling that you’ve been somewhere.  And an imported sky backdrop helps too.  But notice the shadows in the image: the sun is behind us, somewhat high in the sky, like about 9 in the morning or 3 in the afternoon.  The weather looks good so we can take our time wandering around until sunset.  The photographer was careful to maneuver their own shadow out of the frame of the photograph.

Chamber by 3dickulus

Chamber by 3dickulus

In the words of the master himself: “I simply can’t get enough of this object… fascinating endless variety”  Once again this is an excellent example of vividity.  That’s the awesome version of vivid.  I feel this is underwater and although we’re in a dim, cool place, the shaft of sunlight pouring down suggests it’s a bright, hot day on the surface.  I might have labeled this “Neptune’s Throne” because it has a majestic quality to it.  3dickulus has more like these on (the throne of fractal art).  They all have this interesting liquid style to them with lots of endless variety as he says.  The coloring fits in nicely with it to give them a “painted sculpture” appearance.

A Quiet Spot by fraxialmadness3

A Quiet Spot by fraxialmadness3

Yes, that’s lake effect at the bottom.  But it actually adds to the awesomimity instead of what it usually does.  I think it adds some sort of rhythm that enhances the soothing and dreamlike visionary effect of the image.  It ought to be a haunting image with those dark forest shadows in the background, but I have a feeling that whatever disturbing thing comes out from there will be transformed once it steps into the light of the glowing spiral tree galaxies.  This is a bit old school now and goes back about 6 years but fraxialmadness3 “nailed it” as they say on hip television these days.  A simple but powerful scene which is even more incredible since, as you may not have noticed yet, it’s entirely monochrome.  How many monochrome fractals do you see that look great like this?  If there was a textbook for fractal art techniques, this one would be in it.

Uf1992 by 0Encrypted0

Uf1992 by 0Encrypted0

Encrypted has a lot of awesome stuff on his Deviant Art gallery.  I just looked through it while trying to find the title for the image above and thought I could do an entire posting just on a few of the things he’s got posted there.  Encrypted is one of the few fractal artists who works well in both 2d as well as 3d fractals and his recent Ultra Fractal postings really show this.  Some people just have a good eye for design and composition and that seems to be 80% of good fractal art.  In addition to that, he’s got a sort of da Vinci style to his 3d images that is unique; and personal style is a hard thing to accomplish in algorithmic art where we all seem to be fishing in the same pond most of the time.  The 2d image above has a nice balance between action and intense detail versus quiet and plain textured areas.  It’s a good example of what I call the image within the image genre which is easy to find in fractals but not so easy to select and crop.  It just takes a sort of instinctive ability that one also sees in photography:  some people just frame stuff up better than the rest of us.

MB3D_0810_hd by 0Encrypted0

MB3D_0810_hd by 0Encrypted0

I remember seeing another (awesome!) image like this I think I also reviewed.  I often save images I see while browsing the internet but only give them an ID number that refers to a URL in a text file.  The result is I often forget who the artist is until I decide to include them in a posting which can sometimes be years later.  I would never have connected this image and the one just before it with the same artist but fractal art is always full of surprises.  This one has that renaissance feel to it I was suggesting before with the da Vinci thing.  But it’s also a rather unique 3d fractal in that it seems to be made entirely of gold foil or, perhaps, wisps of toffee.  Just like alexl’s image earlier, this one begs us to step over the picture frame and walk around.  It reminds me also of old fence lines around fields in the country that often formed a wall of scraggly, thorny trees with the occasional break between them that cattle would occasionally squeeze through and make into a gateway.

In the heart of Trantor by Bib

In the heart of Trantor by Bib

The lighting, coloring, detailing, shadowing, and just about everything-ing is simply awesome in this one.  This is actually one of my all time favorite 3d fractal images.  Remember the Death Star in Star Wars?  Do you know how much time and money they spent designing and building it?  And all the people involved?  This fractal image just makes them all look like fools.  Look at that gleaming cliff face up in the middle of the top section; just awesome.  And the whole place has the feel of an abandoned ruin, too; the feel of an Egyptian tomb.  Or a dusty shelf in a huge warehouse.  There’s a surreal, modern/ancient, crowded/desolate, theme to the image as well.  The mixing of moods that doesn’t naturally occur.

The Fractal Stage by arteandreas

The Fractal Stage by arteandreas

As the gallery comments from the Deviant Art page say, there’s a surreal feel to this one.  I think it’s because the image is both realistic as well as abstracted; it treats the simplified, abstracted imagery as if they were real by giving them texture and especially, that shadow cast across the blue “lake” in the middle.  I sensed a connection with backbones in the curving, semi-porous “cliff face” in the bottom section: subconscious association, another surrealist overtone.  It also suggests the reservoir of a hydro-electric dam in the mountains.  The image is richly symbolic and diagrammatic while at the same time composed of unique, individualized elements with elaborate detail.  The symmetry magnifies the interest by making everything in the image appear to have a symbolic form like a crest or coat of arms.

Space Kundalini 7 by Dorianoart

Space Kundalini 7 by Dorianoart

Here’s another (awesome!) example of pattern and artistry.  And color; Dorianoart always manages to do rich color in a tasteful way: saturated but not over-saturated.  As always, I like the old style digital elements like the blocky bits and glassy claws.  Notice, by “zooming out” a bit, that the left half is blurry and blue while the right half is clear and bright.  That’s the aerial perspective technique I learned about in high school art class: bluish haze naturally conveys an impression of distance and gives a landscape depth.  This being a digital landscape, and sideways, too.

MidspaceTraces II by JoeFRAQ

MidspaceTraces II by JoeFRAQ

This one is awesome for something that may not be apparent at first:  it is an extremely real and function scene.  People don’t draw fractals, they alter the parameters that draw the fractals.  Of course one can stick in all sorts of other imagery but this one is astonishingly convincing all on it’s own.  We see hallways; not surprising in any 3d fractal image but they also have overhead and ground level tracks like you’d find in a underground train tunnel or in a warehouse or manufacturing setting: the basic elements make functional sense.  The doorways are framed which is a natural element in any passageway that passes through a wall (door frame, window frame).  The green roundish thing above could easily be a light fixture, ventilation duct or camera fixture, while the similar element on the floor could be a drain suggesting that the bluish haze over the floor area represents water and the floor is in fact flooded.  This could easily be some sort of spent nuclear fuel storage pool or a surreal Turkish bath complex.  The pastel color scheme fits with either one but I think suggests more the illumination in a  nuclear fuel storage pool.  Let this be the first official record of realism synchronicity (new term).

Desert Diner by mclarekin

Desert Diner by mclarekin

I think this was posted to as a humorous offering, but upon looking closely at it, the way all the elements in this image work together to convincingly portrays a “Desert Diner” is awesome.  Notice the little green windows where windows are supposed to be;  I don’t know where the door is but I’d try for the window area that doesn’t have the middle white bit; it’s probably a double doorway (busy diner).  If you’ve ever been to New Mexico, down in the US southwest, you’d know that there really are rock formations like this and I wouldn’t be surprised if someone built a diner right into one as a gimmick to lure tourists off the interstate highway.  I find these sorts of 3d fractal images that so easily lend themselves to real world comparisons make the concept of virtual space much more compelling and multiply the possibilities as well as the intrigue for fractals.

Edifice by Dermis

Edifice by Dermis

As the title suggests, this image bares a notable resemblance to a monumental building.  I’ve never seen any 3d fractal that combined both the geometric qualities of a functional building shape along with the organic qualities of carved wood or marble.  This is something new to me.  Once again 3d fractals make better movie sets than Hollywood does.  Roman ruins would be much more impressive if they had the creative touch these virtual ruins have.  Or are they geometric tree trunks?  You see what I mean by the hybrid look of architecture and organism:  Man-made and natural growth.

MB3D_0774_hd by 0Encrypted0

MB3D_0774_hd by 0Encrypted0

My goodness, that’s three awesomes for Encrypted.  There’s an old song off the radio that has the ridiculous line in it: “We built this city; we built this city on Rock ‘n Roll. We built this city; we built this city on Rock ‘n Roll!”  To which I would add (30 years later), if ever there was a city built on the cosmetics industry… it would look just like this image here.  In fact, like the old song, this image has a shiny, elegant 80s look to it.  In fact, some of those lipstick tubes are the size of a football, just like the big, mammoth, eye-catching display versions you see on the counters and display shelves in the cosmetics department of a store.  Same for the square, golden face powder boxes the size of washing machines.   But, you’ve got to admit that there is no better example of an awesome cosmetics department fractal than this.  Note that there’s no price tags: nothing’s on sale in this place.

Map of the Mandelbrot Set by billtavis

Map of the Mandelbrot Set by billtavis

I’m sure someone has made something like this before, but this is different, this is awesome!   Being a Geography major back in my university days, I had a natural affinity for maps, especially old style ones.  This image combines both the genuine facts of the “places” of the Mandelbrot set along with the romantic allure of an old map.  If this doesn’t bring out the virtual Sindbad in you, then nothing will.  I’m sure everyone who’s ever explored the Mandelbrot set has some sort of map-like concept in their mind which this map here captures and enhances.  This ought to make a fine commercial venture since it has real appeal to both the science crowd as well as the fractal art fans.  It’s also explanatory and as such makes a great gift for people who know nothing about fractals or how much you might have paid for this unique print.  Of course, once you see the printed version you probably won’t want to give it away.

ABoxvaryshape1 by Ellenm1

ABoxvaryshape1 by Ellenm1

Another (awesome) hybrid.  This time it’s the colorful, cartoonish drawing style of 2d fractals merged with the monumental architectural style of 3d fractals.  Nicely rendered too, which can take some time with 3d fractals, I’ve heard.  I don’t know who Ellenm1 is.  Sometimes I discover that two different screen names on two different sites are actually the same artist, but from the content on her main Flickr page, I’d say she’s not one of the usual fractal art crowd.  But why should she be?  She’s awesome!  Outsiders have that brief opportunity, before they become insiders, to approach and think about fractals in innovative ways.  For the rest of us it takes years to shake off what we’ve “learned from others” and get back on that less traveled way.  Follow the eye: the eye will lead you to the Land of Awesome!  The eye can’t lie: it’s too simple minded.

In the words of Niel Young:

It was then I knew I’d had enough,
Burned my credit card for fuel
Headed out to where the pavement
turns to sand
With a one-way ticket
to the land of truth
And my suitcase in my hand
How I lost my friends
I still don’t understand.


Remembering Paul N. Lee

Image 06-B by Paul N Lee, 2001, made in QuaSZ

Image 06-B by Paul N Lee, 2001, made in QuaSZ and Bryce

I should begin by mentioning I never actually met Paul –offline, that is. But I suspect that describes most of the people he knew, since he was so active in the online world. In fact, I was invited to his wake solely on the basis of being in his email contacts list. Paul led a virtual life and perhaps it’s us virtual folks who knew him best.

My first encounter with Paul was, I suspect, like that of most people:  as someone interested in fractals and surfing the net I discovered his Fractal Database.  That is where the memories start.

My first impression was that Paul was just eccentric.  Later on I thought he was hostile.  That was because of all the “personal” information he was posting in such an easily accessible way on the internet.  Back then, like a lot of people, I saw the internet as a mysterious and threatening place where special precautions had to be taken.

But I grew up and with that so did my impression of Paul’s fractal phone book as well as my impression of Paul:  he was obsessed, but only with fixing some of the structural problems with the online fractal world.  Fractal artists are a very touchy group and naturally they felt profoundly violated by having all their important names and email addresses hung out a window so any passerby could look at them.  The Lilliputians didn’t see the bigger thing that Paul was working to build, only their little unpermitted piece of it.  For those of you still suffering, don’t despair; it won’t be online much longer without Paul around to look after it.  Only Paul had the determination or boldness to attempt or maintain such a project.

Which brings me to a major reflection: over the years I noticed that Paul’s online adversaries tended to become mine also.  But then, like Paul to a lesser degree, I was obsessed with fixing the fractal world too.  But I’m over that now.

To me Paul was two things:  technically savvy in the technically oriented world of fractal art; and also, someone with a real understanding of art and some professional training to go with it.  As a result, Paul often did know what he was talking about when it came to fractal art’s dual aspects of technology and art.

But Paul’s main interest was always in meeting and introducing newcomers to the world of fractal art to the art form’s tools and technicians.  In addition to his fractal directory, he also ran one of the few active e-groups for fractal art.  I checked it out once and noted that is was almost entirely Paul giving links and recommendations to the new and the curious who happened to find it.  Paul was pretty much alone in this sort of thing but his independent attitude made that easy for him to do.  For many years Paul was a sort of unofficial ambassador for fractal art.

I think that’s what attracted Paul so much to later on: it really embodied the sort of open-air venue where the new and curious could find out about fractal art, ask questions and grow.  I think Paul was well known there for always making a point of answering first time posters and welcoming them.  Some people might say Paul was a hostile fanatic but interestingly he never seemed to have any real problems with the folks on Fractalforums.  And like I said about me and Paul having similar adversaries, we both seem to have been big fans of Fractalforums.  I think we both valued the non-partisan mood that generally prevails there.

So what about Paul’s art?  Was Paul a fractal artist?  Was he any good?

Well, Paul has a lot of stuff online that I just don’t understand.  But I was never part of the Fractint phase of fractal art.  However, his alter ego, “O” had some interesting works that made me think that me and Paul had some similar interests in fractal art, with respect to the highly synthetic, design-oriented type of imagery.  I wrote a post on them a while back when the true identity of “O” was just a rumour.  Not very many people in the fractal world have a lasting interest in fractal artwork that no longer represents the cutting edge in graphical rendering.  What made Paul different was that his interest in fractal art was rooted in artistic merit and not the trend of the day.  But I know that still doesn’t explain his own online gallery

It may interest the readers of Orbit Trap to know that after the initial group phase of the blog failed, me and Terry considered asking Paul to join us as one of the three editor/contributors.  Maybe this really sums up just what Paul was to the fractal art world and why we considered him for such a challenging job;  Paul was: original; intelligent; vocal; literary; independent; vocal; independent again; and vocal, but worth reading; maybe too independent?;  no trouble at all speaking his mind; and perhaps unpredictable? but certainly worth reading…

Paul N. Lee was one of a kind and now he’s gone.  For those of you who never really liked him, you’re the ones who ought to be feeling a sense of loss.  You’ll never know the man we knew.

Let’s face it: Fractal Art really is a Computer Science Club


Fractal art got the boot a long time ago…

Let me start with an interesting quote from the (archived) Wikipedia talk page:

This article should probably be merged with fractal.—Eloquence 17:12, Dec 23, 2003 (UTC)

It’s the very first comment on Fractal Art’s Wikipedia page.  I love the irony of the username, “Eloquence” because he’s arrived at –back in 2003– the exact same conclusion I have, here in 2014.

But is this person really qualified to have much of an opinion on where the topic, Fractal Art, belongs in the Wikipedia?  From the profile page for “Eloquence” we find this:

My name is Erik Möller. I am the current Deputy Director of the Wikimedia Foundation, but also a regular Wikipedia editor.

There’s some more on his “meta” profile page:

I joined Wikipedia in 2001 and have since been involved in the project in pretty much all different areas. I spend most of my available time these days in my professional role, but you’ll still see me occasionally doing some semi-useful volunteer work, I hope. :)

I’m not making this up.  You see, it’s not just me and Terry, there’s others.  Fractal Art belongs back on the plain old fractal page of the Wikipedia because it remains a computer science topic.

And what’s WRONG with that????

Yes, why do so many fractal “artists” dislike being described as a computer science club?  I remember back a few years ago when I referred to as a fractal art venue, the owner (and moderator, contributor, TV host, etc…) Christian Kleinhuis corrected me by saying that it was a fractal site, not a fractal art site.  And if you follow the postings at Fractalforums you’ll see just how much the “technical” discussions vastly outnumber the art ones.  (Especially if you’ve been following it this summer.)

I am puzzled why “fractalists” (a better term than fractal artist) would object to the removal of their “art” status from their beloved hobby.  What is it in the terms, “art” and “artist” that they seem to want so much?  Is there some hidden ideological quest like that of, say, proving the possibility of “technologists as artists”, similar to the old, and ongoing challenge of demonstrating the existence of artificial intelligence?


I think it’s because they see “art” as a special, higher status to something that would otherwise be described as “graphics” or “graphical applications of fractal formulas”.  But really, many great artists are despicable people with all sorts of emotional and sexual problems and whose work is just as easily defined as infamous as it is famous.  Or clinical.  Some artists can be diagnosed by their work.  They’re not taking the rorschach tests, they’re making them.

The jury is no longer out

If someone was to say that Fractal Art is a new art form and it’s too early to say what it’s going to become, I think most people would agree. I’ve been hearing that for the dozen years I’ve spent in the fractal art world now and I’ve always accepted it. It’s become something of a habit, nodding to statements like, “…but fractal art is still so new”. But how long can something be new before it’s –not new– anymore?

I’m taking the stand that the future of fractal art –that visionary tomorrow– has already arrived and that fractal art’s debut status on the world stage is over.  I base that on the fact that fractal software has been widely available to whoever wants it for a good 20 years now.  I’m not even counting the previous two decades where fractal graphics were more primitive and less accessible (but more significant); that would extend the time span to almost 40 years.

But some will still insist on the label of newness, not on the basis of young age but from the notion that fractal art is as yet undiscovered by the majority of people, and in that sense it’s a new thing to the rest of the world.  But this too makes little sense considering we are living in the age of the internet, where nothing can stay hidden or obscure for long (even if it wants to).  Have most people with internet access never seen a fractal?

Description -not Definition

Let me describe “Fractal Art” instead of offering, yet another, clever definition of it.  Definitions tend to be abstractions and fractal art is no longer some sort of artistic infant whose future we can only speculate about.  Fractal art is what it is.

Here’s my description of what it —is:

1. Just Fractals

Fractal art is just fractals.

Fractal art is a technical pursuit rather than an art form. The term, “art” is used deceptively to separate from the fractal sciences a sub-category that is merely the graphical applications of fractal geometry. Although this sounds like something with artistic motivations and intentions, (it’s got that “art” word) praise and attention in the fractal art world come from technical innovations like rendering technique, formula enhancement and software development rather than the creative use of existing tools.

Old artwork is of little interest in the fractal art world and new works accordingly loose their appeal as the technology that made them becomes more widely used and is no longer fresh, like last year’s photos from a space probe.  This has unfortunately lead to the general condition of fractal art where the “art” functions merely as a reflection of the technology and the technology has become (and likely always was) the real subject of fractal “art”.

2. Both your mother and father must be a fractal

Artwork that incorporates other technology (post-processing) is irrelevant because it can’t reflect fractal technology for the obvious reason that it doesn’t use it; a criteria which simply establishes fractal art as both “anything you can make with a fractal program” and “only what you can make with a fractal program”.  Ironically, fractal art has come to be constrained by fractals because it’s defined by fractals.  Fractals have become the limits to fractal art instead of its beginnings.  The beginnings of a more loosely defined digital art form whose creative options would have been exponentially greater and one in which fractals would probably have been a prominent feature.  Fractals are the best source of digitally generated imagery for processing.

Fractal “artists” defend such a “fractal” restriction on the logical grounds that only “fractal” formulas produce “fractal” art, and in doing so reveal an exclusively technical attitude.  Only a scientist is more interested in creating “artwork” whose classification system is more impressive than it’s appearance.  This rigid definition of fractal “art” (and anyone who adheres to it) shows better than anything else that fractal art is a club for computer scientists.

Such attitudes are the norm in the fractal art world and as a result, fractal art as a category contains nothing much that would distinguish it from the illustrations for a mathematics lecture. The label, “fractal graphics” would be a much more appropriate name for the category.

3. Fractals don’t interest artists

With a few trivial exceptions, fractal artists are really just fractal “lovers” (fractalists?). The group doesn’t attract people with an art interest because, from a purely graphical perspective, fractal programs are just a type of shape and pattern generator, and one which produces imagery that has a tendency to become monotonous and pattern-forming. Fractal artists want their little hobby to be an exciting art form rather than just a cabinet of science curiosities (eg. BMFACs).  But they think the problem is with their audience and not themselves and so they’re constantly trying to change the impression the world has of them, rather than changing the thing that creates the impression the world has of them (ie. the art).

Some really artistic fractal artwork would go a long way to redefining fractals as an art form rather than a computer science club.  But, as I hope by now you’ve come to realize, that big leap forward is only going to happen when the medium expands and the creative options become broader.  And that’s something that would destroy fractal art in the minds of most of its “artists”.

It’s all hopeless but read the conclusion anyhow

Fractals need help; they’re pretty well limited to cool looking designs and largely ornamental or neat pictures that have a sudden wow factor as well as a sudden shallow artistic appeal.  Nobody really tries to do anything visually creative with fractals.  In fact, fractal images, despite their variety on technical grounds, are rather predictable, which is the opposite of creative.  “Creative” in the fractal art world means new formulas, new rendering methods, –new technology.  That’s a computer science club’s idea of a good time and an “exciting new development”.  And furthermore, as I mentioned in a previous posting, fractal-looking imagery is not even the exclusive domain of fractals.  Fractal programs are just more sophisticated when it comes to generating weird shapes.

As the history of the fractal art Wikipedia page shows, outsiders have never seen any difference between fractals and what is called “fractal art”; it has never distinguished itself from its parent page.  It’s ironic that it’s the people who “know nothing about fractal art” that seem to know it better than those who do.  Or, as I so eloquently put it in the title of yet another previous posting, “Fractal Artists are Deluded Narcissists”.

Why doesn’t Fractal Art have a half-decent Wikipedia page?

It’s useless, and although there have been efforts to build something substantial there, ultimately the page keeps reverting back to a few shallow paragraphs that fail to even offer a basic definition.  I’ve been going there for several years and have always wondered why it never seems to develop into anything, but now I think I’ve figured out what the problem is and it goes to the very heart of  what “fractal art” is all about.


Wikipedia’s Fractal Art page

Unlike most websites, the Wikipedia documents almost every edit made to its pages and even has a separate page for discussing what should be done to improve the pages or any other “concerns” about it there might be.  Each Wikipedia page has its own corresponding talk and history page and for Fractal Art it supplies something that is quite rare: serious criticism.  It’s quite refreshing to see someone besides Orbit Trap actually express some sober second thoughts about Fractal Art.  Unfortunately, the way the Wikipedia works, it’s unable to take that next step and give a coherent, single-minded expression to what  it thinks.  Unless, of course, that mostly empty page on Fractal Art sums up what “the Wikipedia” thinks about Fractal Art; that is, not much at all.

I’ve chosen a couple of salient incidents from the Wikipedia Fractal Art page documentation to answer the question I posed in the title, “Why doesn’t Fractal Art have a half-decent Wikipedia page?”

The Rise and Fall of the Fractal Art Manifesto

If you want to read the whole story, or at least follow the history of edits to the Fractal Art page, all you have to do on that or any Wikipedia page is go to the “view history” tab at the top right of the page.  Click on any “cur” link in the list and then click on “previous edit” near the top of the left column.  This is what I did and it allows you to then read the editing history “Next edit” by “Next edit”.  This link is to the very first entry, the initial creation of the Fractal Art Wikipedia page.  Click on the “Next edit” link on the right to start your journey.

This is where I discovered the fate of  the venerable Fractal Art Manifesto (FAM) by Kerry Mitchell and its treatment by the Wikipedia editors.  I wrote a blog posting about the FAM back in 2011 and part of the motivation for that was it’s (at the time) high status on the Fractal Art page where it had advanced from not just an “External link” but was enshrined in its own separate section as you would expect any historic milestone for a subject to be.

But four years previous to that, in 2007, its presence in the External Links section of the Fractal Art Wikipedia page met this fate by “TheRingess”, that powerful queen of Wikipedia’s Fractal Art page:

Thou art banished!

Not Wiki-worthy!

As much as I’d like to do the same thing to the FAM, I thought, “What’s wrong with a personal essay?”  I mean, gee, it’s still worth a link.  And then I thought, “Doesn’t the word, ‘personal’ describe more or less everything in the whole fractal art world?”  Aren’t all my own (great) blog postings just “personal essays”?

Anyhow, the FAM was resurrected a few years later and even given its own separate section on the page, as I mentioned.  To anyone in the fractal art world this might seem reasonable, since the FAM reads like it has authority and also because there is nothing quite like it in all the fractal art world.  Like any other art manifesto it seems to define the art form and be, in itself, of historical importance.  How it got chopped from the Wikipedia page is as enlightening as it is somewhat humorous.  Enlightening because it says something about why fractal art is a difficult subject for things like the Wikipedia, and humorous because, well, just read this item from the Fractal Art “talk page” for yourself:

Wikipedia's verdict on the FAM (and everything else to do with fractal art)

Wikipedia’s verdict on the FAM (click to read original text on Wikipedia talk page)

Pretty rough, eh?  But what the Wikipedia editor is getting at here is not a personal attack on Kerry, but rather a professional  attack on Kerry.  He tosses Kerry’s FAM out the window because he doesn’t see any authority behind it.  That’s why he dismissed the Lulu books: they represent one’s own efforts and not the decisions of an editor and publisher.  Like Ringess, he just sees a “personal essay”.

Reliable Sources…

What I’ve come to realize is that the Wikipedia looks to build articles out of what Senor Service referred to in his verdict on the FAM as “reliable sources”.  And in the fractal art world there aren’t any.  Everything I’ve ever written would get tossed out the window by the Wikipedia as a “personal essay”.  The best of us might get our names Googled, but only to discover that we’re all “non-notable”.  There are no authorities or resources that aren’t merely the product of one person or at best, a group of friends.  Fractal art has no professional presence or institutions.  And remember, Senor Service’s Googling was done in 2013, after, not before, the esteemed Benoit Mandelbrot Fractal Art Contests and Exhibits of which Kerry was a judge all three times.  They think that’s “non-notable”?

That’s the big problem with fractal art as far as the Wikipedia is concerned: there isn’t anyone reputable enough to be quoted.  But that’s not the only problem…

{{No more links}}

Over the years a number of people have showed up and added their own artwork (personal!).  Some of them were quite relevant, but, alas, charged and convicted with link spamming.  I often admired their persistence in reposting their links in the External Link section.  So did “the Editor” who responded, finally, with this warning comment on the editing page:

==External links==
{{Prone to spam|date=September 2012}}
{{Z148}}<!– {{No more links}}

Please be cautious adding more external links.

Wikipedia is not a collection of links and should not be used for advertising.

Excessive or inappropriate links will be removed.

See [[Wikipedia:External links]] and [[Wikipedia:Spam]] for details.

If there are already suitable links, propose additions or replacements on
the article’s talk page, or submit your link to the relevant category at
the Open Directory Project ( and link there using {{Dmoz}}.

But there’s a good Wikipedia explanation for this:  the Wikipedia is trying to create encyclopedia articles.  If  there’s something really good in those links then put it in the article and publish it right here on the Wikipedia.  That’s why they’re so link-averse (and why the page is so empty…).

Are we all losers?

My own opinions about fractal art would be Wikipedia-worthy if I had some fractal art qualifications; degree, office, professional designation, published in a fractal art journal.  As it is no one has anything like this –except– on the technical side, which, as I mentioned, is a completely different section of the Wikipedia:


Fractal page from Wikipedia. Not to be confused with the “Fractal Art” page.

Funny eh?  The Fractal Art page is nothing more than a few simple pictures and a couple of banal paragraphs while the main “Fractal” page is up in the intellectual stratosphere, too high, apparently “for most readers to understand.”  And they’ve got real, serious external links.  There isn’t even a gigantic warning message about “{{No more links}}” on the main Fractal page.  Of course, that’s because in the area of fractal science, there’s plenty of qualified (i.e. PhD) sources and professional materials (TV documentaries, books, professional journals).  It’s makes the Fractal Art page look like some Nobel Prize winner’s retarded brother.

Start spreading the news, I’m leaving today…

Alright, what to do about this?  How do we clean up fractal art and get it into the same sort of shape as the fractal sciences?

Well, I think the Wikipedia just isn’t the right venue for information on a topic like Fractal Art.  Like I said, there’s nothing official, it’s all just us amateurs and hobbyists.  The big Benoit Mandelbrot Fractal Art Exhibits were just fractal art’s link-spamming in its highest form; it’s most muscular example of “self-promotion” as the Wikipedia often calls it.  If you though the BMFAC was going to launch your career in fractal art, I’m sorry but you never actually left the ground.  Even the judges are “non-notable” as far as the Wikipedia is concerned.

Orbit Trap is the only thing closest to being a real authority in the fractal art world:

Yes, but how long will it last?

The only Fractal Art link Wikipedia readers really need

YouTubers Mock Fractal Art

I logged out of one of my YouTube accounts and before I could log into the other, I found myself on the main YouTube page with links to the dumbest junk I’ve ever seen.  I knew there was a lot of senseless stuff on YouTube but I never paid any attention to it until this:


It’s tabloid newspaper trash meets YouTube.  If you’ve ever wondered what the end of the world might look like, or at least the end of intelligent life, this is it.

I can’t imagine Fractal Art would be this big a draw to the JunkTube crowd, but there’s more:


Why would they care so much about what people, or “YouTubers” think about flame fractals?  Does this sort of empty-headed abuse serve any purpose?

Not content to trash fractals among a purely adult audience, they’ve also attempted to poison children’s attitudes to an art form that can have a lot of beneficial educational spinoffs.  But all they care about is cheap laughs:


Out here in the fractal art world we’re used to having to explain to outsiders that our art form isn’t just pushing buttons or harvesting batch Apophysis renders and that one needs to look at the better examples of fractal art before deciding whether they really like it or not; but this sort of mockery just short-circuits the whole fractal art experience and turns off people who will probably never look any further than these “YouTubers” reactions.

If you really want to check them out, this is the link.

Fresh Winds from San Sebastian

It was called the “International Fractal Art Symposium” and was held in San Sebastian, Spain (that’s in Europe) from June 25th to 27th, 2014.  I first heard about it back in December 2013 in a thread on, but reined in my instant desire to comment about it because something made me think it was more like a private party than an International Symposium and so I thought to myself, “let the poor folks have their privacy”.

But watching the growing list on the “Attendees” page on became a daily, maybe hourly, obsession with me and I soon began wondering if this private party might actually end up being something like a symposium after all.  If you could check the web logs you’d probably find me in there as the most frequent visitor to the “symposium” site.

If you’re going, to San Francisco San Sebastian… Be sure to wear, some flowers in your hair…

Don’t these “International Symposium” things immediately excite everyone?  Think of the enthusiasm that was whipped up in past years by the Benoit Mandelbrot Fractal Art Exhibitions (07, 09, 11).  We’re all hopelessly optimistic or something.  Or maybe we see fractal art as held back by something, or held up by something and this year, maybe, fractal art is finally going to break out.

Break out of where it is now.  Where it’s been since the 90s:  A hotbed of enthusiastic (and talented) practioners, albeit small in number (at this point in time) refining and advancing a real art form (if only others understood it (like we do)) waiting for that critical mass of numbers, and the attention of just one Hollywood scout to alert the whole world to this great breakthrough in art.

 The Future of Fractal Art

Program details

Program details

One hour for a group discussion (starting) with the future of fractal art, and then two hours for lunch.

Fractal “Sharing”; “Show-n-Tell”?  They are a parody of themselves.

I am often struck by the wisdom of saying nothing and I have almost knocked myself out this time when I realize how wise I was not to have said anything about Javier’s Barbecue back in December when I first found out about it.

But why criticize or make fun of something like this? (you may be asking?)  Isn’t it just mean?  And, and… why don’t I try organizing something –constructive– like this and see how hard it is?  Or, and this is the perennial thought in fractal art: “Isn’t it too early to say what’s going to come of this?”

The Wreckage of the BMFACs

What if this is all there is to the world’s reaction to fractals?  What if the audience for fractal art is primarily just the people who make it?  Fractal art is so easy to “do” and is so much fun to play with that anyone who has any interest in the art form is only one free download away from joining the ranks of the “artists”.  As a result, what separates the artists from the audience is often nothing at all.  In fact, is there really an audience at all for fractal art?  Who out there is an avid fan of fractal art and doesn’t have an online gallery somewhere?

The Future we Fear

What took place in San Sebastian is what I think fractal art is and will always be: 20-some people hanging out together:  sharing artwork; telling anectdotes; discussing new programs.  Like an endless fractal zoom where we feel like we’re moving but it never seems to end at anything.  How ironic that the future of fractal art should be a recursive loop.


Not with a bang, but a Print Swap

Fuh, fuh, fuh… Fractals!

I apologize in advance if this post seems like nothing more than a roundup of fractals recently posted to, that mega mecca of all things fractal, but that forum site just seems to have the right formula for their fractal flypaper that makes the job of roving scientists like myself so much easier.

Here’s a couple that give me the heebee-geebees…

~Click on images to view full-size on original site~

Memnon by hebegebe

Memnon by hebegebe

The synthetic power of fractals is really seen in this one.  It’s simple and iconic and yet filled with little details and subtleties.  It looks a lot better in full-size which you can see by clicking on the image.  These sort of images remind me of coats-of-arms, the heraldic imagery of medieval kingdoms.  They have the cryptic combination of lines, circular elements and colors that look very deliberate and symbolic and yet… drawn by a fractal formula and not a king’s legal representative.

How to read the herald...

How to read the herald…

Fractals like Memnon suggest some kind of alien heraldry, or a world as strange and exotic as some kind of Tolkien trilogy set in the land of fractals.

FlyingShip_Red Mask by Hebegebe

FlyingShip_Red Mask by Hebegebe

The details are quite interesting in this one too.  Hebegebe has a good eye for color and combined with the fine rendering of the 3D fractal program, makes for some nice details, like this in the bottom middle:

FlyingShip Red Mask (detail)

FlyingShip Red Mask (detail)

How convenient to have a tool-tip in one’s screenshot that displays the image notes…  Well, you can see the notes Hebegebe has included.  I need to do a little tweaking with my screenshot program.  I like the color for the tool-tip though; it goes with the orange-red background.  The digital medium is a living thing.

Anyhow, this FlyingShip is not your usual 3D fractal and in fact, resembles more one of those gymnastic, contortionist quaternions.  I saw something somewhere once that reminds me of this…


Isn’t the internet a much better place for just about everything?  Although I forgot where I got this from… it’s (as you can easily see) an old, 20s or 30s illustration for a sci-fi story.  Do you see a startling, “family resemblance” between it and Hebegebe’s FlyingShip?  If you do, then you’ve developed that artistic 3rd eye, like myself, that I suspect may also be associated with the early stages of either a real understanding of art or some sort of mental illness.  Fractal art is the crazy spaceships of today.  Note even the rich texturing and also, consistent, almost mechanically produced shading that appears all over the images.  This actually looks like it was computer drawn.

I’ve always felt that there’s a common link with computer art and art from the pre-digital age, but it requires a little bit of a leap to make the connection.  Mental connection.  Psychological.

Supraterranean Pipelines V by JoeFRAQ

Supraterranean Pipelines V by JoeFRAQ

Have I become Joseph Presley’s biggest fan?  It gives me a chuckle how things can change in the fractal art world.  The medium is a slippery thing and one can go from making one kind of thing to something quite different.  The power of the medium allows artists to do things with their style that no other medium can.

Once again you need to look at the fullsize to share my excitement with this one.  JoeFRAQ is one of those rendering perfectionists and in the realm of 3D fractals the payoff for that kind of obsession is huge.  I always wonder what sort of rendering time it takes to make some of these images and what the specs on the computer hardware used is.

I should say something about the image:  Nice composition, but Joe’s always good at that; the colors are rich, complex and make the numerous details of the pipeworks much more exotic.  Up in the middle at the top there appears to be some lively bit floating by.  It almost seems to be moving.  And with the stars in the background, there’s a strong feeling to this scene.  Look how sophisticated the world of 3D fractals has become.  Wasn’t it just a year or two ago that the whole mandelbulb and mandelbox thing was invented?

Eternal repeating by abbaszargar

Eternal repeating by abbaszargar

It’s a Symphony in Sand.  Unfortunately the 500px version above has smoothed out all the sand.  That’s usually a good thing in fractal art –anti-aliasing– but in this case it erases the Valley of the Kings majesty to abbaszargar’s work here.  In fact, this one’s so gritty that most people would consider it a rough draft, no pun intended, but I think this is a great example of how less can be more, that is, less rendering can produce something more artistic.  Here’s a lossless jpg crop of the original in one of my favorite “gritty” parts of the image:

Eternal repeating (detail)

Eternal repeating (detail)

Here’s where we separate the art folks from the science fair enthusiasts.  The graininess of the imagery accentuates the eternal repeating –endlessness– of the image in a powerful way.  There are probably many images like this produced by other artists that being (too) well rendered don’t have this Valley of the Kings effect.  Maybe abbaszargar is not you average fractal artist?  Or did he intend this only to be a trial render?  Well, one way or another he made something remarkable and out of the ordinary.  The full-size really shows that much better; hint-hint.

I don’t watch a lot of fractal videos.  But I found this one posted to and something just drew me to click on it.  After watching the low-res version I soon jumped to the Vimeo page to see the hi-res one and it was certainly worth it.  Surprisingly, the author, Julius Horsthuis has managed to put the fractal imagery in a real narrative context of shipwrecked sailors wandering around in a state of semi-delirium.  It kept my attention as well as made me want to see it again in HD, and that’s a real accomplishment since I’m not the most friendly audience for fractal videos.

Navigation in Dreamtime from Julius Horsthuis on Vimeo.

I recently watched the entire Lord of the Rings movie trilogy as well as the two parts of The Hobbit trilogy that have been released, and after all that I had some profound thoughts on the merits and pitfalls of richly expensive CGI rendering.  I’m not a Tolkien fan, but the movies often kept my interest through the exotic scenery.  Interestingly, one of the most captivating scenes was in the Lord of the Rings series (or was it the Hobbit?) where the idiot with the english accent (bad casting) and his hobbit buddies end up walking into a mountain and are then trapped in a room and attacked by the sickly looking orcs.  Anyhow, the interior of the mountain where they come to a city, of sorts, with lots of pillars, was so impressive I wanted to leave the tour group and wander down every corridor just looking around.  Then I realized it was reminding me of the mandelbox and it’s carefully carved, details all over every surface.  In short, 3D fractals are actually better than many multi-million dollar CGI extravaganzas.  (Unless of course it’s a real movie with a story, actors, dialog and plot you want to see.)  But if you just want to run away from the tour group and look around then 3D fractal land is the place to go.  And cheaper too.

The tour starts here:;sa=listall;type=recent

Fresh Fractal Finds

Here’s a bunch of images that caught my eye while out prospecting with my virtual mule.  Let’s take a look while I try to psychoanalyze myself and add another chapter in the book, “Art as Rorschach Test”.

~Click on images to view full-size on original site~



Stratographic detail/ Prince of Persia Sands of Time like awe-inspiring temple magnificence/ and another thing… it seems to be walking!  Can you imagine an elephant as a temple –walking?  Also, you could say it was one of those Star Wars big walking machines on Hoth.

I’d been waiting a while for Kraftwerk/Mandelwerk/Johan Andersson to add  a new creation to his collection of art-work-I-like and now it’s here.  Ironically, I find the little figures don’t add as much to the effect of the image as those sorts of additions usually do in 3D fractal art.  The sky does, and so does the shiny floor and shadows; but the impression of enormousness –and especially that strange, walking feeling– all come from the 3D fractal imagery.  I know it’s not because of sunstroke because I always wear a hat.

Chain Driven II by JOEFraq

Chain Driven II by JoeFRAQ

I’ve never been much of a fan of Joseph Presley’s art but lately he’s been moving in a new direction and it’s quite refreshing.  Black and white is a rarely used palette in fractal art but clearly Joe saw the artistic potential in it for this image and he did the right thing by abandoning colour altogether (unless you consider BW to be a colour all its own).  The steeliness is accentuated; the mechanical parts are emphasized and yet the image rather than becoming flat has clear depth to it.

Here’s one that shows Joe’s good eye for fractal forms and the ability to orchestrate it with real world imagery.  My goodness, two images by Joseph Presley; I’m becoming a real fan.

BX3000 Steam Punk Organ by JoeFRAQ

BX3000 Steam Punk Organ by JoeFRAQ

You really need to see the full-size version to appreciate the details.  I was just stunned when I saw this one on  It’s genuinely fractal and yet blends seamlessly with the real world keyboard at the bottom.  I wonder if Joe made the keyboard in Ultra Fractal too?  I also like the use of symmetry (the left and right sides are identical), it gives the machine a man made look despite it’s genuine algorithmic pedigree.  I wonder if this was made in Xenodream?  Joe has a large collection of “Musical Art” of which this one, oddly enough is not part of.  Perhaps the arrival of the 3D fractal wave has energized Joe’s creativity.  He wouldn’t be the only one.

While we’re on the topic of artists I usually dislike, let’s take a look at this one:

Steelcurtains by Jimmie

Steelcurtains by Jimmie

I’ve been noticing “Jimmie’s” work on for quite a while.  It’s usually the sort of highly polished ornate UF stuff that also turned me off Joseph Presley’s earlier works.  Then, all of a sudden, Jimmie posts this incredible, transcendental House of Doctor Zhivago vision.  Here is where mine and Jimmie’s tastes in fractal art meet.  I don’t expect it to happen again for quite some time, but who knows where anyone’s art is taking them?  Each fold in the curtain tells another fragment of the story of a majestic castle enthroned in perpetual winter.  A sort of Fall of the House of Usher meets Baba Yaga in the Gulag.  I don’t think Jimmie intended that, but that’s what I see.  Steelcurtains is a nice neutral, non-suggestive name, though.  My names are all crazy.

Well, I can see this post is taking on a life of it’s own and charting its own course.  Now here’s not one but two images by another artist I used to shrug off but now have come to appreciate.



Guagapunyaimel creates a lot of these types of image which I would loosely describe as “window worlds”.  Although I don’t know what program this was made in, Guagapunyaimel is one of the few Chaotica devotees creating flame fractal artworks with that special program.  I’m sure there’s plenty of fractal folks out there who don’t care for:

1) Black and White, monochrome anything

2) Images without a nice, rational central focal point that can be talked about

…then I think you’re someone who doesn’t really like the fractalness of fractal art.  Ironically, this one’s title suggests a new definition of fractal art and I think it fits quite well.  What would Che Guevara do?



Check out the full-size version to see the richness that the fractal detail adds to this one.  This one is very fractal both in word and deed.  Unlike the previous one which has no central shape or focus, this one has a very clear design structure to it which the smaller elements both emphasize, alter and embellish.  This one has a Chaotica look to it, but there’s no hint on the deviantART page as to the program used and I’ve learned not to guess about such things.

While we’re on the topic of Chaotica, any of you readers will have noticed the recent thread about Fractal Architect vs. Chaotica.  Among other things… it rapidly boiled down to which program produces the better art.  Only a technically obsessed software developer would ask such a square-headed question, but it does raise an issue which is worth considering: What makes a fractal program a good fractal program?

Well, I would say the output (success) of any fractal art program depends as much on its userbase (or lack of) as it does on the program itself and whatever special features it may have.   Chaotica clearly has an enormous lead in this respect compared with Fractal Architect as its larger user base has taken this program and really transformed the world of “flame” fractals into something much more interesting and much less “flamey”.  Chaotica still has the capability of producing the usual assortment of glass bubbles, neon flowers and glowing water sprinkles that have come to characterize the world of flame fractals, but it also renders things which are dramatically different than theses common gas bubble things.

I definitely agree that a fractal program is best judged by what people make with it (because that’s what fractal programs are for) but unfortunately for the software developers that depends more on how the users use it than on how the developers have developed it.  In short, the question is never definitively answered because what a program is capable of –especially a fractal program– is never fully and completely demonstrated.  It’s a bit like asking, “What can be done with a paintbrush?”

To answer the question, “What can be done with Chaotica?” or rather what can we begin to do with Chaotica, let’s look at this freshly posted image from deviantART:



Tatasz is a new name to me, which probably shows how little I’ve bothered to follow the progress of Chaotica’s userbase and its “artbase”.  I  found it rather quickly by browsing the Chaotica Fractals group Featured gallery and that’s probably the best place to start if you want to see the “artbase”.  At least you can be sure what program has been used.

Winds by tatasz is an interesting image regardless of the context one views it in: Chaotica Fractals; Flame Fractals; Algorithmic Art; etc..  The full-size is much more impressive because you can see the exquisite “painterly” style to the image.  I think tatasz has been doing some real, cutting edge experimentation with this sort of Chaotica imagery.  I read that somewhere.  Back to the image…  This is the bottom of a frozen lake? or, snow covered spruce trees in the wind?  Here’s something interesting to compare it with as we take a giant leap from the digital to the old-fashioned paintbrush world:

A Young Tree by Emily Carr (1931)

A Young Tree by Emily Carr (1931)

This one is a painting, of course, but I think you can see the potential Chaotica has in the hands of someone who has a feel for using algorithmic software (not all developers are as handy creating with their software as some of their users are).  The future of Fractal Architect, like all software art programs, is in the hands of its userbase.  Hopefully that will grow.

Fractal Architect is a Mac program and here’s something else of interest from the Apple world:



Made with the Frax app for iOS (iPhone, iPad…).  I’ve always considered the spiral to be not so much a fractal cliche as it is a sub-genre of fractal art.  Similar in this respect to what still life (paintings of fruit bowls) is to painting.  How cliche a spiral looks depends on what the fractalist does with it or to it.  Something one could say about the entire genre of fractal art.  There’s an interesting detail in the lower left corner:

Not so blue -detail- by Aqua-Loop on deviantART

Not so blue (detail) by Aqua-Loop on deviantART

These are the dreamy details that capture the viewers mind.  The shine of varnished oil paint, the colloidal creaminess of marble paper, northern lights in a winter night sky, sheet music shooting out of the Sun.  You see?  If you’re going to turn your back on the fractal spiral you might as well turn your back on all of fractal art.  You don’t really like it.  That’s what the Rorschach shapes are saying.

The Synthetic Aesthetic 5: Surrealist Pioneers

The work of some surrealist artists back in the early 20th century involved the use of creative methods that are almost analogous to many of our modern computerized algorithms and effects.  For people like myself that are currently exploring the creative potential of photoshop filters and other graphically creative computer things, the smoke drawings, photo choppings and experimental painting techniques of the surrealists are an instructive as well as encouraging gift from the past.  They are fellow “syntheticists” because even though they worked in a very different, non-digital medium, they merely worked with different machinery while pursuing the same graphical philosopher’s stone as the digital syntheticist does: creativity that isn’t trapped in the wheel-ruts of the human mind.

Yes, human thought and expression can be plagued with “wheel-ruts”.  Nothing shows this better than synthetic creativity.

Surrealist art was obsessed with the human mind and in particular the so-called subconscious mind that was the focus of psychological investigators like Sigmund Freud and Carl Jung.  While some surrealists explored their minds and created works based on that sort of self-directed, introspective method, others took a contrasting path and tried to provoke their imaginations and those of their audience’s from the outside with automatically created graphical works (“automatism”).  (Check out Surrealist techniques on the Wikipedia.)

While psychiatry considers automatism reflexive and constricting, the Surrealists believed it was a higher form of behaviour. For them, automatism could express the creative force of what they believed was the unconscious in art. Automatism was the cornerstone of Surrealism. André Breton defined Surrealism in his Manifeste du surréalisme (1924) as ‘psychic automatism in its pure state’. This automatism was ‘dictated by thought, in the absence of any control exercised by reason, exempt from any aesthetic or moral concern’.

Jennifer Gibson (From Grove Art Online) See MoMA Automatism

Surrealist art is a pretty broad subject and there’s a lot more to automatism than synthetic creativity so let’s just focus on what the Merriam Webster dictionary says about automatism:

suspension of the conscious mind to release subconscious images <automatism —the surrealist trend toward spontaneity and intuition — Elle>

This, from the Merriam Webster dictionary site is helpful too:

Method of painting or drawing in which conscious control over the movement of the hand is suppressed so that the subconscious mind may take over. For some Abstract Expressionists, such as Jackson Pollock, the automatic process encompassed the entire process of composition. The Surrealists, having once achieved an interesting image or form by automatic or chance means, exploited the technique with fully conscious purpose. See also Abstract Expressionism, action painting, Surrealism.

As you can see, the concept of automatism diverges into a number of applications depending on how much the interfering influence of human artistry is excluded; but surely the creation of imagery through solely mechanical means is the purest application as such a mindless process excludes any sort of intentionality.  The art (if any) is accidental.

If you think that sounds like a recipe for junk then you ought to remind yourself that much of what is called fractal art is made this way.  Many of the most confusing masses of graphical imagery found in the great (infamous?) works of  Abstract Expressionism and Action Painting involved much more human artistry and involvement that the most heavily layered fractal artworks.  We can all laugh at Jackson Pollock’s drip paintings but it’s the winners of the Benoit Mandelbrot Fractal Art Contests that are trying to get public recognition and acceptance in the art world, not Jackson Pollock, whose “junk” is now icons of 20th century art.

But getting back to the freaky surrealist art techniques…

I spoke about Decalcomania in the last part, Part 4; it’s not really algorithmic like fractals are, but it is mechanical.  One doesn’t draw with Decalcomania, they squish paint onto a canvas, or board with a glass plate and hope it provokes (after numerous attempts) something magnificent and deeply psychological.  Probing the mind and exploring psychological themes was a big part of surrealism and that’s where the experimental imagery came in:  Art as Rorschach test.

Here’s an article on surrealist art techiques.  It seems to have formed the basis for the Wikipedia page about the same topic.  I wonder which came first?


They all seem to be French words.  Here’s a quote:

Another surrealist technique was known as fumage (smoking). Pioneered by Wolfgang Paalen (1907-1959) during the late 1930s, it involved placing a candle under a sheet of paper to form patterns of soot. Moving the candle varied the patterns.

~Click on images to view on original site~

Ciel de Pieuvre (1938) by Wolfgang Paalen

Ciel de Pieuvre (1938) by Wolfgang Paalen

Here’s an image made in the program, Fyre (no pun intended) that utilizes the Peter de Jong map (algorithm).  Not exactly a great work of art like Paalen’s but I think it shows some similarity in the type of imagery formed by a smoky algorithm instead of a smoky candle.

An image made with Fyre

An image made with Fyre

Of course the best modern computerized analogue to the surrealist’s Fumage technique would be the gas fractals made with Apophysis.


Cubomania is a method of making collages in which a picture or image is cut into squares and the squares are then reassembled without regard for the image. The technique was first used by the Romanian surrealist Gherasim Luca.


cubomanie-24 by Gherasim Luca

cubomanie-24 by Gherasim Luca

Here’s the Mona Lisa run through the photoshop filter, Flip Chop, made by Mario Klingemann:

Mona meet Flip Chop

Mona meets Flip Chop

The idea the surrealists had with chopping up photographs was to create the suggestion of something else, something new.  The result was almost always an image that “worked” differently that the original.  Naturally it was fragmented but there was also a creative and often psychologically stimulating effect from the new mental as well as physical arrangement.  Flip chop does this with almost no influence from the “artist”.  I’m sure there are other filters that will allow for more variation, like a random seed or something like that.


grat·tage (gr?-tazh’) n. A surrealist technique in painting in which (usually dry) paint is scraped off the canvas. It was employed by Max Ernst and Joan Miró. [< Fr. “scraping”]

Grattage 1955 by Mario Deluigi

Grattage 1955 by Mario Deluigi

Yes, digital artists weren’t the first ones to go texture and gradient crazy.  Do we need to see a digital example of this?  Here’s something I made with a block wave filter that has the same effect, although not as elegant as Deluigi’s.

Cherryorchard, made with Showfoto's block wave filter

Cherryorchard, made with Showfoto’s block wave filter

Click on Deluigi’s image to view several more.  It’s a fascinating type of imagery and one that easily makes the move into the digital realm of synthetic imagery.

Now scraping paint off a canvas isn’t exactly a hands-off technique, but other examples, especially by Max Ernst, also involve placing the soft canvas over a rough surface or item and yielding some of the shape or texture of the object underneath in the scraped canvas result.  Ernst also used the technique to inspire himself and as the basis for other hand-painted final works.  These synthetic methods of the surrealists, owing to their non-digital mediums, were not as mechanized and automated as today’s computerized methods are.

The hallmark of synthetic art is the lack of intentionality.  It’s lacking because the processes are disconnected from the artist’s conscious control.  The artist works by remote control and through mechanical means.  It makes the artist more productive as well as, perhaps, less of an artist in some people’s eyes.  The artwork is what’s important, not how much we can boast about it.  Surrealists pursued this unintentionality as much as their non-computerized tools would allow them precisely because they wanted imagery that was not an expression of an artist’s conscious (scheming, defensive, lying…) mind.

What’s important to note is that they pursued such methods for their artistic value despite the fact that at first glance such methods seem to be the antithesis of art.  The surrealists showed there’s artistic potential in the graphical synthesis of things like smoke, chopped up images, and scratched up canvases.  Today’s photoshop filters and the persistent experimentation with cheap graphical effects continue the exploration of that vast, rut-less wilderness .

The Synthetic Aesthetic 4: The Creative Device


The Creative Device

Synthetic art has only one principle to it: the creative device.  As a result, the synthetic aesthetic is not bound to any particular medium but rather is a way of being creative within any medium.  The computerized medium holds the most potential for synthetic art because it allows for much easier creation of visually creative devices.

Another way to grasp the concept of synthetic art is through the “inverse selection” of this principle of creative device.  The opposite of the creative device is of course the manual, hand-made expressions of a person (i.e. artist).  “Hands-off art” would not be a bad definition of what the synthetic aesthetic pursues and presents.

A word about art definitions

One shouldn’t approach artistic categories the way one does mathematical or scientific ones; fractal geometry is much easier to define than fractal art, for instance.  A little bit of non-synthetic “embellishment” doesn’t constitute the sort of fatal contamination that would relegate an image to the proverbial “mixed media” category.  One needs to exercise a bit of judgement and decide what the “substance” of an artwork is comprised of rather than waving an artistic geiger counter over it to locate subtle contaminates.

You won’t find clean categories in art, but the synthetic principle is such a strong one and wields such enormous artistic influence that perhaps it is one of the few categories of art that is both meaningful as well as easy to define.  Start by looking for a creative device.

Decalcomania: Squishy da Vinci

As an example of an art device and also an example of how “unclean” art categories can be, consider some of the works of Max Ernst (1891-1976).  I posted about him earlier but without the crisp, well-focused context that this series of postings on the synthetic aesthetic gives to his work.

~Click on images to view full-size on original site~

Lone trees and other trees, Max Ernst

Lone Tree and United Trees, by Max Ernst 1940

The device used here is that of squishing paint between two surfaces such as paper and glass, or canvas and glass.  It’s a mechanical thing because the results are created entirely by the apparatus and only modified slightly by the operator/artist.  Obviously there was more to the making of this painting by Max Ernst than merely squishing paint.  Ernst would often add human figures but its the decalcomania imagery that creates the surrealistic impression here.  It’s hard to leave synthetic imagery alone since it often inspires and suggests.

You have to remember that synthetic processes are merely techniques that one pursues in the hope of making something that looks good.  They aren’t a treasure map to a place where one goes and digs up great artwork.  The use of synthetic machinery is a skill all its own.  Perhaps even something of a talent rather than something one can learn.  You have to see the potential in it to keep at it long enough to see results.

As an interesting comparison, consider this fractal collage (below) by Segami:



The synthetic aesthetic is there in the form of the detailed coral shapes.  The effect is “weakened” by the artist’s assemblage of the fractal elements into an easily identifiable natural form (coral reef), but he’s following in the steps of Max Ernst who, like Segami, was inspired by the images and modified them somewhat.  I say “weakened” because of course many viewers will consider the artist’s influence on the final work to be an improvement.  But I find truly synthetic artworks to have an alien spark to them that is worth seeking out in its natural form and preserving.

Mark Townsend, more well known for his fractal artwork, has made a number of decalcomania works.  Here’s an example:

20061015-decalcomania by Mark Townsend

20061015-decalcomania by Mark Townsend

I remember a conversation I had with Mark at the time in the comments section of Orbit Trap (or somewhere) where I described the technique as algorithmic and he disagreed.  He was right about that, but I think what I was trying to get at was that the technique was not handmade and was produced by a creative device.  “Algorithmic” indicates a process that works by applying rules or predetermined instructions, like a fractal formula.  In a sense though, squishing paint is a type of algorithm whose outcome is defined by the materials and not the user.  The difference however is that the initial conditions of paint placement and the subsequent squishing motions on the glass or paper are not so carefully programmed or choreographed to be considered “formulaic” or rule-based.  And yet, decalcomania images have a distinctive look that transcends the influences of their individual “artists” and gives the impression that they were all painted by a single pair of invisible hands.

Art that invents itself

“Hands-off art” is really a matter of not drawing and not painting; not using one’s hands to make something from one’s imagination.  Synthetic processes involve the use of one’s hands but only as operators of the machinery.  The human mind is disconnected from the artwork in the synthetic process while in the non-synthetic processes, drawing, painting, sculpture, etc… it is connected through the movements of the artist’s hand in the action of drawing or painting.

Synthetic artwork provokes the artist’s imagination; handmade artwork expresses the artist’s imagination.  It’s interesting how Max Ernst and other artists using similar synthetic techniques back in the early days of Dada and Surrealism emphasized the “mind-less” nature of the synthetic creative process rather than trying to hide it or trivialize it as most fractal artists do today as they try to make themselves appear more dignified and worthy of the title of Artist.  To people like Ernst the inhuman quality of synthetic imagery was exciting and probably the only reason they pursued it since they were all capable painters themselves and synthetic processes merely offered a way to disconnect from that and produce imagery that was impossible for them to make with their own imaginations.

Painting is not for me either decorative amusement, or the plastic invention of felt reality; it must be every time: invention, discovery, revelation.  -Max Ernst

This is why I said the synthetic aesthetic was so powerful that one doesn’t need to so carefully define it using the sort of detailed and subtle characteristics that are normally used to draw boundaries in the art world.  The alien presence of mechanical artistry is easy to spot for its lack of intentionality and deliberateness.  To build on what Ernst has said, with creative devices there is no attempt at beauty (i.e. decorative amusement) or, reflection on reality, because the devices lack the capacity for both those sorts of activities –such activities which are the hallmarks of the human artist.

However, mechanical artistry’s lack of intentionality and deliberateness (i.e. brute stupidity) can sometimes produce, by virtue of its capacity for producing prolific quantities of imagery, works that possess a new kind of beauty and new kind of realistic expression.  The “artist” is simply the first member of the audience and before his eyes the art invents itself.

One simply has to pursue “invention, discovery, revelation” with as much effort and thoughtfulness as artists in the past pursued their handmade crafts of painting and drawing.  In the synthetic art form, one directs the creation of artwork rather than performing it themself, and then one selects from what is made with the caprice and pickiness of one who has at their disposal a buzzing hive of eager and indefatigable machinery.

In part 5… the pioneering efforts of the surrealists and how today’s cheap photoshop filters are carrying on what was started almost a century ago.

The Synthetic Aesthetic 3: Ultrashop and Photo Fractal

This is the third part of a series on The Synthetic Aesthetic: artwork which is mechanically made as opposed to handmade ( Part 1 / Part 2 ).  Fractal art borders on this synthetic realm because it is one of the most powerful tools for the computational generation of imagery.

Most people commonly think of fractal art as the visualization of math or of at least having a unique character because of its inner workings that draw on the principles of fractal geometry.  However, I think fractal programs have for years been used primarily to synthesize artwork of a much more general nature and the connection with fractal math is an exaggeration.  If someone can make the same kind of fractal art in Photoshop as one does in Ultra Fractal but without the use of fractal algorithms, then surely the fractal link in much of fractal art these days is truly weak.

This doesn’t mean fractal art is no good anymore.  All of the fractal artworks I’m going to review here and compare have been selected by others for their artistic merit.  My point is that fractal programs are capable of producing highly distinctive works exemplifying the graphical creativity of fractal geometry, but also of producing things that are much less distinctive and best regarded as just digital art made in a fractal program.

That “digital art made in a fractal program” is an example of the synthesizing capabilities of fractal programs.  Fractal artists these days chose to pursue the more wide-ranging, synthetic themes than the classical fractal shapes and structures of the past.  While doing so, however, they blurred the distinction between Ultra Fractal and Photoshop, which I think you will see in the images below.

fractal dimentia front page art by Mark Townsend

Fractal Dimentia front page art by Mark Townsend (fractal)

I have used fractal images that were chosen for the Benoit Mandelbrot Fractal Art Exhibits (winners) since I wanted to used fractal art that was representative of a consensus of opinions and therefore exemplary of fractal art today.  I could have chosen eccentric examples from unknown artists but they could easily be shrugged off as not representative of anything except themselves.  Mark had an image similar to the one above included in one of the exhibits and this one here is from the front page of his online gallery site; clearly a favourite of his.

Below is an image by Randy Kochis.  He says this about it:

Here’s a new abstract piece that was done using a wacom tablet and some filters. You can’t really appreciate the detail with this size but you can tell it has a lot going on.

Whether one is better than the other is not what these comparisons are about.  The style of imagery is essentially the same and yet they were made in two very different programs.  One using fractal algorithms and the other a stylus and Photoshop.  Granted, Mark’s image doesn’t depict complex fractal structures that would be difficult to duplicate with non-fractal methods and so it’s not really an example of Ultra Fractal vs. Photoshop for making fractals.  But that’s the whole point that much of fractal art today isn’t reliant on the complex drawing powers of formulas but rather the creative possibilities of rich rendering methods and the careful selection of zoomed-in areas.

cartoon-show by Randy Kochis

cartoon-show by Randy Kochis (non-fractal)


Intrepid 1 by Yvonne Mous

Intrepid 1 by Yvonne Mous

Yvonnes’s image was a BMFAC winner.  The similarity between it and the image below by Deviant Artist, Irn Bru, is the fact that either one could have been made in either UF or PS.  Of the two, Yvonne’s image looks more processed because of the chopped up look but I suspect that’s just the result of a sophisticated rendering method in UF.  Irn Bru  says this about his (non-fractal) image below:

I created this in Photoshop as a texture for my ‘Abstract Ornamental’ piece.

In Cinema 4D, I created a new vray texture and selected the ‘Diffuse Layer 1’. Loaded the image as the texture map and set it to 100%. Then all I did was check ‘Specular Layer 5’ and left it at default.

Abstract_Ornamental___Texture_by_irn_bru (non-fractal)

Abstract_Ornamental___Texture_by_irn_bru (non-fractal)


Fusion by Sandra Reid (fractal)

Fusion by Sandra Reid (fractal)

Sandra’s image, another BMFAC winner, is perhaps too good of an example of the minimal role that fractals have in today’s fractal art scene.  Although the title fits the work nicely and perhaps is an allusion to the fusing of classic fractal imagery with the newer, general synthetic variety (i.e. detailed background), it could almost be considered a “token” element.  Take a look at Randy’s “non-fractal” spiralling mass, and ask which one would be easier to make with tablet in Photoshop.

Randy adds these notes about the image:

I had fun making this image with a Wacom tablet and a cool brush in Photoshop. Mostly playing around but I think it turned out pretty good. The original image is huge and the detail is amazing!

Note, once again, the allusion to amazing detail.  That’s the sort of thing one expects from fractal imagery because the formulas are so good at calculating such things, but it appears to be characteristic of many kinds of computer graphics.

Spirals1 by Randy Kochis

Spirals1 by Randy Kochis (non-fractal)


Imaginary Mine by Maulana Randa

Imaginary Mine by Maulana Randa

I hope Maulana will forgive me for this, but I’m not suggesting her his work is nothing more than a few splotches from a “brush” in PS.  This was made in a fractal flame program like maybe Apophysis (I’m guessing) but even flame fractals don’t look  like they used to.  Anyhow, my point (I hope it’s not too sharp) is that PS also makes such examples of rich jewelled and metallic looking wonders.  Clearly fractal art, even in the flames area, is just one way of rendering such artwork.

There are no notes for the image below; it’s simply the sample image from a PS tutorial.  By the way, check out the nicely textured background.  Importing backgrounds are a snap in UF.  I’m guessing they are because they’re used so often.

easy-abstract-photoshop-tutorial-2 by Rocka J

easy-abstract-photoshop-tutorial-2 by Rocka J


20061012-vor10 by Samuel Monnier

20061012-vor10 by Samuel Monnier

Alright.  Remember the point of this posting is that many fractal artworks have moved into less distinctive territory and because of this one often finds similar artworks that are not the result of fractal formula rendering.  Sam’s work above was part of a BMFAC exhibition in the judge’s category.  While it has detail that would be pretty hard to imitate in PS, it also has an aesthetic that is much less exclusive.  Geometric assemblages and patterns are an example of what I would call the fractal aesthetic,  a fractal style of imagery associated with fractal programs and not strictly fractal math itself.

This cellphone case wasn’t made in PS obviously but being made of sequins and metalic shapes, the star shape being most prominent, it does reflect the same style –but different source idea– that I’ve been talking about.  Sam’s image is of course a much more sophisticated and elegant work of art than the cellphone case below, but the two objects have an awful lot in common in a basic, visual sense although  they are not of the same quality of work, clearly.

dream star swarovski elements crystal Iphone cases cover by Swarovksiiphone

dream star swarovski elements crystal Iphone cases cover by Swarovksiiphone

I hope at the very least you’re seeing a glimmer of my idea that many highly esteemed fractal artworks aren’t really all that unique when compared with some of the things that can be made without any fractal formulas in Photoshop or even crafting class.  But we shouldn’t really expect such exclusivity when we consider how wide-ranging the rendering capabilities of a program like Ultra Fractal is, and has become, and especially when we take into account its non-fractal features like image importing and various layering abilities.  You can’t expect the same old stuff when you’re using software like that.

Fractal art by default has come to be defined by whatever you can make in a fractal program.  As a result, when fractal programs add rendering and processing features this literally redefines the genre.  The result is that fractal artists have greater latitude in what they can depict in their artwork and they’ve naturally drifted away from the cliche and common, classical style of fractal imagery towards fresh horizons.

But is that still “fractal enough” for those who look to fractal art for the depiction of more obvious mathematical themes?  I can’t help but wonder if the ICM, the original sponsors of the BMFAC have no fractal art exhibition listed on their 2014 website because they no longer see this fractal art stuff as having any serious mathematical connection?  Is it all too much of something else?

Synthetic is what I think that “something else” is and it’s been there ever since the computer rendering of fractals began.  Fractal artists have turned their eyes from capturing visualized math to beholding bold new graphical concoctions.  And in the next instalment, Part 4, I’ll have something more definite and clear to say about that.

The Synthetic Aesthetic 2: The Re-Introduction

In the first part of this series, I introduced a few new ideas which have a central part to play in my concept of the Synthetic Aesthetic.  I believe it might be of great benefit to pause and clarify those ideas before moving on to examples of actual artwork that illustrate these trends.

Here’s the idea:

Fractal art has become progressively ambiguous in terms of what it looks like and depicts (i.e. subject matter) to the point that now it is no longer unique and distinctive and could just as easily be given a generic label like “synthetic” rather than “fractal”.  Fractal art is no longer an art form exclusively dedicated to “math visualization” as fractal artists have abandoned that easily identifiable visual theme in the pursuit of a broader artistry defined only by whatever can be done with a “fractal” program.

While doing so, they have produced artwork with greater artistic appeal but at the same time with less mathematical relevance.   Although the inner workings of the software still remain fractal formula based  –the only thing that distinguishes fractal art as a distinct artistic category in the first place– the role of these fractal algorithms are now largely employed by artists in “anonymous roles”, unrecognizable and becoming mere anecdotes to the finished artwork rather than the essential element.

This is much the same way that Terragen’s computer generated and photo-realistic landscapes can be said to have a fractal connection because they were “made with fractals” — that is, deep in the inner recesses of their computer code; a trivial distinction which has never made anyone seriously consider them as “fractal” art.

Four nicely numbered points

So, two things have occurred:

1) Fractal art has become much broader in scope and now includes artwork which in appearance is quite similar to other computer “synthesized” art forms despite their widely differing software origins;

2) Fractal art has created a look or visual style that has come to be associated with its fractal algorithms but is really much more a product of its many rendering methods which apply computer graphical rendering techniques and effects, some of which can also be found in computer graphics programs and there used to produce artwork with the same “fractal aesthetic” as fractal art although no fractal algorithms are actually used, only similar graphical rendering methods directed by other, non-fractal methods.

This has lead to a third occurrence, the logical consequence of the two previous items:

3) While the term, fractal art might be confusing when applied to those “fractal-looking” artworks made in a graphics program, the term, fractal art is probably just as confusing when applied to those “synthetic-looking” artworks made in a fractal program.

Which leads us to a fourth item:

4) If one considers solely the visual style and creative method of artworks and forgets for a moment what they were made with, there will appear a rather logical grouping to a wide variety of artworks which previously had been separated by their apparently distinctive mediums or tools but actually fit together like scattered puzzle pieces when rallied under the simple label of “synthetic” art.

Fractal art has actually lead the way in all this and stands as the strongest tool for “synthesizing” art.

Un-defining fractal art

Anyhow, the fractal art world has changed.  The boundaries are different now.  Actually, the boundaries have disappeared.  It all happened when, deliberately or not, fractal artists came to define their art form as whatever can be made with a fractal program.  With the arrival of exotic rendering functions and graphical features like layering, these new tools redefined fractal art because they redefined the fractal program –the de facto specification for fractal art.

Perhaps the word is not so much “redefined” as “un-defined” since the results of expanding the toolset of fractal artists has been the creation of  artworks characterized by some very “un-fractal” features found in graphics programs like Photoshop.  The end result we see today is that the domain of fractal art partially overlaps the domain of what I would describe as synthetic art.  A domain distinguished by a style or aesthetic lacking the involvement of the human hand and instead expressing only that of the algorithmic, the accidental or the mechanical.

In the next part, Part 3, I will show some relevant examples of what I’ve been talking about which ought to make things a lot clearer  by making them less abstract and more concrete.

The Synthetic Aesthetic – Part 1

This is another one of those theoretical postings; you might want to skip it and go look at some fresh fractal art instead.  But if you’re still interested, in this posting I intend to examine what fractal art has come to be and show that this evolution of the art form has made fractal art much less relevant as “math art” and instead gradually transformed it into a less exclusive computer art genre of “synthetic art” uniting it with a wider array of software and methods, all of which do much the same thing and collectively exemplify what I call, “The Synthetic Aesthetic.”

By “aesthetic” I mean the basic style, appearance and themes that come to identify a genre of art –what the art form depicts and likes to express.  Impressionism, Photo Realism, Surrealism; these are all aesthetics.  Grunge is an aesthetic made of rough, worn, grungy things.  Oil painting is not an aesthetic, it’s just a much broader kind of thing called a medium.  The type of art one pursues and creates with oil paints can form an aesthetic, however.  Pointillism is an aesthetic characterized by points of color rather than connected brushstrokes.  Surrealism is an aesthetic defined more by a common theme than a common visual style or method.

An aesthetic is formed out of a complex collection of things and as such the term naturally involves some amount of generalization; some works in the same genre being strong examples while others may be weak ones.

If I showed you the UF parameter file, then would you believe me?

Could a “fractal” program produce this?

The Fractal Aesthetic

Firstly let’s consider the possibility of a “Fractal Aesthetic” –a distinct and recognizable graphical style associated with fractal art.

I have often sensed a disconnection between fractal math and fractal art but been at a loss to explain it since you obviously can’t have fractal imagery without a fractal formula and therefore the two can’t really be disconnected, can they?  But from the perspective of a viewer of fractal art, fractal art exhibits very little of the visible geometric and mathematical relevance that it did in its early days when artworks could also be the subjects of mathematical discussions and include intriguing image notes.  All those traditional scientific aspects to fractal art have drifted into a behind the scenes role while the increasingly dazzling graphical rendering techniques have taken center stage.

Few fractal artworks seem to contain the distinguishing characteristics of the formula used to create them.  This is because, knowingly or otherwise, fractal artists simply use fractal formulas to create a source of imagery –a pool of imagery– from which they fish around in and select from.  The fractal formula’s unique characteristics is rarely the actual subject of their work.  It could be if they wanted, but that isn’t what seems to excite fractal artists much or draw their interest.

This shifting of the spotlight from clear fractal formula structures and characteristics to fishing around for whatever looks “awesome” isn’t a product of the medium, it’s a preferential choice made by artists.  Perhaps straightforward, identifiable fractal images with spirals, mandelbrots, minibrots, and julias and so on are seen as cliche and dull by most fractal artists today?

It might be ugly, but is it also a fractal?

Would you recognize a fractal imposter?

I once argued that “un-fractal” imagery was the pursuit of most fractal artists nowadays.  If it is, then it’s a reasonable and expected sort of behaviour as even the most exotic fractal formulas like the buddhabrot, for instance yield more creative power from tweaking their rendering options and carefully selecting detailed areas of them than they do from tweaking their formula parameters.  Rendering is where the artistry takes place.  Also, artwork that focuses on the formula tends to have less of a “personalized” appearance and represent less of an artistic accomplishment.  Once again we’re back to the problem of creating work that avoids anything that is perceived as being cliche, something that formulas of any kind are apt to produce.

The fractal aesthetic is easy to describe and identify.  Basically, whatever looks like it was made in a fractal program is literally the fractal aesthetic.  That might sound rather simplistic and vague because fractal programs produce such a wide range of imagery and offer such a wide range of rendering options, but actually the fractal aesthetic is easy to spot by people who, ironically, are not fractal artists.  Try uploading a fractal image to the wrong category on Deviant Art and see how quickly someone “spots it”.  Fractal artists might think their genre is one of subtleties and arcane mathematics but to everyone else it’s pretty plain and obvious.

Oops.  I can't remember the formula I used, can you?

Guess the fractal program, win a prize…

Synthetic Shapes and Patterns

Fractal programs have created an aesthetic of artificially composed synthetic shapes and patterns.  For example: arrangements of twisted tubes; balloon like sausages; lightning bolts in crushed paper; vast fields of fractured glass; bubble vistas; gardens of glowing gas; anything with a spiral (that’s an obvious one); jungles of geometry; simple shapes with subtle changes in color and texture across every pixel; mettalic imagery that radiates with infinite detail;  etc…  These are the hallmarks of fractal art; occasionally the elegance of math, but always the wonders of exotic rendering options.

We have collectively created an art form which is quite distinct and quite distinctive.  It’s just that the thing that distinguishes fractal art is no long fractal geometry, its the synthetic rendering techniques; these have become the “face” of “fractal” art.

A Summary

Fractal programs “draw” just as people draw using a graphics program.  Fractal programs, however, draw with the stiffly deterministic but amazingly talented robotic arm of a fractal formula.  It’s the drawing styles of fractal programs (rendering methods) which have become the focus of fractal art rather than the fractal formula which is directing the program’s “pen” or “brush”.  The subject matter therefore of most fractal artworks is usually a zoomed-in fragment of a rendered formula which depicts some interesting effect created by the rendering technology –or exaggerated by it– rather than a unique and identifiable piece of the formula’s mathematical anatomy.  Artists could chose to focus more on mathematical and scientific “portraits”, but most chose not to and subsequently fractal art has come to be an art form of “renderisms” rather than famous formulas.

Terragen and Fractalgen

Again, I don’t see any of this shift to “renderisms” as a bad thing.  In fact, I find the whole thing rather exciting, now that I see what’s going on.  Fractal art is an artistic pursuit and fractal artists care a whole lot more about how artistically appealing an image is than how well it depicts fractal geometry (if at all).  In fact, and this is my main point here, fractal artists hardly ever attempt to display recognizable fractal characteristics in their images because that’s not what interests them.  Nobody is ever worried that their artwork will lose it’s “fractal status” as long as they stick to using fractal software.  The creative process is such that the formulas become the graphical engine of the fractal software while the rendering techniques for the most part determine what that artwork looks like.

This of course is what makes Terragen, a graphical landscape generator, although it utilizes fractal formulas, disqualified from creating fractal art: it just makes pretty landscape scenes with the help of fractal computer code.  Fractals are merely part of Terragen’s graphical processing.

Terragen is an extreme example of fractal algorithms creating un-fractal art, but many fractal artworks whose subject matter is some (magnificent) detail plundered from the deep recesses of a fractal image and rendered in an exotic way are just as cut-off from their fractal roots as any sun-splashed mountain scene from Terragen.  The only difference is that Terragen scenes are immediately recognized as something familiar and easily classified –as landscapes.  Everyone knows that Terragen images aren’t fractals because they can clearly see that they’re landscapes.  The hidden fractal characteristics are merely an interesting anecdote to go along with the image as well as any other trivial about “how they were made”.

Which brings me to the title of this posting, “The Synthetic Aesthetic”.  Fractal art settles quite logically and reasonably under the graphical label of “synthetic” rather than “fractal” just as “Terragen Art” fits intuitively into the category of “landscape” rather than “fractal”.  Fractal art is the use of fractal formulas to synthesize art.  But that synthetic art, although distinctly derived from the processing powers of fractal formulas, resembles in appearance many other kinds of computer synthesized artwork.

In fact, I think the distinction between fractal art and any other kind of computer synthesized imagery is entirely a matter of tradition, specifically a tradition that has assumed that fractal art was a special form of art because it was uniquely mathematical and therefore “different” because of that.  Fractal art is uniquely fractal in its method of creation but that feature no longer leads to the creation of artwork that is graphically unique in its appearance when placed in the context of other computer synthesized artworks.  In fact, ironically perhaps, the fractal aesthetic has actually come to be one of the best examples of the synthetic aesthetic.

I have more to say about this.  In Part 2 I will try to show how “synthesized art” is so close to fractal art aesthetically that separating the two groups from each other is creatively inhibiting as well as artistically retarded.  But I won’t use words like that.

Paint by Fractals

What shower of insults and rotten tomatoes are provoked up by such a play on the expression, “Paint by Numbers”?  And yet, to those who know what galactic boundaries are quickly traversed by just a few (million) iterations of the simplest of fractal formulas, the phrase “Paint by Fractals” is nothing short of rocket-powered creativity.  For those of you who aren’t sure of what I’m getting at just look at the pictures.

~Click on images to view full-size on original sites~

Double apparition of Louis XIV at the stairways of a Mini-minibulb in the Versailles of Mandelbulbs by Kraftwerk

Double apparition of Louis XIV at the stairways of a Mini-minibulb in the Versailles of Mandelbulbs by Kraftwerk

How does this one make me think of “painting”?  Although the elegant curves and ridges of the mandelbulb suggest a rich picture frame, what catches my eye and makes me say, “Son of da Vinci!” is the background imagery on the right-hand side, middle to top.  It’s the sort of painterly touch that one often sees in renaissance portraits like the Mona Lisa; misty, hazy panoramic landscape.

Dodgeball with Flash Gordon by Sitting Duck

Dodgeball with Flash Gordon by Sitting Duck

Maybe the “painterly” style is just the preference for subtle shading and the appearance of natural light.  I have no idea who Sitting Duck is.  I think he’s one of the many new names drawn into the orbit through their recent contest.  If so, then the contest has been a success.  This image reminds me of the many sci-fi fantasy paintings done by Frank Frazetta back when that sort of thing was popular, that is, before the advent of CGI when fantasy became reality.  I like the overexposed areas of bright light and of course the multiple shades of rusty brown that would have caused even Da Vinci to start using a bigger palette –the old-fashioned, non-indexed type.

For which of his paintings would Frank Frazetta have ever have written a description like this:

Mandelbulb 3d DEcombinate of: Amazing+Surf Quaternion+CommQuat+IdesFormula | Bulbox+_AmazingBoxSSE2
Same as “Shiny bug transfixed by entomological pin” but from another angle.

Truly, “Painting with Fractals” puts us in a completely different league.  And language group, too.

Eat your Veggies! by indavisual

Eat your Veggies! by indavisual

This one caught my eye for what is probably the most important aspect of the painterly style for fractal art: creativity.  The painterly style challenges the opposing style of precise, slick rendering.  The painterly style is a reminder that art is a matter of impression and not precise, diagrammatic or photographic depiction.  We applaud the skill of painters when they paint something that evokes great thoughts and feelings, but when a talented painter paints a great photograph and imitates a camera, then who cares?

This one really shows how the distorting effects of whatever this guy did to this mandelbulb image can create something new and different where sticking to just the parameter settings of the program would yield something much more commonplace.  The painterly style could be described as semi-destructive or even sloppy.  The impressionist painters were described that way not because they actually were sloppy but because that’s how their work appeared when placed in the more established context of the (overly) realistic style of painting that came before them.  Compared to a photograph, even the Mona Lisa would look “smudgy.”  On it’s own, almost anyone can begin to see the artistry to such works as this one by indavisual (nice, multi-expressive screen name).

And that’s what fractal art as opposed to fractal science is all about:  artistry.  Of course it’s not too easy to define what is artistry and what is merely tech-nistry, but it’s worth loosening the bolts on one’s mind once in a while and seeing what comes from a more expanded visual range.



Rembrant-ish, but more than that.  The radiating details that draw our eyes into the smudgy shadows are beyond the sort of hypnagogic visions that Rembrant’s own shadowlands ever depicted.  Hypnagogic means just before you fall asleep.  And Turner, too.  This has all the subtle light shades and murky shallows of a Turner seascape with clouds, dying twilight and those things that only the eyes understand.

Calligraphy mountain by wackwang

Calligraphy mountain by wackwang

From the gallery page:

Description: calligraphy of Chinese characters as single elements, expressed the relationship between global and local, which is the calligraphy and fractal embodied.And I make it feel like Traditional Chinese painting as a form of expression.

This is not really a painterly example, strictly speaking, but the cellphone signature chop mark combined with the fractal cloud/mountain/trees structure does evoke a strong resemblance to Chinese art as the artist intended it to do tying it in closely to more traditional, non-digital imagery.  I missed the 2d barcode (red mark) at first and only on closer examination realized it wasn’t a traditional Chinese signature stamp.

Hardwired Transcendence Engine by egress

Hardwired Transcendence Engine by egress

Smooth rendering and, once again, the smudgy-ness are the beginnings of painterly style.  Of course you still need an interesting image and composition and all those other serious art things.  The swirly cables/wires and steel parts forms a nice composition as well as something with a little bit of a realistic touch that allows us to begin to think we know what we’re looking at when in fact we’ve been drawn into something strange and other-worldly.  The cables in the bottom right are really fantastic.  They look quite hand drawn although I’m sure it’s just the careful rendering selection that makes them look that way.  This one looks like maybe it took some time to render.  Does an airbrush count as a painterly tool?

Orbit Mandelbrot No. 2 by element90

Orbit Mandelbrot No. 2 by element90

The Buddhabrot is always quite a painterly looking construction so one has to really do something special to produce an exceptionally painterly looking one and element90 has done that here.  It looks like parchment or skin or maybe thin aluminium.  But the reddish/burgundy shade which takes over in the smaller parts starts to suggest leather.  Or is it a recursive construction of old “pop-top” pop can tabs?  One can never be sure what the audience sees when looking at fractal art.  Just be glad someone is looking is all.



A detail from a painting by Escher?  Once again, subtle shading from various degrees of combinations and permutations of light –isn’t that 90% of what oil painting is? — light?  I like the combination of the sphere with the triangular shapes and squares.  One would almost think it was a deliberate attempt by the artist to suggest a round square or something alchemical like that when in fact it’s a deliberate output from the formula.  Of course the selection of this scene was the artist’s choice.  Selection is a big part of fractal art.

Cliffs of Antartica by Kali

Cliffs of Antartica by Kali

From the gallery page:

Description: Experimental Kaliset heightfield render.
Based on Knighty’s Mandelbrot heightfield implementation included in the latest Fragmentarium version.

This is exquisitely painterly.  Hard to believe it’s machine made, but then Kali has magical powers when it comes to working with machines like Fragmentarium.  If this was a painting it would be acrylic: bright, modern and powerful.  Colors da Vinci could only have dreamed of.  Although, I think one would detect some mixed-media accents in the form of sketched-in outlines and structural markings.  This could be pen and ink or pen and airbrush.  See what I mean about Kali’s sophisticated rendering methods?

MengerKoch23hrddh_4 by ellenm1

MengerKoch23hrddh_4 by ellenm1

Ellenm1 has a rather interesting collection of mandelbulb images on Flickr.  This one I find to be the most painterly of the lot, however there’s a few other that remind me of Bosch and other famous painters not because of the lighting alone, but also because of the creative composition and un-precise, warped fractal imagery.  To me, this is a face, the bottom being a monstrous mouth while the top morphs into a cut-away cranial dome.  There are almost brushstrokes in some of the lip-things at the bottom.  It’s refreshingly fluid and non-squarish.  Perhaps that’s another painterly principle.

tumblr_mjsuarRvm71rswrhdo1_1280 by jakeronomicon

tumblr_mjsuarRvm71rswrhdo1_1280 by jakeronomicon

To see a world in a grain of sand… or in this case, a world on a shelf.  If this was a drawer in a museum, it would be labelled “sunset”.  This is the kind of image that gets written off as a preliminary render but is in fact quite an advancement over the more complex, precisely rendered kind of thing.  Perhaps that’s because the artist, Jacob Bettany has only been working with fractals for less than a year and hasn’t picked up the bad habit of only making crisp scientific images with a fractal program.  To render this more would be to render it less.  To render this more carefully would be to render it more crudely.  To render this richly would be to render it worthless.

94bf751edf4f11e2af4522000a1f8f13_7 by Jacob Bettany

94bf751edf4f11e2af4522000a1f8f13_7 by Jacob Bettany

This one’s off Jacob Bettany’s Instagram site, a service I’ve got very little experience with but looks very art-friendly in its format.  Although clearly a mandelbulb derivative, this image does not seem to suggest zooming into it any more than one would step closer to a canvas hanging on a wall to take in the brushstrokes.  I like the color and the flatness to this one.  Flatness is something often neglected in 3d fractals.  This would be a watercolor if it were a real painting.

Well, there’s plenty more I could show here but I think you get the idea of what the “painterly” style is all about and how it works.  Hopefully more artists will take up the smudgy, over-exposed, flat and shadowy style a little more.  Sometimes it takes real genius to see just how simple, and how simply made, good art can be.  Especially in such a technology-laden, expert-heavy genre as fractal art where it’s much easier to make perfect photos than it is to make unique and stylish artwork.

Fractal Getaways: Your Electronic Vacation

Our brains need a vacation.  And what could be a better Brain Resort than the electronic paradises of the fractal realm.  Here’s a sampler of some of the most interesting fractal scenery and composite images I’ve stumbled upon over the last few months.

Although we’ve already arrived at our electronic destination, let’s do the old-fashioned pre-electronic drive to the airport.  We pass through some new construction downtown via the expressway:

~Click on images to view full-size on original site~

Ship by Dominique_Peronino

Ship by Dominique_Peronino

Dominique chose to call this a ship for some reason, but I’ve been looking at it in my Viewmarks collection for more than a few months and I always see a new highrise in the making.  In fact, when driving down the downtown expressway now I’m reminded of this image when I see any highrise in its early construction phases.  Life is starting to imitate fractal art.

These sorts of 3D jackposts and concrete floor images are quite common now but this one is special because it looks like more than just the regular tube and slab stuff.  The sky background might have played a role in transforming it although it seems to be just a simple gradient.



Something strange and astronomical is going up at the airport it looks like.  Haltenny has always been something of a pioneer in the 3D fractal world.  I suppose this one isn’t all that pioneering in the technical sense but I’ve never seen such an interesting concrete ball structure as this.  It almost looks like a fossilized thing with those embedded circular structures.  Or is it more like a semi-constructed stone Death Star?




Looks like Haltenny got the contract to do the parking garage too.  It really pays to explore fractals, 3D or otherwise, because that’s how I’m sure people like Haltenny find these sorts of things while others seem to just find what’s already been found.  Images like this really renew one’s excitement with 3D fractals.  It seems like there’s always something new waiting around the corner.  That aspect to fractal art is still the same.

My Home Town by Frakkie

My Home Town by Frakkie

Uh oh.  I don’t think we’re in the parking garage anymore.  We’re in the Twilight Zone where reality and fractals meet.  It happens in the realms of electronica that airports are grown, not made.  This is proto-airport and the runways will be the lava beds once they’ve cooled.  There will be no need for planes because all the departures will be arrivals: your itinerary is written on a mobius strip.

It’s a neat image, not really a super technical feat or anything, but just for the artistic impression which is what counts in all this really whether you’re aware of that or not.  What I like is that the imagery really does suggest a sort of half-real, half drafting board state.  It hasn’t finished calculating yet but we’re here already.  The crisp contrasts are very digital and yet the lighting also gives the image a very vivid depth and realistic feel to it.



Yikes.  Ample parking means walking a few miles to the terminal.  I’m so glad this is all electronic and nothing is ever more than a mouse-click away.  And no baggage either.  In fact, I’m sitting in my basement with barefeet.  What’s so special about this one?  The simple depth and perspective is done well.  Also, it has the feel of the outside and yet it’s inside.  A sort of interior exterior.  It looks like snow has fallen on a shallow river bed but how can it snow inside a tunnel like this?  A nice example of how 3d fractals can conjure up some extraordinary scenes.  Like Escher’s work; impossible scenes that just look natural.

Plaza Organica 7 by Tom Wilcox

Plaza Organica 7 by Tom Wilcox

Similar in some respects but having a very different feel.  The full-size version really shows the smooth, almost abstracted style to this image.  Abstracted?  You see how hard it is to tell what reality is on these electronic vacations?  Isn’t it all abstract?  Also, as a side note, I found this one via Haltenny’s Deviant Art favorites list.  A good favorites list is the best way to browse Deviant Art.

Tom is well known for his very polished and refined style of fractals of which the image above is a good example.  This is from his deviantART page:


And now for our in-flight dream…



I declare the birth of a new fractal genre: Dorianoscape; in honour of Doriano Benaglia who is the unrivaled master and inventor of the art form.  Encore!  Encore!  …here it is:



Panoramic; timeless; digital surf crashing on the pixel-grained beach.  Note the subtle horizon touches like the hills on the left and the little star in the middle.  He doesn’t just slap these things together, he composes them.

The dream continues…



The images have this effortless quality to them and yet they are also uncommon and unique.  Artists make art and you can recognize the artist from the art, but in the fractal world I’m sorry to say that the technology is what really makes the art and we are more likely to recognize the software than the artist by looking at the art.  But not with Dorianoscapes.  500 years from now when someone finds an unknown Dorianoscape on a vintage 21st century usb stick unearthed during renovations of an old villa, it will be immediately recognized as the originator’s handiwork and not one of the thousands of imitators who I’m sure are bound to spring up in the years to come.

MB3D_0474 by 0Encrypted0

MB3D_0474 by  0Encrypted0

This one is a real masterwork in the sense that it’s rich with all sorts of details as well as having a strong overall composition to it and multiple impressive themes like shadow lands; bubble worlds; majestic heights; and more if you study it longer.  It’s not a typical work for Encrypted who usually makes very intricate, jewelled 3D fractals.  This one is very painterly and full of smudgy suggestion and panoramic silence.  You know,  maybe fractal art really will become a rich art form.  All it needs is a few people with that special skill of working with its special machinery.  Encrypted’s got it.  Let’s hope more people will find it too.

Cendria by lxh

Cendria by lxh

This one looks old-fashioned to me.  I noted some similarity it had with an old photograph on Wikipedia that I stumbled on:


Boulevard_du_Temple_by_Daguerre (1838)

It’s the roof lines, chimneys and evestroughing of this photograph of Paris in 1838.  (Actually, a daguerreotype, an early form of photography.)  Interestingly, this photo is perhaps the oldest one showing a living person according to the Wikipedia author.  Only the man getting his shoes shined (left-foreground) showed up in this long exposure while all the other people and street traffic disappeared in a blur of (relatively ) fast movement.  Lxh’s image takes us up to the chimney tops (where troubles melt like lemon drops) and we exchange the rest of the Parisian cityscape for fields of clouds in the sunshine.

Fractal Rock by Axolotl

Fractal Rock by Axolotl

The Ayers Rock of fractaland.  More photoshop than fractal but the importance of the mandelbulb sitting off in the distance is great enough in this image to make it “fractal” (whatever that really means).  Nice use of lighting and all that serious art technique stuff.  Axolotl must know something about making artwork because this sort of thing doesn’t come naturally.  Do you feel like walking in the sun like the woman; or do you feel like sitting in the shade like the man?  Couldn’t he at least drive her over to the Fractal Rock?  And what’s with that steel umbrella that looks like a covered serving platter?  A nice early use of composite imagery (Mar. 2011) that has stood the test of time and still looks good despite how retro the mandelbulb now looks to all of us.



I think this is just a filtered and processed photo that resulted in something cool looking.  I throw it in because it fits with the electronic vacation and what exactly is the difference really between fractal art and all the other digital stuff, exactly?  Don’t know who Magritte is?  Those title allusions are just extras.  The image creates its own fantastic context. (“Better” than Magritte?)

Here’s something Magritt-ey:

Rain of Pain by CO99A5

Rain of Pain by CO99A5

Why pain?  I guess the dark sky and dark below-sky (not really land) suggest dark things.  Rene Magritte liked to include stark geometry into his nicely pained images.  Nowadays we like to include nicely painted images with our stark geometry.  If Magritte were alive today he’s be laughing!  And he’d be out of a job, too.  Buried alive by the style he created.  Hey, that’s painful.

What’s a vacation without a hotel?  And if electronic hotels have hand made paintings on the wall, then real hotels must have electronic paintings on their walls.  And who knows electified art better than Zone Patcher?  But first the art:

Reappearance of Ancient Luminous Connections by Zone Patcher

Reappearance of Ancient Luminous Connections by Zone Patcher

From Zone Patcher’s Flickr notes:

….SOLD….to The Park, New Delhi… Hotel company…everything inna da rooms will be white..everyting..except…my Fractal Collages…heee..

And here’s the hotel room ($140/night):

Room photo The Park Hotels, Goa, website

Room photo, from The Park Hotels, Goa, website

Of course our electronic itinerary includes a lot more artwork, but you’ll have to sleep on the floor (your own floor).  They weren’t kidding about everything in the room being white.  That big black box thing with the mail slot is a drop safe, I think.



Nice simple straight-forward image made in Fractal Explorer using a Sterlingware formula that would look nice in any high class hotel.  Fractals are the ultimate public art since they’re decorative and completely lacking any sort of real world connection that could lead to them becoming politically incorrect sometime in the future or even later this day.  Look hard at this one and try as much as you can to be offended by it.  It just can’t happen.  The title is a reference to the recent passing away of the beloved singer Maria Elena Walsh.

Since Goa is a short walk from downtown Europe in the fractal realm, let’s visit some of the cultural wonders amidst the electronic cafes (bring your own coffee).

MB3D_0563_hd by 0Encrypted0

MB3D_0563_hd by 0Encrypted0

Another fresh view of the 3D mandel-things.  Note how it gets Escher-esque on the far right and how the structures vary from straight to curved and from golden to soot-covered.  Such a rich variety of things in this one.  Is it an electrical station or a steel making factory?  Or a clock tower?

MB3D_0554_hd by 0Encrypted0

MB3D_0554_hd by 0Encrypted0

Like great symphonies, 0Encrypted0 (that’s how he writes it) gives them simple, unassuming numbers.  This one really is a symphony of imagery.  I really like the left side wall of shelf things and its lighting especially, and then the depth to which the top right moves off to.  This one is strangely panoramic although everything appears to be inside and enclosed.  It’s a city of cities within a city.

MB3D_0575_hd by 0Encrypted0

MB3D_0575_hd by 0Encrypted0

I rarely pay much attention to the names on images like this posted to  I just bookmark the ones that look great and so it’s by accident that I’ve reviewed three in a row here by the same artist.  This one is a fantastic example of rich design in a 3D fractal.  It must have really boggled the mind of 0Encrypted0 when he found it.  The square areas act like frames and similar to the photography theme of memory boxes, wooden boxes with all sort of inner partitions each one holding some different object or curio.  The description note says: “Amazing Surf CrossBiFold _RotatedFolding _FoldingTetra3d“.  And that’s a pretty good description, too.

ModularNexus II by MarkJayBee

ModularNexus II by MarkJayBee

I must have gotten off at the wrong subway stop because everyone speaks English here.  There are no signs in the electronic worlds because you’re always “here”.  This was just posted a few months ago and shows how Mark’s painterly style has not been a one time thing (like a mistaken keystroke).  I don’t know if they’re tearing this down or building it up.  But then, what does any of that mean in a place of virtual reality?  There’s a million shades of brown here; some suggesting rust and others polished granite.  There’s the big palace up top in the sunshine being built, but then there’s the grim, subterranean foundations holding it up.  Someday writers might actually write novels for specific pieces of cover art.  Do e-books really have covers?



These images go so well together I don’t know whether he added the photography to the fractal or vice versa.  Here’s what Vidom says:

Here I made a single layer fractal architecture, where my main goal was using fog settings to achieve a glassy-windows appearance on the right lower part.
Testing some of my photographs to choose a simple sky, I instead decided to set a natural lush ambiance, with a single photo of a pond I took in a Milan park.
The fractal itself isn’t changed but it’s quite hidden now, so it’s in manipulations category.

By the way, Vidom’s entire deviantART gallery is a vacation all its own with all sorts of panoramic and intense mechanical constructions combined.  He also posts very high resolution images so you can wander around the image the same way you can with large works of art in an art gallery.  He should charge for admission because it’s better than Disneyland.  Each image is almost a virtual day trip in itself.



This is perhaps the most detailed panoramic 3D fractal I’ve ever seen.  The original is 2300 x 1380 px and to me resembles a sports stadium the size of an entire planet.  Vidom says this: It suffered a lot with resizing, it went from 65MB to 2.2MB, but it’s still interesting even with less details.

It’s something worth noting that this image was made with the same software as every other Mandelbulb3D image.  The sky and the cloud-shadows on the “seating”  (left of center)  were added, I assume, but it really shows how operating the machinery is the key skill in fractal art.  If it weren’t a skill then why do some people come up with things like this repeatedly and others don’t?  The creative process is different in fractal art than it is in the traditional hand-made genres.  The paint brushes have a mind of their own.

Well, it’s time to leave.  Let’s head back to the hotel lobby to sneak check out:



Even the greatest hotels of reality-land can’t compare with the Vidom Hiltons of fractaland.  Consider this lobby-scape of the Burj Al Arab in Dubai ($1500/night):

Bird's eye view of the lobby of the Burj Al Arab in Dubai

Bird’s eye view of the lobby of the Burj Al Arab in Dubai

I don’t see anyone at the main desk so I guess they don’t care if I leave without paying my bill…

I get a window seat on the plane and take these photos on arrival back home.  Something’s happened since I left.

bbrot1 by William Brodie-Tyrell

bbrot1 by William Brodie-Tyrell


bbrot5 by William Brodie-Tyrell

bbrot3 by William Brodie-Tyrell

bbrot3 by William Brodie-Tyrell

I found these buddhabrot images via a posting on recently, but I think they may date from 2004 if they’re of the same vintage as most of the other stuff on the original site.

Reality can be edited in fractaland.  I quite like this one.  The effect is great even though the parts put together are quite ordinary.

Fractal by Alizadeh100

Fractal by Alizadeh100

Fractaland, it’s just a click away.

Psychoanalyzing Fractal Art: Fractalsport Psychosis

Yes, fellow patients, and particularly those in the line-up waiting for shock-treatment, we are sometimes gripped by that psychotic condition which I would label, “fractalsport”.

What is fractalsport?  You know what fractalsport is and are exhibiting its symptoms right now with your attempts to deny it.  For those of you whose brains are still effervescing from shock-treatment, fractalsport is the making and posting of fractal art for the purposes of competition and taking part in competition rather than the simple, straight-forward pursuit of fractal art for normal, healthy, well-adjusted  reasons.

Since I understand the mental state of those afflicted by this condition better than they do, let me avoid enraging you with medical terms and just show you a picture:

The precursor of all fractal art contests

The precursor of all fractal art contests

Note particularly the spiral decorated top spinning off the board and into our laps.  Spirals were made for fractalsport and epitomize it: fast, attractive and begging to be spun.

I hope this next image isn’t too much of a sudden shock to the system:

Yes, they even had usernames

Yes, they even had usernames back in the proto-fractalsport era

Any website or web-space can be quickly converted into such an arena-o-art with the sudden announcement of "contest" or, for those who are suffering deeply from this, the latest term, "compo"

Any website or web-space can be quickly converted into such an arena-o-art as this with the sudden announcement of “contest” or, for those who are in a profound state of fractalsport and more accustomed to degenerative street language,  “compo”

Now that we’ve come to acknowledge our diseased state of mind and the pathology of our art form, let’s look and see what the latest “compo” has inspired and forget about seeking medical treatment.  In the words of Dostoyevsky: My art is bad, well–let it get worse!   Hey, I’m feeling better already.

~Click on images to view full-size on original site~

Mariana Trench by Aqualoop

Mariana Trench by Aqualoop

I’ve never heard of the user, Aqualoop, so this is a double-prize: new art and a new artist.  If that’s the case then this latest outbreak of fractalsport is having some beneficial effects; just like a high fever killing off one’s malarial infection.  What do I like about this image?  I find it to be Dali-esque.  If Salvador Dali, the great surrealist painter was to take up fractals, I think this is the sort of thing he’d get excited about.  The melted, distorted look is almost a “Persistence of Fractals”.  The lonely, barren, sun scoured landscape in the top-left corner also suggests to me the mark of the master himself.  Then there’s the embyonic forms floating around and the overall fluid, flowing feeling connecting such small scale items with large scale things like a spiral galaxy in the mid-right.

This image is a good example of how subtle fractal art can be and how it can strongly appeal to one person, like myself, and possibly not appeal at all to many others.  I’m going to be quite disappointed if the Aqualoop battling-top gets bounced off the board by another.  But that’s the way of the compo.  It always happens that the real art gets trodden on by the imitations.

It Happened by arteandreas

It Happened by arteandreas

Philosophically speaking, I really ought to dislike these images made from combining realistic elements with fractal ones but something in my mind keeps overruling that other sense of propriety and good taste.  Perhaps it’s because this one has such a great narrative to suggest: a meeting of the digital and the real; the portal to the parameter worlds.

When you want to tell a story you don’t need much to illustrate it if it’s a good one.  A little nudge is all the reader/viewer needs to have.  I suspect these composite images are going to be much more common than they were in the old days before 3D rendering.  3D fractals seem to mix better with our inherently 3D realistic world imagery.

Friends: Fractolotl and Octofractalpus meet in the garden by Lambarie

Friends: Fractolotl and Octofractalpus meet in the garden by Lambarie

Yeah?  So what.  I like it.  Now let’s try to figure out why.  I’m not too excited about the yellow snail or the bright orange fern-thingies on the axolotl creature (it’s a long story, the axolotl thing –and category).  But the grainy gold, blurry-layered, spiral creature bits have some dreamy quality to it.  And the garbage UF style over-layered background normally makes me gag but this time, combined with the goldy swirls, transcends the usual reverse peristalsic outcome from such workings and becomes something that I’ve actually been staring at for some time now.  Maybe it’s because the smeary background resembles the background of a microscope slide and that sets a new context –discovery– for the golden creatures.  Have I failed another Rorschach test?

Mr. Crabs nebula by Knighty

Mr. Crabs nebula by Knighty

The buddhabrot is like a lobotomy: bold and simple, it never fails.  In fact, all the buddhabrot formula needs is some good coloring, which is what knighty has introduced here.  Or as he says: “Just experimenting with Metropolis Hastings method for rendering the buddhabrot and thought that one is good enough for participating in the compo. Hope you like it.”  The buddhabrot deserves an entry category all its own.  Knighty has always had a good sense of color.

Brahmabrot Ganeshi Nilgiri by Alef

Brahmabrot Ganeshi Nilgiri by Alef

Brahma-brot?  Hey, expect the unexpected from Alef.  I’ve always liked his simple renderings which allow the fractal formula to do the drawing.  He’s done something special here with the formula.  Since I don’t understand what it is, I’ll let him explain:

Description: Multi layer and part render of my buddhabrot version aka brahmabrot of  mandelbrot set with subtracted unit vector.
z=z – 0.375*z/|z|

Really this weren’t meant to be a winner, it’s meant to be good contest entry.

NOTICE: Now its OK.

Pervij n.

Although I think the buddhabrot is a 2D formula, it’s always had a sort of 3D appearance even when rendered in 2D.  I’m not surprised to see someone like Alef experimenting with variations as, like I said before, the buddhabrot deserves its own category because it produces such rich and intense imagery.

Waves by Phtolo

Waves by Phtolo

I’m impressed more with fractal art that looks raw and alien rather than with the stuff that’s touched up and skillfully presented.  Maybe that’s because it’s more fractal or because it’s less human and therefore more unexpected.  There’s a style that comes with such arbitrary imagery that is captured in the wild and never domesticated.   Maybe most fractal artists don’t really like fractals? Phtolo I’m guessing is another newcomer to the scene although one can never really know when it comes to usernames.  The sense of wilderness which a turbulent seascape exemplifies is certainly in this image but the fractalness of it adds a strange sense of order, deliberation and primordial thinking to the scene.  Each wave is doing its own thing and reaching out for something to pull back into itself.  Does that sound crazy?

The Circus at the End of Time by Brummbaer

The Circus at the End of Time by Brummbaer

Another fine example of how small realistic elements can act like a spark setting off a whole new impression in your mind.  But didn’t I say I was more impressed with the raw, untouched stuff?  But this is what makes the incorporation of realistic elements such an artistic challenge.  You have to find something that fits with the fractal and when combined creates synergy, something that works with and multiplies the effect of the other.  Also, incorporating other elements doesn’t have the same graphically distorting result that global effects do.  Brummbaer is pretty good at this delicate job of sparking the image.  Are those hills in the background really clouds?  Isn’t it winter?  Or some kind of fifth season?  I hear music.

Description: The Circus at the End of Time
When you get closer to the circus you will find a door that says:
The Magic Theatre, for madmen only – price of admission, your mind.   (Steppenwolf by Herrman Hesse)

Well, there you go.  According to the compo closes for entries at the end of May and then the “voting” (whatever that means) starts.  But in the world of fractal art the game never ends!  Competitions come and go and the losers always win.  Let’s hear it for the next bunch of winners.

Fractal Artists are Deluded Narcissists


First, let me explain.  I make such a bold statement not because I hate fractals (or fractal artists) but because I love fractals and include myself among the hopelessly deluded.

A quaint anecdote

I came to this realization in a rather unexpected way: through rediscovering the joy of fractal artistry.

For the last year or so all I’ve been doing as far as fractals are concerned was merely reviewing other people’s artwork as well as attempting to understand and explain fractal art from a theoretical, art criticism, point of view.  I hadn’t really been making any artwork myself for over a year.  Then just this past weekend I rediscovered the joy of fractal artistry.

Like most computers mine has a screensaver and like all screensavers they only display when you’ve stopped using the computer for some length of time.  Only then, when you’re not using them do they appear.  From time to time my computer would start drawing Lyapunov fractals in a screensaver called  XLyap by Ron Record (1997).   I had never thought Lyapunovs were very creative until I saw them rendered in the primitive, colored greyscale method of XLap.  I became re-enthused with Lyapunovs after seeing their  artistic potential demonstrated.

I was already somewhat familiar with Lyapunovs from using Sterlingware, that great fractal program by Stephen Ferguson.  I remembered the Lyapunov formula section in Sterlingware and thought it might be worth checking out one more time because if this screensaver, XLyap from 1997 could make interesting stuff out of Lyapunov fractals, then surely that powerful troika of: me, Sterlingware and a graphics program, could do even better.

The Fractal State of California c. 1825

The Fractal State of California 1865

While rediscovering the secret joys of fractal exploration with the many Lyapunov parameter options in Sterlingware (never underestimate a simple fractal program) I came to realize (that is, re-realize) just how much fun fractal art is to make and at the very same time (still over-analyzing everything) just how cut off from all this fun-factor the audience of fractal art must be.  This became rather obvious when I reflected on the excitement of exploring these wonderfully irregular and asymmetrical Lyapunov fractals.  It also became obvious when I saw that my mass of saved images was becoming a fractal “rock collection.”

How can fractals be so engrossing to make and yet look so awkward as art?

Awkward, because surely, to an outsider, that is, someone not initiated into the arcane world of fractal graphics, it’s all just technological weirdness (“Awesome! How did you make that?”).  I mean, they’re not something like a portrait painting or a misty morning photograph of “park bench and trees” that makes almost anyone stop and make an instant emotional connection with the intent of the artist who made it.  Fractals are more like Rorschach tests and the viewer’s reaction says more about their own insanity than that of the artist’s.

I see a crushed butterfly

I see a crushed butterfly, and my first grade teacher

So what does that suggest about fractal art as an art form?  (More analyzing)  It suggests something disturbing which I’ve sensed for some years now: the audience for fractal art is fractal artists.  And when some of those fractal artists get together and try to get the rest of the world to discover fractals and “see the light”  they unwittingly reveal the depth of their own narcissism and the subsequent flood of delusional thinking that causes them to believe that all people from every tribe and tongue will join them in worshipping fractals if only we can distract them for a moment and get them to look at some really great examples of fractal art.  The promotion of fractals as an art form requires religious zeal and a faith in fractals that transcends reality and is able to calmly walk across the coals of art criticism (and self-criticism).  Why else would anyone push this stuff?

The Metropolitan Museum of Mental Art

Back to reality.  Fractals are the Rorschach Tests of our generation but since in our generation everyone is an authority, the diagnostic tests have been developed by the mental patients instead of the doctors and being crazy, we, the patients, have hung them on the wall as art instead of hanging them on the end of our hospital bed as charts that display the severity of our disease.


The deserted shore Sinbad was stranded on

I suggest a name change:  since fractal art is really rock collecting and rock collectors call themselves “rock hounds” let”s stop calling ourselves fractal artists and instead use the term, “Fractal Hound”.  For example: The Benoit Mandelbrot Fractal Hound Exhibition.  Our official symbol won’t be a spiral it’ll be a wheel barrow.

In case I’ve failed to make a coherent point in this posting, let me end with something straightforward: fractal artists (I mean hounds) need to take themselves a lot less seriously.  We have an oddball art form that doesn’t do what most art does.  It’s a niche art form and appeals to the typical niche dwelling life forms like spiders and cockroaches.  Our audience is us.  Your audience is you.  And it wouldn’t surprise me if my audience is me.And now, back to staring in the pool.

3D Printing: Will this be Fractal Art’s Big Break?

With 3D printing technology, fractal art can cheaply and easily enter the domain of sculpture.  It’s an exciting development and offers the ever dazzling world of fractals another venue in which to capture that proverbial and elusive, “mainstream” audience.  Will this be fractal art’s big break or just another demonstration of how hard it is for “normal” people to relate to fractals?  But first a little explanation of the technology.

They call it 3D “printing” because the objects are built up, layer by layer, from the bottom to the top.  This is “additive” rather than the old fashioned “subtractive” method of carving out the object from a block of material like they do in machine shops.  There are various 3D printing processes, some resemble an inkjet print head or laser plotter moving around quickly adding layer after layer of 3d pixel bricks while other methods fuse the powder in a large sand pile into smooth, delicate pieces with the precision of a master craftsman.  (Here’s two basic links for more info: Wikipedia: 3D Printing, and a very good Economist article.)

Naturally it all starts with a 3D digital model.  And although I’m sure there’s got to be some limitations as to what you can make with 3D “prints”; such as you can’t have parts of the model floating in mid-air; it looks like the only real limitation is your imagination.  That is, what you can dream up in a 3D digital program.

Here’s where fractals have the real advantage: what could be a greater source of 3D dreams and imaginative works than 3D fractals?  What could be a more exciting and better use of this custom sculpture technology than rendering the kind of complex and beautiful 3D fractals we’ve seen fractal artists making for years?

Consider what this new technology means:  Isn’t it just like the early days when fractals were first graphically rendered –in 2D?  That was the great debut of 2D fractals and this is the same historical event but now in the much more sophisticated medium of 3D.  Fractal art has now moved into the medium of sculpture and would it be premature to expect it to take on a much more radical popularity?  Who can come up with more amazing, and a much more prolific amount, of 3D objects than a fractal artist?

Jeremie Brunet (aka bib) has been posting photos on of his recent 3D prints made at, one of the leading 3D printing companies.  Shapeways will render your 3D image file and also give you a gallery on their site so you can exhibit it and even sell them to the public, just like Deviant Art does for artists with 2D prints.

When I first saw Jeremie’s photos on Fractalforums I thought they were just digital images using a new photo realistic rendering technique.  As we all know, 3D digital art can look pretty realistic these days but as it turns out his photo realistic images were real photographs of real objects, some of which were sitting in his hand.  I think it was the sight of that hand that started me thinking, “What the what?”

~Click on images to view full-size on original site~

3D printed fractal by Jeremie Brunet on

3D printed fractal by Jeremie Brunet (in the Master’s hand) posted to

3D printed fractal by Jeremie Brunet

3D printed fractal by Jeremie Brunet

3D printed fractal by Jeremie Brunet

3D printed fractal by Jeremie Brunet

Box Pillar by Jeremie Brunet

Box Pillar, 3D printed fractal by Jeremie Brunet

There’s a lot more by Jeremie in this post, Shapeways for 3D printed fractals. Some are metallic and others, like the Box Pillar above, show you how detailed and “fractal” the images –sculptures, really– are.  It literally is the equivalent of printing out a fractal image in 3-dimensional form.  You can see more of Jeremie’s sculptures at his account.  In fact, you can buy your own copies of some for as little as $6!  Buy some before he becomes famous.

Infinitely replicating slugs of ignorance - Fractal Sculpture by Kraftwerk

Infinitely replicating slugs of ignorance – Fractal Sculpture by Kraftwerk

Jeremie isn’t the only one getting into this.  Here’s an excellent example by Kraftwerk (aka Mandelwerk, Johan Andersson).  Fractals should have the potential to be the Michelangelos of 3D printing because no other method creates such intricate and novel objects with such ease and in such quantity.  Compare the 3D print above with the original, “virtual” 3D image below:

The infinitely replicating slugs of ignorance and the false revelations induced by their phlegmatic movements by Kraftwerk

The infinitely replicating slugs of ignorance and the false revelations induced by their phlegmatic movements by Kraftwerk

Although the 3D “print” isn’t as rich and nuanced as the original image, it does illustrate how the aesthetic qualities of 3D fractals can be transferred to a 3D printed object.  And the process is only going to get better –and cheaper.  A fractal on every coffee table –or hanging from every rear-view mirror like CDs were back in the 80s.

Here’s a short, two minute video from showing how their 3D printing process works and how it can work for you:

My favorite bit in the Shapeways video is where they lift the finished products out of the sand.  It was like seeing buried treasure being uncovered.  Your 3D files and Shapeway’s machine can turn that industrial sand pile of theirs into a never ending archaeological treasure hunt in the Valley of the Kings.

Of course fractals aren’t the only thing that’s being “printed” there.  But like I said in my introduction: what could compare to the visual wonders of 3D fractals?  They’re sculptures; mathematical masterpieces that you can hold in your hands.  They’re things that no human mind has imagined or could imagine.  What is there in the world of 3D printing that could possibly rival fractals for the top spot?  What could turn the heads of anyone once they’ve stumbled upon the mathematical majesty of 3D fractals?

How about My Little Pony?  Yeah, look at this:

Art category from the front page of

Art category from the front page of

And skulls.  Who wants to look at the wonders of math made flesh when they can oogle over an ornately carved human skull?  Fascinating, isn’t it?  It’s this apotheosis of mediocrity that really struck me when I visited 3D printing hasn’t changed a thing for fractal art.  It’s still the same old world where people’s attention is monopolized by trivial things and stuff they’ve all seen before.  What in the Sam Hill is wrong with society?

Now of course Shapeways isn’t trying to promote “art” they’re really just trying to promote art sales, that is, sales of the 3D objects exhibited on their site.  It’s just like Deviant Art going out of their way to get visitors to buy prints of the artwork they’re browsing and thereby convert as many of their visitor stats into art sales.  Shapeways is a business.  But so is just about every art gallery, too.  Art has always been commercial.

I think Shapeways can give us a little insight into how fractal art fits into the rest of the art world by virtue of how much or how little they showcase 3D fractals over 3D skulls and 3D cartoon characters.  For what it’s worth, in the “Art” category image above, fractals, or at least something geometrical, has equal billing with My Little Pony.  Let’s look at some other 3D printing categories:



Fractals have intricate detail but apparently there aren’t any on Shapeways to compete with Loser Man, or spinning tops (are they geometric?), little cars and the inevitable cartoon bunnies.  How about another category?  Can I have the envelope please…



Oh!  “Featured Picks” and not one a fractal or anything geometry-like.  Just a Steve Jobs Lego-like head, an iPhone case (kinda fracktally) and, well, who cares what those other two things are?  Perhaps Shapeways is trying to feature the capabilities of their 3D printing technology more than the quality of the items that can be made?  Even still, wouldn’t Jeremie Brunet’s second image, the geometric cauliflower thing be a much more impressive example of 3D printing?  Or is Shapeways more interested in showing how –ordinary– the output is?  How it can be like: all those cool things you’ve seen before.

What next?



Jewellery holds some promise for fractals, I think, based on the geometric, curio-type objects being showcased there.  What could be more “curio” than 3D fractals?



Check it out for yourself, but so far I think the audience for 3D fractal printing is going to be the same audience that already exists for 2D prints.  Despite the inherent qualities of 3D fractals to astound and amaze in 3D format, most of the world still seems more interested in the things that they’re familiar with and have an established presence in the traditional arts and crafts world, such as skulls, cartoon characters and mobile phone cases (the tie-clips of our time).

Is there something about fractals that makes them too odd and weird to ever have mass appeal?  I get the impression that fractals are something that most people have an immediate but brief interest in and can’t get interested in on any sort of deeper or more lasting level because their appearance is inherently artificial, synthetic and unnatural looking and for that reason lacks the warmth and attraction of real world objects and imagery.

It looks like fractals are still a niche art form and always will be; whether they’re in two-dimensions or three.  But maybe it’s too early to render such a verdict?  Could there still be a massive invasion of 3D fractals into the mainstream world?

Watch the skies!  Watch the coffee tables!

X-ray of art! Fracplanet 0.4.0

From the developer’s, Tim Day’s site:

Fracplanet is an interactive tool for creating random fractal planets and terrain areas with oceans, rivers, lakes and icecaps. The results can be exported as models to POV-Ray and to Blender, or as texture maps for more general usage. The code is licensed under the GPL. It uses Qt and OpenGL.

At the Sourceforge project page for Fracplanet, where you can download the program, this note, by Tim Day:

I’ve been using various versions of fracplanet for sometime now, and it’s extremely useful in creating planets. What you can use the program for is quite varied.

“What you can use the program for is quite varied.”  With that begins our x-ray of art.  Zzzz-zap!

But one more software detail.  I tried out Fracplanet with the hope that it might do what Terraform, another little project for drawing landscapes, used to do.  I say “used to do” because it no longer seems to be available as it’s been abandoned and no longer kept up to date with the latest compiling and other technical software things that are beyond my own reach and expertise at present –the versions are old and won’t run on the latest Linux releases.

Terraform could render eerie, x-ray moonscapes with relative ease.  Terragen, the well-known and highly capable landcape renderer, seems in-capable of doing this.  Why?

To put it into technical, graphical terms:  Why is wire-frame rendering not seen as the most important and best artistic use of a fractal terrain generator?

To most readers the answer is painfully obvious.  Who wants to look at wire frame imagery?  The whole purpose of terrain generators is to create realistic looking terrain, not retro graphics.

Which brings us back to the x-ray vision of art: “What you can use the program for is quite varied.”  That’s good because what I want to use the program for is not exactly what the program was designed to do.  Fracplanet, and Terraform (how I miss it!) were designed to do normal things like this:

Fracplanet 0.3.0 with terrain exported to POV-Ray and Blender. (from Tim Day's site)

Fracplanet 0.3.0 with terrain exported to POV-Ray and Blender. (from Tim Day’s site)

Neither Fracplanet or Terraform (RIP) advertise their wire frame features.  That’s because wire frame for most users is nothing more than a degraded version of an image presented for planning purposes.  Nobody intends to actually build landscapes out of wires –especially black and white, monochrome wires.  Like this:

This is art

This is art

Art?  In some ways, Fracplanet is better than Terraform because its default image shape is a sphere –a planet.  Sphere’s are circular and the circle is probably the most creative of all shapes by virtue of its great potential for doing all sorts of shape-y things.  Carl Jung, the high priest of 20th century abstract art, said it this way:

“The circle has had enduring psychological significance from the earliest expressions of human consciousness to the most sophisticated forms of 20th-century art.” Aniela Jaffe, ‘Symbolism in the Visual Arts’ Man and His Symbols (Carl Jung)

I guess he’s actually quoting Aniela Jaffe?  Here’s another “super-shape” quote:

“The circle is a symbol of the psyche (even Plato described the psyche as a sphere).” Aniela Jaffe, ‘Symbolism in the Visual Arts’ Man and His Symbols (Carl Jung)

I know it’s all psychology mumbo-jumbo, but it looks great when you mix it with art.  Circles have an extra dimension to them, visually speaking.  Who knows why?

Another question:  Why do fractal terrain developers never quote Carl Jung on their software sites?

Which brings us to this “x-ray” question about fractal art:  What is more important, the fractal or the art?

I mention this because although Fracplanet and Terragen (the Photoshop of terrain generators), use fractal algorithms in their creation of realistic looking landscapes, they aren’t really what I think most people would consider to be “fractal” programs and therefore “fractal art” programs either.

I was quite happy that Tim Day, the author of Fracplanet included “frac” in the title because that made it much more easy for me to pawn off whatever it could make under the label of “frac-tal” art.  Or is all landscape a type of fractal imagery and therefore fractal art of the most fractal-ish kind?

I don’t really care about the answers to questions like that.  Which leads me to ask the question:  Why don’t I care about the answers to questions like that?

It’s because what I’m really interested in is the imagery that fractal algorithms can produce and that includes the imagery that fractal algorithms can help in producing.  “Help” as in creating the initial imagery that can then be transformed and photo-shop-filtered into some sublime thing.  The frankenstein art of post-processing.

In that sense, the label, “fractal art” is as loosely applied to the output of a program like Ultra Fractal, a standard fractal art program, as it is applied to the output of Fracplanet –that is, if the goal is to produce art and not images for a science textbook.  To carry this thought a little further:  One ought to consider how “adulterated” and contaminated fractal art has always been since the very day fractal algorithms were given visible appearance.

There’s always been a touch of mystery in art when one thinks about it and especially when one attempts to explain it.  Call it “subjectivity” as in the phrase, “art is subjective”; but that is only the acknowledgement that art is oriented around the mind and not the tools that make it.  An art form defined by its toolset, its medium, is bound to be limited by “tools”.  That’s tools as in “you stupid tool”.

Great art is not the product of a great medium or of great tools.  Often it’s more of an accident or the result of someone like Roy Lichtenstein who saw something alluring and intriguing in making “paintings” of comic book images –the wire-frames of his times.

“What you can use the program for is quite varied.”  I think all developers are aware that what users will want to do with their programs will always extend beyond what it was they actually designed them to be used for.  And so, people have used Microsoft Excel to draw fractals instead of creating financial reports, and similarly “abused” the text-only capabilities of computer consoles to “draw” Ascii art instead of configuring their operating system.  Or Fracplanet to draw wire-worlds using the parameters in unnatural combinations:

Made in Fracplanet 0.4.0

This is more art made in Fracplanet 0.4.0

Fracplanet allows you to set the colors for several landscape features, mostly height-dependent like snow, mountains, hills, lowlands, shore, ocean –highest to lowest; but also rivers.  This allows one to create a two-color “monochrome” image.  It resembles a cheaply printed book illustration.

Screenshot from 2013-02-21 20:48:43

Yet more art made in Fracplanet 0.4.0

Altering the “Power Law” under the “Basics” tab allows for the generation of much more misshapen freaks of planetary nature such as this one.  That’s what power in the wrong hands will do!  The (so-called) “shore line” becomes the “frame of the ocean” and you can make it a transition color blending the land and sea together.  Note how the “planet” is now taking on the appearance of a microscopic dust particle.  Isn’t that ironic?  Or have I simply reduced a great program to nothing?

Is it better than the Mandelbulb?  That sounds ridiculous doesn’t it?  But really, such comparisons ultimately revolve around what it is that one wants to do with a program.  I’ve noticed that not everyone makes fractal art for the same reasons that I do.  Not everyone is pursuing the same interest.  There are a variety of interests in fractal art, that is, some of us are more interested in oddball imagery than rich, photo-realistic renderings.

How did such a disparate group of people (or am I the only eccentric one?)  end up being grouped together under the same label of “fractal art”?  In the words of the “developer-sage” Tim Day, author of Fracplanet…

“What you can use the program for is quite varied.”

Jump into Fractals!

Stop what you’re doing, forget everything you know –and just jump into fractals!

~Click on images to view full size on original site~

alienFlower by love1008

alienFlower by love1008

Synthetic.  That’s a good word in computer art.  You like synthetic things if you like computer art.  There’s too much color in this?  It looks unnatural?  It’s synthetic, just like those chewy fruit candies that don’t really taste like real fruit.  They taste better than real fruit.  Space age flavours.  This image has space age colors.  Love it, or the image will delete you.

Based on that watermark in the bottom right corner, I think love1008 would like you to visit his Deviant Art page.  If you’re color blind you won’t see anything.

Now, I know this is going to sound a little weird, but I find the next image to be fractal like even though it’s a four hundred year old painting of Mary Queen of Scots:



Here’s a fractal made with Sterlingware, the fractalist’s fractal program:

Queen Mary by King Fractal

Queen Mary by King Fractal

Don’t see a resemblance?  They’re both made up of curves, lacework, smooth textures, and all arranged in an almost –fractal-like way.  One just happens to have a women’s face in it.  All the rest is pure geometry.  I’ve seen better fractal examples of this sort of lacework, frilly, curving portrait like imagery, but this is the only one I could find easily.

MB3D_0443_hd by 0Encrypted0

MB3D_0443_hd by 0Encrypted0

Little things, like exponents, negative signs and zeroes have the ability to transform context and context transforms everything else.  Is this a particularly artsy, expressive kind of image?  I don’t think even the artist thought so or he’d have given it a more sublime title.  What I think makes this image so interesting is the thing in the upper left corner and middle that resembles a hillside at night with city lights on it.  Here’s a detail from the full size:

MB3D_0443_hd by 0Encrypted0-detail

MB3D_0443_hd by 0Encrypted0 (detail)

Then the bright, glow worm, firefly image in the center and the dark, shadowed, silent area to the lower right give the image a strange depth and contrast between brilliant, energetic and moving and the other: subdued, silent and secret.  I was a little confused when I first saw this image because it seemed so vivid and alive and yet appeared to be, on the surface, made up of such ordinary things.

Data136pic10035s by Trafassel

Data136pic10035s by Trafassel

Trafassel is always doing bold and unique things, but here what’s remarkable is the nice simple style of the image.  It’s haunted.  A city of cities built in the dark, or built for the dark.  Here’s the finest part of the full size image:

Data136pic10035s (detail) by Trafassel

Data136pic10035s (detail) by Trafassel

As weird and intriguing as a pulp sci-fi cover.  That light edge shading and marble surface texture looks painted and not computer calculated.  A rare glimpse of style in the land of fractals.

The image comes from a posting on Fractalforums that appeared over the recent Christmas holiday season announcing a new type of 3D fractal, tentatively named the Mandelex.  This image above was Trafassel’s experimentation with that new formula.


mandelex 2 by Hiato

Although I think Hiato was probably working in black and white for simplicity’s sake, the stark color scheme is perfect for the type of intense patterning that this formula does.

mandelex 2 by Hiato

mandelex 2 by Hiato

Click to view the larger versions so you can get a better view of the rich detail.  Hiato mentions the serpienski pattern at the corners which is another interesting feature.  Unfortunately the thread seems to have gone dead with nothing else posted to it for a month now.  But that may just mean Hiato and the others are tied up with other things for the time being.  I think this could be an interesting development for the future.  It was mentioned in the recent Chaos TV video from’s sponsor and owner Christian Kleinhuis.

Navalis_Ignis_Pauldebroti by Alef

Navalis_Ignis_Pauldebroti by Alef

Similar to the Mandelex, this one has raw, graphical creativity.  Although it’s just a variation (I think) of the Burning Ship formula, that one was pretty good all on its own too.  Note how the orange area goes from being sky and background in the upper left and then turns into a precisely cut wall or slice in the bottom.  Likewise there are similar “multi-dimensional” effects with the dark areas becoming space and then silhouette.  And then there’s the hazy sun image in the “sky” of the blue figure in the top right area.  It’s an object that defies objectiveness, just like the tricky optical illusions in Salvador Dali’s many surrealist paintings.  Raw fractals sometimes need nothing but a frame and that’s all Alef has done for this one.  That’s a mark of genius in the fractal art world.

FonkyBonkers by lxh

FonkyBonkers by lxh

3D fractals could almost be considered a type of synthetic architecture.  Art Nouveau, an architectural style as well as a style of painting and decoration, would be just the category for this image.  This is one of a new type of image that features the curving, non-squarish style of imagery.  I think it’s going to be a whole step up for 3D fractals because the addition of such curving surfaces and designs makes for much more creative and interesting forms.

Speaking of Art Nouveau, here’s something that looks like one of Gaudi’s famous buildings.  All it lacks is a little more curvy-ness  to offset the sharp edges and regular lines, but it makes up for that with that extremely ornate and creative point.

PALACE by abbaszargar

PALACE by abbaszargar



This of course is a painting, watercolor maybe, in the Art Nouveau style of Charles Mackintosh who apparently was Scottish.  Rather unusual location for the Art Nouveau movement, but like many ideas in art it resonates with artists from all sorts of backgrounds.  I included this because it’s a great example, as is most Art Nouveau, of flowing, geometric imagery.  And so are most types of fractal imagery.

I think fractals are most powerful in impression when they exhibit this sort of symmetry and complex pattern and simple shapes.  That’s all this image really is; the hand painted faces, which fractals can’t produce, add something to the image but could easily have been substituted by simple shapes.

Rise by Tim Emit

Rise by Tim Emit

What makes this image remarkable and worth turning our attention to?  I don’t know.  But there’s something compelling about that big lump of fractal thing.  It’s like a photo from a fractal biology textbook.  This is something exotic and found growing only in remote places.  Smaller versions have been grown in the laboratory, but they lack the robustness and size of ones like this that grow wild, on the side of a mountain, only lately discovered.

pot4b by RamiGraFx

pot4b by RamiGraFx

What is it?  It’s a hand.  See the red box thing in its palm?  It’s a hand showing you this thing it picked up.  It’s been picking them all day and that’s why its fingertips are all covered with red stuff.

wallpaper_hyperbolic_garden by thargor6

wallpaper_hyperbolic_garden by thargor6

I think this was made with Apophysis.  Not your average flame fractal image.  Once again, I present an image with strong geometric characteristics.  That is, except for the interesting woven sticks things in the center and other ball like structures.  I think that’s what caught my eye at first.  This image is a wide screen wallpaper and you really need to see it in its natural size to appreciate the detailed concentric circles.  It looks very Christmassy, but still has enough general appeal to be looked at all year round.  Perhaps it’s an aerial view of a forest and we’re looking down at the round outlines of the trees.  The biggest one in the center being set high up on a hill.  Apophysis can be used for good and not always for evil.

Life as we don't know it by Kali

Life as we don’t know it by Kali

Kali’s been on a roll lately.  Coming up with all sorts of graphically intriguing stuff.  I think I mentioned his sea creatures and especially the scary, scary elephant worm in a previous posting.  Recently he’s come up with animated fog for one of the 3D mandelbulb programs that looks like it was made in the computer lab of a major movie studio.  And there’s the exploding mandelboxes, too.  I can’t show any of them here because they’re flash applets.  Step right this way folks, to see the floating brain and also the amazing liquid planet (scroll down to it).

This image incorporates, I suspect, some of the volumetric fog rendering techniques he’s been experimenting with.  Depicting depth is technical challenge in all computer rendering because the appearance of depth, if you think about it, is the result of many complex things, such as air, which have to be deliberately programmed into the imagery.  Perhaps it’s harder to generate the impression of depth than it is to program the fractals themselves.

The fog is used to create the appearance of distance as more distant objects are deeper into the fog than closer ones. It also produces a rather nice effect in general making the image look more painterly than the average mandelbox.  But it also has nice coloring and a fine use of lighting.  Lighting is something that is a parameter –adjustable element– in 3D fractals and it can be used for better or for worse.  This is an example of the better use of it, in fact, it’s an excellent example.  Not only that,  there’s a nice space at the top right for the title of the 2014 Calendar to go.  It’s a natural choice for the cover and exemplifies the latest rendering techniques as well as the exotic sights that fractals can produce.  Furthermore, this one has real commercial appeal to it being so well composed and finely rendered.

Rainbow Armada by isight

Rainbow Armada by isight

Heavy duty 3D programming here.  If you click on the image you’ll discover how easily it was to make: just a camera click.  I’ve always felt that there’s more to fractal art that pertains purely to the eyes and mind than there is that pertains to the programming and math.  From such a perspective, such a radical, precarious perch, comes the intuitive notion that other things are close to fractal art even though they are not anywhere near fractal math or programming.  Here we start from the premise that the medium of fractal art is pixels –imagery– and not parameters.

Is that crazy?  I think I hit my head.  That can happen when you just blindly jump into fractals.

Ode to Mandel Donut Vegas

Dave Makin, in a thread over at suggested that the mandelbulb deserves more attention:

From, click to go to the thread

From, click to go to the thread

Anyhow, while still shaking my head and wondering (like taurus66 in the quote) why anyone would be interested in that puffy, spiny thing called the mandelbulb,  along came someone else, in a completely different thread, posting their marathon session, 6-core rendering of “that puffy, spiny thing:”


From, click to go to thread

From, click to go to thread

So I’m a sucker for anything that looks like it might be something new in the fractal world, and also a little bit curious to see what on Earth could be worth spending “10 days on 6 cores” to render…

Mandel Donut Vegas by Furan, click to view the 35mb version

Mandel Donut Vegas by Furan, click to view the 35mb version

The full-size is …big!  A screenshot says it better.  I had to shrink it somewhat to fit it into a blog posting:


Big is a relative thing, but this is biggy-big to me.

Print size is saying it’s nine feet wide… although at only 72 ppi…

But my browser doesn’t seem to do scaling very nicely so I looked it over at full resolution and I slowly realized that maybe that spiny, puffy mandelbulb really is worthy of more experimentation and general attention from fractal artists.

Even the title is hums with excitement: Mandel Donut Vegas.  Las Vegas, I’m sure he means, and the Mandel Donut bit is something that has a literary term for it where one contrasts two words with each other; the scientific Mandel and the truck stop Donut.  They get married in Vegas?

“Electrified Pumpkin” would not be as good.  I guess “Vegas” says electric better.  The top rings almost look like LED lights in a clear plastic tube.  And that’s the sort of schlocky, kitschy atmosphere of Vegas all over again.

At full size I was impressed by how much detail and variety there is in this “mere mandelbulb”.  It glows and the light fills, overfills and spills out in a hundred different ways.  This thing is more like a giant Disney World attraction than a simple 3D fractal image.  It must be the high resolution that makes such an impression possible.

Which brings me to another thing, that being the observation that while most fractal images look better as thumbnails (sad, but true) because they lack interesting detail when viewed large, a few, like Mandel Donut Vegas, can handle the close-up inspection and high resolution heavy lifting of a truly intriguing art object.  In fact, this thing looked better and better at high resolution.

Let me give an example:


Mandel Donut Vegas by Furan (detail)

Power, excitement; is it a roller coaster or blazing theatrical event?  Electric cables or ancient Egyptian mummy bandages?

A technical note.  You ought to be wondering what program this was made with.  Doctor Furan explains:

I’m rendering in my own Fortran 77 program (I’m working on implementation of material models to FE-systems. Now only in F77, so it’s a sort of an excercise.)


Mandel Donut Vegas by Furan (detail)

Allusions to the ruins of the Colosseum of ancient Rome?  I particularly like how the colors sometimes become too intense and overwhelm the image.  Lava flowing?  It’s all there –and more.  What are words compared to these sights?


Mandel Donut Vegas by Furan (detail)

Line and over-line.  Light and shadow; hot and cold; the burning and the burned.  Yes, that old puffball called the mandelbulb has a few thrills left in it.

Not to be confused with these things:


The original, original Mandelbulb

And now, back to lurking at Fractalforums.

Almost forgot: Furan has a website with more images:

Food for Thought

I travel the internet, I make “Viewmarks” of artwork worth reviewing, and sometimes I end up with little scraps of things that I just can’t seem to fit into a proper blog posting.  But I keep them around anyhow because they’re food for thought, so to speak; singular ideas with potential.

Here are a few of these favorite things.

I found this great image, below, on Deviant Art.  Then, for some strange reason I browsed through the comments, which I rarely do, and stumbled on something –special.

~Click on images to view full-size on original sites~



Check out the added lights and other details which are best seen in the hi-res version.  There’s some new formulas or variations out there that are interesting like this one.

And then this comment:

Comment from below image on Deviant Art

Comment from the above image on Deviant Art

Most comments however, follow this simple, straightforward, business-like style.


Comment from Deviant Art

And now for something completely different:


I forget where this one came from.  Sometimes that’s a good thing.

Now here’s something I quite like which I found, and probably would never have found unless it hadn’t been in Haltenny’s Deviant Art favorites collection:

U.F.I.-015-020512-020 by Ghostwritersociety

U.F.I.-015-020512-020 by GhostWriterSociety

Nice colours, high contrast, simple but interesting colour combinations and a great use of symmetry, something which works so well in design although I can’t figure out why.  It has a golden, polished sense to it (if that makes any sense).  I thought perhaps it was a collage because of the wide variety of imagery, but the image notes didn’t give any hint as to how it was made, only this:

MNDB3D/ U.F.I.-015-020512-020 is a Fractal Art Image, created and owned by Peter Spangler, PRSJ22, GhostWriterSociety. It is protected under Copyright: MCN C4TIH-T2YA1-HKHS6

I hope that you enjoy these images.


Founder of #Fractal-Group-UNLTD

You are invited to stop in, take a look around, and see if you would like to submit to one of our galleries. Our membership is open to all artists, upon request; send me a personal note as to your interest in becoming a member.

Interesting.  But not as interesting as this from the main gallery page:

ghostwritersociety notice

ghostwritersociety notice

I hope the image gave you “PERSONAL ENJOYMENT”.  Because if it didn’t, you’re in big trouble.  But take heart, “YOU ARE VERY ‘WELCOME’!”  It’s ‘WELCOME’ in quotation marks.  Could that be different than the regular welcome which doesn’t have quotation marks around it?  (Is whatsoever really spelt with hyphens?)

Anyhow, lets not stand around here, I think I hear dogs barking.

Autumn's Smile by Marty Strutt

Autumn’s Smile by Marty Strutt

They put warnings on cigarette packs here in Canada.  They take the form of horrific images of cancer patients and other scary things along with some sobering statement about the risks of smoking.  This image would go great on any pack of oil paints or beginner’s art kit to warn users of the long-term risks of painting.  In fact, it ought to scare digital artists too.  Sorry it’s out of season, but I suspect the type of audience this is aimed at is in a perpetual “autumn frame of mind”.

fractal pattern doodle from

fractal pattern doodle from

What’s fractal about it?  That is the entry-point to a very profitable discussion.  Has the artist captured something of the nature of fractal art?  Or at least, fractal art as it commonly appears.  Is it “better” than fractal art?  I can see infinity –and more.  Thought snacks.  Crunch, crunch.

Hafnium crystal bar by Alkemist-hp on Wikipedia

Hafnium crystal bar by Alkemist-hp on Wikipedia

This was featured on the front page of the English Wikipedia a few months ago and I immediately saw a resemblance to Jackson Pollock’s drip paintings.  I don’t think this is technically a fractal thing, although perhaps closer inspection of the crystal might reveal something of that nature.  There’s movement, there’s all sorts of things suggested, even some colors, which might be reflections of things outside the view of the photograph.  But none of those things are really there, which makes us feel insane.  If any art form can have ready-mades, fractal art is it.

Wavy.gif by someone at NASA

Wavy.gif by someone at NASA

Thanks to Alef over at I found this scary octopus creature.  It’s just a demonstration of some wave formula, but look how weird and other worldly such humble things can be!  Worthy of any TV sci-fi episode.  Speaking of which…

Space 1999 screenshot

Space 1999 screenshot (1976)

Dig the groovy op-art or math thing on the wall.  It may surprise some of you youngsters to know that there was a time when mechanical looking artwork was considered cutting edge and not primitive or retro as it is in today’s millions of colours, photorealistic Disneyland kind of world.  Somebody in set design thought this was likely to be the kind of thing people in the future would consider decorative.  Why not?  Nobody at the time thought it was any good.  It must have been ahead of its time.  There’s was more to the 70s than Planet of the Apes.  By the way (btw) click on the image to go to the YouTube channel which hosts the entire two seasons of Space 1999.  The year, 1999, used to be the unimaginable future.  Now it’s the unimaginable past.  But I still love the lunar scenery.

untitled by Dan-Florian Nitoi on Facebook

untitled by Dan-Florian Nitoi on Facebook

I like it.  A fine example of how a simple fractal shape can become something greater than a great fractal shape.  There’s no explanation or notes about it.  I’m not even sure the guy who posted it actually made it.  Perhaps it’s only a fractal in name.  A secret fractal.  Can you tell?

Digital Dharma Buddhabrot by Alef

Digital Dharma Buddhabrot by Alef

Alef kind of apologizes for the rough look of this image, “My quasijulia mandelbrot buddhabrot brahmabrot. It lacks glamorous touch of photoshop, so watch it a bitt away from monitor, > 1m.”  But that’s one of the reason’s I happen to like it.  That, and the radioactive pink, red and blue color scheme.  And the wispy, shadowy, “memories” of fractals.

Land of Layers by daimbramage

Land of Layers by dainbramage

Dainbramage (not his real name) says this: “Nothing special.  Came across this in a negative Amazing Box using _RotatedAbs as formula 2.”  I’ve been seeing it in my Viewmarks, thumbnail bookmark collection for quite a few months now and always stopped to look at the exquisite use of black and white, light and shadow, and of course, depth and levels.  This is Geometry made flesh.  Naturally, it’s even more impressive full-size.  And the shapes, both the shapes themselves and the empty spaces between them.  We should all suffer from this sort of braindamage.

Untiled Faces by Nathan Selikoff

Untiled Faces by Nathan Selikoff

You fiddle with the stick controllers for one display and it changes what you see in the others, with the right one being a zoom of what you select with the stick in the first display.  Notice the wierdo retro monochrome dislay, not unlike some of the mini monitor screens in Space 1999.  The artist explains it better, perhaps:

Untiled Faces is an interactive sculpture that mixes a chaotic dynamical system with its “meta” representation, allowing the viewer to explore the four-dimensional parameter space by moving a series of levers. The left pane of Untiled Faces shows a 32 by 32 grid of images. As the left lever is moved, a red square over one of the small images moves, updating two variables that affect the center and right panes. The right pane shows the selected image from the left pane at a larger size. The right lever moves a small red target within this image, updating another two variables that affect the center pane. The center pane shows a chaotic attractor, whose four coefficients are taken from the positions of the left and right levers. The center lever adjusts the virtual camera viewing this strange attractor. Thus, all three images are linked, and in a somewhat mysterious way show the relationship between a strange attractor and its Lyapunov exponent.

It won the “Most Innovative” award at the “Bridges” conference.  But that’s not too surprising when you see the other entries.  The math and science crowd seem to have a whole different perspective on “art”.

Pink Hibiscus by

Pink Hibiscus by Amanda Moore

Very nice “colorama”.  The image tags for this on include the word fractal and useful combinations of “canvas prints”; also, apophyis.  It could be processed but what does that really mean anymore in the world of advanced fractal features?  I had to fish this out of my browser cache because the site disables all the right-click functions on the mouse and the image was too tall for a screenshot on my laptop’s short screen.  No threatening copyright notices written with barbed wire, though.  But I suppose most of you artists reading this think all those things are good ideas.

I’m still hunting around for fractal images; it’s always exciting to find a new online art venue.  So far it looks to be suffering from the same malaise as Deviant Art and all the rest.

Poelzig Hans (1869-1936), Großes Schauspielhaus in Berlin (1919): Innenräume im Bau. Foto auf Papier, 18 x 24 cm (inkl. Scanränder). TU UB Plansammlung Inv. Nr. F 1600.

Poelzig Hans (1869-1936), Großes Schauspielhaus in Berlin (1919): Innenräume im Bau. Foto auf Papier, 18 x 24 cm (inkl. Scanränder). TU UB Plansammlung Inv. Nr. F 1600.

All that text was in the meta part of the jpg file, I guess.  Pretty convenient.  Note the groovy Greek capital beta letter and the double dot, umlaut things.  It’s going to be a dull world when everyone learns English.

This was how the Mandelboxes of the past were rendered.  There really is a fractal aspect to this one.  And that’s precisely what the architect was trying to depict, I’m guessing.  Things like this are planned out carefully ahead of time.

The fractal art world, on the other hand, is different:

Deviant Art is practically a mountain of art!

Deviant Art is practically a mountain of art!

Somewhere on Facebook

Somewhere on Facebook

If you build it they will come!

If you build it they will come!

From the National Post newspaper

From the National Post newspaper

This isn’t a fractal, obviously, but then again it really isn’t not a fractal, either.  It suggests fractal to me.  It has all the attributes of a nice 3d fractal to it: depth and layers; nice surface texturing which repeats the forms from the large scale view; basic geometric shapes -circle, line, rectangle, symmetry, curves; a nice little bit of realism added in to enhance the context of the image.  Oh, I forgot; it’s ornamental, that makes it very fractal too.



This on the other hand is definitely in the fractal/chaos theory realm of imagery.  Mario837 says this about it: “Made with Chaoscope 0.3.1 – Lorenz-74 attractor, Solid render.”  I like the shape and also the color.  Very few fractal artists experiment with color, in my opinion.  Color can transform things –for better or worse.  In this case it’s for the better.  Nice simple piece of algorithmic artwork, even if it does resemble a cross between a Cuisinart blade and a toilet seat.  Simple shapes can be not so simple sometimes.

ultraLucia 667 of 760 by Dan Wills

ultraLucia 667 of 760 by Dan Wills

I don’t know if the link will take you directly to the full size image, but it’s worth a try.  Dan’s in a category all his own.  To really appreciate his work you have to stroll through it like one would a large exhibition.  Then I think you begin to see things the way he does.  Sometimes making great fractal art can be as simple as just wandering around in a formula and letting your eye set the course.

ultraLucia 634 of 760 by Dan Wills

ultraLucia 634 of 760 by Dan Wills

There’s been a lot of talk (by me) about whether or not fractals can ever produce artwork that has as much substance and expressiveness as what is called (by some) to be Fine Art, Mona Lisa kind of stuff.  I’m of the opinion that it just doesn’t have the basic ingredients and structural requirements to do the job, but this image comes close.  It’s almost a Mona Lisa like thing, but the greenish shape is the mysterious, smile element of the art work.  Just as viewers stare at Mona’s smile to carefully read it’s subtleties, something’s there in this image, a mandelbrot man, probably, but the coloring is spread over an uneven surface which makes one have to look carefully to make out the faint outline of …what?



Am I dorianoart’s greatest fan now?  Maybe some of you think that all these are just variations on a theme, but then of course they are: variations on a great theme!  Nobody else makes images like this.  I don’t think they have the “vision” to do it.  It’s a subtle style and in the world of art subtlety is a powerful thing.

Sea Dragonfly by Lawrence Morell

Sea Dragonfly by Lawrence Morrell

Although not exactly fractals, they do depict the fractal like patterns seen in butterfly wings.  Of course it’s the transformation these things have when rendered in frosted glass that really makes them interesting.  Glass is such a strange medium since it naturally distorts light and behaves with a mind of its own sometimes.  You can see more at the Portland Fine Art website or on Lawrence’s own website named

Lawrence Morrell's work at Portland Fine Art

Lawrence Morrell’s work at Portland Fine Art

2dbarcode from Wikipedia

2dbarcode from Wikipedia

This is meatiest of all food for thought bits.  Real art in its most energetic, catch it if you can, style.  Is this a piece of information, a diagram to explain how to read two dimensional barcodes?  Or is it the first step into the world of digital art?  The first step which requires your eyes –and the mind they’re plugged into– to be calibrated for the new medium.

Digital art can be read.  This is why mathematicians can get excited over rather dull images that are perfect graphical renderings of mathematical formulas and expressions.  That’s a bit of what I meant when I said the math and science crowd have a different perspective on “art”.  I’m sure Benoit Mandelbrot went bananas over the first computer printouts of fractal formulas; it was like seeing the face of things he’d only known as expressions of numbers and greek letters.

I like that “quiet zone”.  A digital DMZ?  Or is it just the digital equivalent of lawns and parkland?  A minefield for rogue pixels?  Do not go gentle into that good Quiet Zone!

I think the food’s all gone.  I’d better stop now.

Panorami Frattali by DorianoArt



DorianoArt has a real talent for mixing fractals with photography and doing it with style.  It’s not the typical marriage between earthy fractals and leafy scenery.  It’s more like an extraterrestrial romance between mother earth and alien invaders.

Despite such a disturbing courtship, the results are quite natural, or rather, quite unnatural, a hybrid landscape, a cyborg environment of majestic mountains and expansive pixel plains.

DorianoArt’s talent is playing match-maker to two fundamentally different image types and bringing about an unexpected harmony.  They complement each other, instead of curdling each other like orange juice and milk would.  Of course it’s not for everyone, especially for those who see no natural beauty in proliferating plastic scenery.

But for those who do, you can learn a thing or two from DorianoArt’s fractal panoramas.  They involve more than just slapping a clip-art sky over a fractal.  These sorts of images require a considerable amount of pre-marital counselling.

~Click on any of the images to view full-size on their original site~



Was he just lucky with this one, or does Doriano know something about composition and design?  The mark of a real professional is that you don’t see the marks, it all looks natural and effortless.

In case you’re thinking that this is actual snow and ice, I invite you to click on the image and view it full-size.  Then you can feast your eyes and the wondrous moire effect, the hallmark of true digital artistry.  The sky is real (you knew that, didn’t you?) and yet it blends seamlessly into the ice fields at the horizon.  And the sunlight too.



Is this the same mountain and hill from the first?  The sky is the same too.  But one barely notices this because the rolling expanse of striped cylinders draws our attention away and on down to that hazy vista of gently rolling geometry.

There is absolutely nothing natural about these striped cylinders (with purple ends).  In fact, they’re almost abstract.  Who would ever have thought of combining two things like this?  Not even Dr. Frankenstein.



There is nothing short of pure chemical joy to be found in both the chromafied sky and the pixel-gritty foreground of mercury drops.  The glass –-something— in the right midground is just a pleasant extra which, now that I notice it, leads our eye off to the vanishing point of this computerized carpet.  The moon, or is that the Earth? is conveniently located right where it is.  Who is this master of the fantastic?

DorianoArt ID on

You know, these images do remind me a little of the cover images for video games.  Slick, amazing alien landscapes and impossible combinations of technology and nature.  I also remember that the cover art was sometimes more impressive than the games.

It’s refreshing to see an artist who actually displays their real name on the internet.  Reminds me of the old days when people had real names and you knew who was crazy because they were the ones walking down the street waving their hands and shouting like they were on the phone.  Back to the art…



Oh no.  He’s gone too far with this one.  Mandelbulb, okay; and blue sky shining through the mandelbranches like in a forest, that’s okay too, but the troll kids?  Troll kids are too much.  Let’s let Doriano (I know his real name, now) explain:

Several things here starting from a wood photo in the background…(just an hour ago I was in a wonderful wood five minuts from my house) -then Mandelbulb 3D – and finally in the foreground the little people are (Gosha character) rendered with Poser 7. Final adjustments of lights in Photoimpact/Photoshop

It’s all fun and games until the Posers show up.  Creepy.



Doesn’t that bronze, or orange-chrome tubular thing just fit in perfectly with a south-western U.S. desert landscape?  Although, I think those objects on the horizon on the right, which are conveniently located at the vanishing point of the metal drops, are skycrapers and not buttes or rock pinacles.  A nice use of pattern, irregular objects, photo-sky and natural city scape.

You see?  I told you it wasn’t as simple as just slapping two things together.  Doriano is an artist not just a computer graphics wizard.  Son of da Vinci!



I present to you, loyal Orbit Trap readers, the Mona Lisa of our time.  Compare it with the real thing, if you’re not familiar with it.  Here we have a head-like thing in the foreground with nothing else but a dim, undetailed landscape for a background.  Of course, I don’t think Doriano intended such a allusion.  But then, did Leonardo intend his audience to fixate upon his subject’s smile?

Artist’s create but the audience interprets.  At any rate, I find it to be a richly colored and rendered mandelbulb image.  I can’t quite figure out what makes it so interesting, but as I said earlier, good art is a bit of a riddle.

The notes say “Here are two Mandelbulbs + a Terragen background for this “neoclassic” mandelbulb sculpture…..



One of the images of mine I more love returns here in another version…Hope You can appreciate it!  (mandelbulb 3D -terragen)

Hmmn…  So the sky and mountains aren’t photographs at all,  they’re made in terragen, the artificial landscape generating program.  That’s an interesting combination, although the terragen landscapes are so realistic they might as well be photographs.

The “mandelbeetles” are an interesting element adding synthetic animal life as well as synthetic ground to the lifelike horizon and sky.  Perhaps this is their hive and they are hatching out or tending the next generation.  Of course, the truth is probably that they’re both part of the same mandelbulb image and it’s the formula that connects them.



This one is pure syntheticism.  The land is artificial and the sky, whatever it is, is not even the color, much less anything else sky-like except that it is above.  Once again, the colors are rich and multi-faceted which is a talent of computer graphics.  Moire and pixel-grit add another scale of artistry here so you’ll want to click on the image and view it full-size, that is, if you like this sort of computer abstract expressionism like I do.



I don’t know if Doriano made the city imagery in the top, but he complemented it well with the orange energy collecting cells at the bottom.  The lighting is quite well done as if both these image areas were created together.  That’s the sort of harmony I was talking about at the beginning.



I couldn’t find the first Sindragosa, or the first Robotika one either.  I don’t like the search function on Deviant Art.  Nothing works as well as Google.

This one makes me think of an illustration for a book, perhaps one of Sindbad’s adventures, lost in the desert and arriving suddenly at a mysterious place, which of course shines like gold.  What great looming thing is causing that shadow we’re in?

I’m sure many people will find Doriano’s mandelbulb/box renderings a little rough, but I find that stylish.  It adds a unique texture to the images and uniqueness is something that one doesn’t see much of in the fractal world; it’s just too easy for all of us to follow the same path without realizing that there’s a lot more creative potential in how you render something than what you actually render.  And you won’t get to be the leader of the pack by stepping off the trail.

Doriano’s not a formula trail-blazer or technical pioneer (as far as I know), but he’s done great things by being creative with the artwork rather than the tools, and in the end it’s that fresh approach that makes his work stand out.


Pauldelbrot’s Mandelbrot Safari and other Journeys into the Unknown

Back, several postings ago, when I reviewed the latest calendar, I heaped abuse on Pauldelbrot’s image from his Mandelbrot Safari series calling it retro and not cutting-edge.  The owner of and publisher of the calendar, Christian Kleinhuis, informed me that what Pauldelbrot was doing was in fact very cutting-edge as it was utilizing new methods that enabled him to zoom to a much greater extent than had previously been possible.  And something about a new coloring method too.

But as an illustration of how weird fractal art as an art form can be, Pauldelbrot’s work can be kicked and abused in one review and then praised in another, just a month later as you will soon see.

Let me explain this apparently senseless thinking:  For the calendar, I didn’t think Pauldelbrot’s work had commercial appeal (as well as just about everyone else’s work in the calendar); But in this posting I present his Mandelbrot Safari images as epitomizing the pastime of fractal exploration (and a fresh example of that) as well as a good example of classic-style fractal art.

But most importantly, I rather like many of these images myself for their own sake, and the fact that they’re from the Outer Limits just enhances that.  One shouldn’t talk too much about fractal art.  Perhaps most readers have already skipped to the pictures.

The best way to follow the Mandelbrot Safari is by reading its own forum thread on  More images, comments, etc…  Who knows?  You might even decide to buy one of the FFs 2012 calendars for no other reason than because it contains one of these Safari images.  Now wouldn’t that make me look stupid after saying they had no commercial appeal?  Buy a calendar —fight the man!

~Click on images to go to original forum thread with larger images in it~

The initial image from Pauldelbrot’s Mandelbrot Safari thread

The safari begins:  fairly common terrain we’re starting off from on May 4th, 2012.  Doesn’t look particularly promising, I must say.  But I’m not the pilot or the navigator on this expedition.  Let’s wait and see what’s over the horizon.  I’m sure he’s got some exotic destination in mind.

evdz1_008_lrg by Pauldelbrot

The game is afoot, as Sherlock Holmes would say.  That’s an odd looking color to be seeing out in this sargasso sea of yellow.  The perennial question:  Where does it go?

evdz1_017 by Pauldelbrot

I jumped ahead a few of Pauldelbrot’s image postings and here we are at the first of many “portals” to the (glittering) unknown.  If you’re anything of a fractalnaut, you ought to be getting excited right now because it looks like this trip is 1. never going to end, and 2. going to be full of surprises.

evdz1_018_lrg by Pauldelbrot

A comment:

Is that the coloring of Pauldelbrot’s image, or of this guy’s hefty signature?  (sorry, couldn’t resist; it’s the duty of everyone on the internet to stamp out signature lines and other forms of “junk mail” content)

evdz1_029_lrg by Pauldelbrot

According to the thread, we’re now zoomed into about 4 e30 magnification.  That’s 4 and thirty zeroes behind it.

evdz1_044 by Pauldelbrot

Pauldelbrot answers a tech question in the thread here about what program he’s using:

…a mix of custom and off-the-shelf code here. Time on these has increased but the latest few have taken a few hours each. The iterations are still pretty low (around 5000) but the precision bits are getting fairly numerous.

A couple hours, each?  We’re obviously on the other side of some computing sound barrier.

evdz1_090 by Pauldelbrot

Note by author:

Now over 20,000 iterations in the shallowest parts of each image, and the magnification has just passed one googol, too…

Sound sci-fi -ish, doesn’t it?  What’s a googol?  Biggy big!  So big it’s covered with big-fur!  That’s the layman’s definition. (it’s this, actually: 10100)

Gets slower and slower with depth…

He’s doing this in Ultrafractal (UF) and makes this comment which sheds some light on the type of technical challenge all this is:

I should warn you that to get close to the quality results I’ve posted you’d need to use 3×3 AA, depth 2, nonadaptive AA because depth 1 isn’t enough oversampling and UF’s adaptive AA seems not to work as well as mine. The deeper images would thus need some very beefy hardware to render in anywhere near a reasonable time; or even a cluster rendering different tiles of the image per machine.

This is what Christian Kleinhuis, the owner (and sponsor) of must have meant when he told me Pauldelbrot’s image in the calendar was actually cutting edge imagery after all.

evdz1_113 by Pauldelbrot

The images are largely like this; circular and elegant, which is the sort of thing that characterizes classic fractal art –highly detailed, organized images.  I guess “complex geometric” is not a bad description, either.

Pauldelbrot says this in response to a comment about the great coloring:

It “discovers” colors, because it keeps shifting and blending them. Colors that are somewhat between pure primaries and secondaries, or somewhat desaturated as well as saturated, included, which may often be overlooked by humans doing things manually.

evdz1_204 by Pauldelbrot

“Overlooked by humans doing things manually”  Computers are more than just powerful paintbrushes.  It’s through this sort of exploration that one can develop a real appreciation for the machinery that they’re using.  That’s half the fun, I’d say.

I’ve just shown a sampling of images here; you’ll definitely want to check out the thread if you find these interesting.

evdz1_218 by Pauldelbrot

Some of the really dark images are the best in my opinion.  This one is from November 30th, 2012 and marks the 7th month of the safari.  It’s still going on, although, as Pauldelbrot said, the rendering gets slower because of the depth of the zoom.  Another image was posted just this week (Dec 11).

Pauldelbrot has embarked on a number of these zoom excursions with the same journey into the unknown feel to them.  Here’s some highlights from some of the others…

511_28_11_12_2_35_18 by Pauldelbrot

A note from this image, from a series entitled “Fall Woods 1”:

This zoom is near the Autumn Forest zoom. However, the area zoomed into is around a seahorse below and to the right of the green period-3 blob in Autumn Forest I. Out here, the “zero basin” doesn’t exist — there is no zero attractor at all. Where that happens, the basin implodes into a disconnected Julia set, which the surrounding seahorse shapes still try to conform to, with amazingly convoluted results!

Images in this series have mostly been rendered at 32000×24000 and downsampled for a whopping 625 samples per pixel, needed to render the “zero basin Julia” regions properly. I was able, nonetheless, to render most of them in under two hours.

Yeah, that’s 32 –thousand by 24-thousand.  Pauldelbrot is no wimp when it comes to making fractals!

511_03_11_12_12_37_51 by Pauldelbrot

511_02_11_12_12_20_32 by Pauldelbrot

Those above are two of my personal favorites from the Autumn Forest II and I series.  The disorienting vastness of fractal panoramas is easily seen in both as well as Pauldelbrot’s excellent coloring style.  In the process of trying to make fractals into art, I wonder how many of us forget how artistic fractals can be in their raw, freshly calculated form –if only we were to explore them and not the latest layering techniques more.

Lilac Exponent by Pauldelbrot, Sept 14, 2011

This is from more than a year ago.  It caught my eye back then because of the intense patterns of shapes and shapes and more shapes.  This sort of thing is an art form that only fractal algorithms can do and they do it very well, especially at the hands of someone as talented and creative as Pauldelbrot.

As Christian Kleinhuis was saying; Pauldelbrot has really done something new and different even if it does lie within the old category of “classic” fractal art.  I think Pauldelbrot has elevated that classical category higher with this kind of work and his probably represents the best of its kind.

Best of its kind so far, that is.  If Pauldelbrot’s herculean efforts and endless hours of rendering have shown one thing, it’s that there’s still much to be explored even in the realm of classical fractal imagery.  I hope he’s inspired a few others to follow this path, even if it takes them away from the seemingly much more advanced 3D fractals that most work on these days.

The Varieties of Fractal Experience

There’s a theme that binds all these images together but I can’t seem to find the right words for it.  Freaky; harmonic; other worldly; sacred symbols; journey into mystery: they all fit for some but not for all.  I guess variety is best; with a play on the famous book by Henry James, The Variety of Religious Experience.  There’s a cult-like, mystical weirdness to these –an attractive kind of quicksand.  Perhaps it can’t be described.  Perhaps it shouldn’t — it mustn’t!

~Click on images to view full-size on their original site~

Some old thing by Brutaltoad

Description: I had this old picture lyin’ around an I thougt it would make a great present for the mandelbulb’s birthday <3

happy birthday, Mandelbulb!

That’s from the gallery page on  It never ceases to amaze me how often the folks at (FFs) stumble across great looking artwork and then casually move on to some deep technical discussion.    I call this one, Return of the Overlords.  Ancient astronauts; landing pads in the Andes; road to the moon.

This was posted in Nov. 2011 and even then was considered retro by its author.  I think it’s one of the best of the early mandelbulb images.  The mandelbulb wasn’t anywhere as interesting, visually, as the things it gave birth to.  But BrutalToad has managed to nudge it into a higher orbit, primarily, it seems, through color and background texture in addition to the nice scene selection as well.  The shadow is a nice touch.

Sacred Maths by Tabasco Raremaster

This one inspired the theme for the whole posting.  Posted just a few weeks ago on FFs it suggests a mathematical, geometrical religious icon.  You’ll note that the five “snowflakes” are each different and yet a variation of the same theme.

Normally fractals produce similar things since that’s one of the main, expected characteristics of fractals.  Of course, things have gotten much more sophisticated lately and this is a good example.  The different shapes suggests human and not algorithmic creation which again gives it a strange feel for a fractal.

Back in classical times geometry and other mathematical subjects were seen by some as semi-religious topics and became part of the culture of a number of religious cults and societies.  It seems ironic to our modern minds that science would inspire thoughts of the supernatural but the topic does pop up from time to time in online discussions about fractals and so the theme, and the title of this image, needs little explanation.

Chinese Royal Doll by Milan Dobrojevic

The alien-ness of fractal art can be clearly seen in this image.  I’m guessing that it was either made in Steven Ferguson’s Sterlingware or Fractal Explorer using one of his formulas.  I’ve never been able to understand why programs like Sterlingware (Sterling; Sterling-Ware…) are used so little by fractal artists since they produce such creative imagery and do it so easily too.  It’s another one of those fractal art things that requires deeper explanation and contemplation, I guess.

From the phone number on his website,, Milan is located in Serbia, part of the former Yugoslavia.  He seems to be very active in a number of fractal related activities and businesses.

It’s a joke now to say that one could stare at an image all day, but for this one by Milan it’s almost true.  Of course, if you have the program you can zoom into it and explore it in great detail which is what people do in art galleries when they move in and look closely at artwork.  One of the things that makes fractals so unusual is this visual playground aspect to them.  It’s almost as if they’re a landscape and the images we see of them are mere snapshots.

Cover Photo 1 by Fractal Art Gallery

I found this one on Facebook, a rather new source of fractal art for me.  This is a brilliant example of how accidentally wonderful 2D fractals can be.  Eyes, hair, fingers; and all that simply from the isolated context all three of these elements find themselves in, in this one selection.

I couldn’t figure out who actually made this image and I had to make up a title for it as well.  Despite the endless self-promotion on Facebook and the flood of junk one has to wade through to find something interesting, I found this and the author is anonymous.

The Paper Caper by Pauldelbrot

According to the gallery page, this is a 2D Mandelbox.  The intriguing details are not so easily seen in this low-res version but it’s good enough to display the contrasting patterns that make this image so… mysterious.

It’s like a big fractal web press printing out little fractals.  Pauldelbrot specializes in these “retro” type images but he gets interesting results because he explores advanced variations of them.  The old style, flat fractals were never a dead end, creatively, they simply require artists with a good grasp of their 2D potential.

Anyhow, Pauldelbrot has flattened the mandelbox.  It’s forwards and backwards at the same time.  Just goes to show there’s always something new and exciting in fractal art if you can think creatively.

The Wall at Sunrise by Tim Emit

Do you think this thing is fascinating?  If you don’t then we clearly don’t share the same tastes in fractal art.  I was stunned when I first saw this on FFs.

To me it’s a stage, and in some strange way that defies logic, there are two lights shining on it.  The patterns and wide variety of them make this one that’s well worth taking a closer look at.

But even in large view the image is great.  Maybe that’s what a great fractal image is: good art at every scale.  The name, “Tim Emit” rings a bell.  Could he be the famous “timemit”?  You can see now why the fractal world needs a phonebook.

It’s a stage that needs no performers because the show is the concert hall itself.  The audience; the orchestra; the curtains; even the backdrop are part of the show.  Should I mention that it didn’t get a single comment on FFs and I was the only one to rate it?  Another mark of greatness in the fractal world.

crystalRock by Tom Lowe

I think I was doing the right thing when I gave Tom Lowe the very first Nobel Prize for Fractal Art; now he’s gone on to create 3D cellular automata.  If you click on the image up there you’ll go to the page that talks about it on his own website for Automata Finder.

Cellular automata are extremely weird as well as being a natural phenomenon.  Seeing one in 3D, or what appears to be 3D is disorienting in a wonderstruck way.

Advantages of this algorithm over standard cellular automata:
  • The automata is embedded in a continuous space and continuous time
  • It can be simulated at any level of detail, allowing it to be simulated in the distance or up close
  • Results are often ‘dynamic fractals’ with the small features changing more quickly than the large features, this matches nature quite frequently

(That’s from Tom’s Automata Finder webpage.)

“Embedded in a continuous space and continuous time”  “Dynamic fractals” — this is the sort of creeping number monster that cellular automata (CA) are, but Tom has jumped the gap and created a the equivalent of a walking Frankenstein.  Although I’m not actually sure about that because I didn’t understand most of what he’s saying on the page.  But that’s what I saw in the video.


Not the sort of thing I’ve ever seen Mandelwerk (Johan Andersson on Deviant Art) make, but this is really a fantastic image for it’s imagery and also the inclusion of wireframe elements.  This is quite ironic when you read the notes from the gallery page:

Just wanted to show you what it looks like when I arrive for a days work at MB3D.

The arrival to a new 3D hybrid fractal world (on a lucky day)

Normally I never submit these kind of first arrival overview renders, but I always do one big to be able to see where the interesting shapes are (if there are any) before I zoom in and get the disposition right. ;)

Clic on the image and check out the full view image, and you might understand how it feels…

A mandelbox in jeans and a t-shirt.  There was a time when jeans and t-shirts weren’t fashionable.  Maybe this will be the next big thing in mandelbox fashions?

Portable Stage Play by FractalJam

Crumbleton Rooftop Terrace by FractalJam

I’ve reviewed an image similar to this by FractalJam in a recent post.  The upper one is the weirdest; they both look like some sort of elegant coffee table but the upper one has what looks to be a snowy forest diorama inside of it.  The lower one is more tropical and suggests a palm tree in the center of the top surface.

They’re very unique mandelboxes as well as very bizarre furniture things.  The coloring in the top one is exceptional.  One doesn’t often find such a combination of intense detail beside areas of no detail.  They complement each other.  I think it’s also a rule of design or something.

Beyond the Familiar, Into the Unknown by dainbramage

The compositioning here emphasizes the central ball node and the koch-like pattern on it.  I think that’s how it works.  The lighting just magnifies that effect.  This type of image is usually dull and monotonous but this one speaks and beams “enlightenment”.  The mark of mystery, the sound of silence; cave of the cosmic tree!  And the tree is covered with trees… the cave itself is a big tree… Where are the leaves?  Our thoughts about the tree are it’s leaves.  How long does summer last around here?

Autumn Leaves by Trafassel

Herr Trafassel, the author of Gestaltlupe and his famous Journey to the Center of the Mandelbox is back again with this very victorian and ornate looking leafy spiral.  Is is a coincidence that it happens to be called “Autumn Leaves” and just happens to follow the previous image of the leafless trees?

On a more serious note, this is actually an image made with the original mandelbulb formula.  It doesn’t normally produce such rich imagery except in Trafassel’s own program, Gestaltlupe.  Or does he have magic powers?

Buddhabrot_moshiahobrot_talis by Alef

This is from a FFs thread discussing Problems with implementing Budhabrot in UF.  There’s a whole bunch of interesting little “rough” images in it.  The Buddhabrot is a very captivating fractal as it often displays this kind of hazy but ordered kind of imagery.  The ghostly appearance and similarity to images of the Buddha have made this fractal an image class of its own.  The golden glow, the obedient sparks; something dharmic this way comes!

Fractal collection by National Post

See any familiar formulas here?  There’s a few that resemble julia sets.  Must be made with UF I’d guess since I don’t know of any other program that gets you that shiny, metallic look so well except for XenoDream or Incendia.  What’s the connection here with the other images in the post?  I’m sure you can see it.  You might need to view the high-res version to be sure.

The Curvaceous Columns of Coldinica by Madman

This one is fresh from the oven, Dec 3rd.  There’s an interesting note on the FFs gallery page:

Description:  Just playing around with MJB’s DE Combinate Technique. Thanks Mark!

That’s MarkJayBee I believe.  Isn’t this the sort of Antarctic city buildings imagined in HP Lovecraft’s novella, At the Mountains of Madness?

At any rate, the shapes and combination concrete/glass/grid construction here is something I’ve never seen even in a 3D fractal.  Clearly, we haven’t reached the end of the varieties of fractal experience.


“DEcombinate in Inv Max mode using: Menger3/Transform2IFS/ColumnsIFS/Trans-qIFS/TilingIFS” –from the image notes on the DA page.

If you view the high-res (1,600px × 800px!) you’ll see the variety of forms from that list up there.  But just looking at the low-res you can easily see that this is something that produces categorically different shapes and imagery.  Quite an exciting development; this one is only from Nov. 16.

Desert Fortress by Kali

This is such a beautiful image and yet it may appear to some to just a new rendering of a common fractal pattern.  It’s made with Fragmentarium, a program made by Mikael Hvidtfeldt Christensen and maybe that’s what gives it its special, spectacular look.

Of course, it could have something to do with Kali, too, who is well known for his deeply weird —livingfractal creatures (and a scary worm, too).  Kali is one of those people who is constantly creating interesting artwork as well as extending the capabilities of the medium itself.

I have often found that its not the developers themselves who get the best results from their programs but rather some user who just seems to have an intuitive feel for what the program does best.  It’s probably the same way with musical instruments and power tools, too.

The desert image is a careful balance between the extremes of  mechanical perfection (i.e. monontony) and slick surface rendering (i.e. obliteration of the subject matter).  These two things meet at the place where they compliment each other and the simple fractal pattern is transformed into an extensive landscape of fractal sand sculptures; each slightly unique and yet connecting with the others in similarities of shape.

MB3D_0174_hd by 0Encrypted0

These are not your Dad’s fractals.  Yet another example of how the fractal art tools are evolving.  I had to look carefully to find something in this image which would connect it in any way to the rest of the 3D fractals I’ve seen.  From the comment on the FFs gallery page, “slon_ru” seemed to share the same sense of wonder:

Is it mandelbulb3d?!

The sophisticated colouring further disorients me because the “alien swizzle-sticks” appear to be individually coloured although a few seem to betray the standard method.  It received a 5-star rating by five members which is quite something these days on FFs.  Unlike DA, where the comments and feedback grow “like lard on a pig”, the FFs crowd seem to be more absorbed with solving the latest math and graphical rendering riddles than concerning themselves with “who’s watching me?”

pain observer by Jesse

Fractal Cabinet of Dr. Caligari; or Aladin’s cave?  Did I just say that the authors of fractal programs don’t usually make the best stuff with them?  I’m guessing that Jesse used his own program here and what a stylish, non-block-like scene he’s found.  The red and blue, Cecil B. de Mille, Carlsbad Caverns, amusement park lighting is caused by the little lightbulb sources that one can orient and adjust in the program.  Most use them to just add light, but Jesse has used them to paint the walls with glowing color.

Well, there you have it.  Expect bizarre new sights in the 3D fractal world in the coming year;  I’m seeing the addition of a few more gears to the fractal engine.  And maybe a few folks will rediscover the potential of those flat fractals.  Does that sound like crazy New Year’s tabloid predictions?

The Epiphytic Art of Comments

Like the elegant orchids and other surface-dwelling plant species called epiphytes, image comments can have a richness and uniqueness that is surprising when one considers their tiny size and extremely casual origin.

And also like the epiphytes of tropical forests, comments can become almost as great, collectively, as the underlying tree they’ve attached themselves to, to the point of obscuring or upstaging the creature that gave them their dwelling place and opportunity to be.

But it’s a safe bet that comments are never going to die out as long as the synergy and mutually beneficial effects of leaving compliments and leaving personal hyperlinks endures.

But then, who would want them to?  They are the graffiti of our times which, like graffiti, started out as merely idle mischief and casual (senseless) expression but subsequently became the subject of art exhibitions.

Photograph by Dirk van der Made (user:DirkvdM). Epiphytes near Santa Elena, Costa Rica, January 2004. {{cc-by}}

In my journeys through the internet I found one particular “tree” on whose prolific collection of epiphytes was arresting.  Like their exotic counterparts of the tropical forest, I found some of them to be quite collectible and consequently have arranged them with digital pins below in a virtual specimen gallery.

Just to make one thing clear: I make no judgment as to the “beauty” or “value” of these comments –positive or negative– or even the image they were attached to.  Who needs to judge or point out natural beauty if it truly exists?

But I do add some comments of my own.  Even I can’t stop the natural growth of these things.

The Epiphytic Art of Comments

Artist bio excerpt:

From the sidebar of the image page:

The image:

The History of the Bioluminoidal Fractalization Process, by Rhonda Strickland, on Click image to visit original page.

And now an assortment of comments starting with some of the oldest and moving down to (some of) the more recent:

(comments were posted over a period of 2 years)

(-something beneath the sea?  Like something dark and murky?)

(nice and to the point.  Does the “~” mean something?)

(-a picture says a thousand words;  this one –a thousand and one)

(-that’s 3 encores)


(all day long…)


(–is she saying the image and music is great, or that she herself is blind and deaf?)


(–look at those two links.  Who’s being featured here?  The artist or the group?)

(–could there be another Fiery-Fire out there?  One on every art portal?)

(–yes, that’s what I was thinking when I started to read these comments)


(–another short, concise, Hemingway-esque comment, “She photoshopped.  She was good.”)

(–hey, this looks big!  Top Ten?  In the whole Fractal Universe!)

(–hmmmn… not all Top Tens are the same, I’m thinking)

(–2nd runner-up?  I guess you need to know Redbubble to know whether this is something to get excited about.  Looks like Rhonda knows Redbubble pretty good.  Me?  I would have said, “Beat it, Ushna!  It hurts just looking at that graphic!”)

(–didn’t he leave a comment before?  Or did he forget?  To err is human, to forget is “superb”.)

(–I just can’t bring myself to use more than two exclamation marks in a row.  I guess I need more practice.)

(–nothing impresses me more than awards with big, fancy, metallic spelling mistakes in them.  But then, who knows how to spell parallel properly these days?  I’m going to go look it up again.)


    (–the mysterious caps; the repetition; very stylish.  The artsy avatar suggests they might have something just as interesting on their site –and all you have to do is click…)

(–am I making fun of these people?  You get favved 50 times and then the Most Favorites Group favs you with the “fav of favs”.  I wonder what their idea of “success” is?  On the other hand; no spelling mistakes in this one)

(–finally, some intentional humour.  Deviants on Redbubble?  That’s comments to the exponent 2)  

(–“You are really great”  No matter how false or shallow, we all love to hear that, again and again…)


(–check out the moronic face in the volkswagen and how neither of the two vehicles seem to follow the obvious curve in the road that they’ve been cut and pasted onto.  Scary photoshop.  More like crashing edge than cutting edge.  Worse than a spelling mistake, in my mind.)

(–three minutes… but that really is a compliment if you think about it –in the online environment where there’s always something else to click on –like the commentator’s linked avatar and name)  

  (–grammar aside, where exactly are these people coming from if their blacklist is made up of: churches; political events; graveyards; or people?  On the other hand, if they’re that picky then being “approved” by them is really something!)

(–Yeah!  The avatar looks like he really means it.)

(–if this one didn’t crack you up good then you’ve either been reading too many comments like these or you’re the kind of person who posts comments like this.  She’d like to recommend this as Digital Art as soon as she can find out if it is Digital Art?  That’s far out.)

(–was it an animated gif and I took the screenshot before all the frames could load?  Or is it just another example of award images that are a parody of themselves?)

(–best of the bunch, my favourite of all of them.  “Absolutely stunning… have a great weekend”.  In the (post-processed) words of T.S. Eliot… “In the room the women come and go;  Saying “Rhonda, way to go!”)

Oh, do not ask, “What is it?”

Let us go and make our visit.

–TS Eliot, here

Well, I hope you enjoyed this lush example of art comments.  If you’re curious about the artist, Rhonda Strickland, you can see more of her work on her Redbubble page.  This particular image to which all these comments were made is apparently presented with music, although I wasn’t able to hear it myself.  She works in a number of genres in addition to fractal art, including that of poetry.

Don’t forget to leave a comment…

Arvinder Bawa’s Fractal Exhibition in Spain

Arvinder Bawa recently had a showing of his fractal artworks in Laredo, Cantabria, Spain at the Sala Ruas gallery.  The poster explains it best:

~Click on images to view full-size on original site~

Advertisement for Arvinder Bawa’s fractal art exhibition in northern Spain

Arvinder has written an interesting explanation to accompany the exhibit.  I like his simple language and layman’s terms:

…For the exhibition it is necessary to write a short explanation of what these images represent and it is hard to find the words to explain the process without drowning the reader in complex mathematics and iterative equation manipulation programming techniques. In an attempt to make a start in assembling this write-up, here is what I have come up with…The geometry of nature – Fractals – Order and Chaos

The images which makeup this exhibition have been generated by a computer program which follows the behavior of some mathematical equations that represent complex dynamics using complex variables. The behavior of these equations is represented by the images where the black regions are zones of stability and order and the brightly coloured areas are zones of chaos.

…it is only in the last thirty years with the invention of computers and high resolution plotters that we are able to enjoy the chaotic behavior in glorious and beautiful images…

…When we view the images it is as if we are in the presence of something cosmic and familiar, and this is because many of the structures in nature and in our surroundings behave in a similar way. The coastline, the structures in biology and botany, the behavior of populations and economies, the meteorology, cosmology and the study of turbulence in air and fluids all have elements of chaos which is essentially what we can see in the images in this exhibition.

~From Arvinder Bawa’s blog, Arvinder, Aug. 27th, 2012

“Behave in a similar way” –I like that.  What we expect from a branching tree or a crack in the road is what we expect in fractal imagery because they’re following the same kind of rules and “behavior”.  We are at home in both places because they are so much alike.

Arvinder’s work is admittedly a little “retro” as he states in the same blog posting:  “Images such as these were popular in the 80s and the 90s, and many books with wonderful images were published.”

Here’s a handful of thumbnails of the exhibition taken from Marisol Cavia’s Flickr page:

Fractals – The Geometry of Nature – an exhibition by Arvinder Bawa at the Sala Ruas, Laredo, Spain, Oct. 2012

Fractals – The Geometry of Nature – an exhibition by Arvinder Bawa at the Sala Ruas, Laredo, Spain

Thumbnails of some of the exhibited images found on Marisol Cavia’s Flickr page

Arvinder Bawa and colleague, at the Sala Ruas gallery, Laredo, Spain.

Arvinder Bawa, Cork Street, London, England, 2012

Well, what about it?  Why an exhibition of images that are so out of style in today’s fractal art world?  I don’t think the Sala Ruas gallery sticks just anything up on their walls for visitors to look at.  What did the curator of Sala Ruas see in these fractals that most of us, “up to date” fractal folks wouldn’t? (key word: most of us).

There’s been a lot of talk in the fractal world about “Takin’ it to the streets” and introducing the rest of the world to fractal art.  That’s supposed to be the whole idea around the BMFACs and yet Arvinder’s work is precisely the kind of “garish, 70s-style imagery” that the BMFACs hope to erase from the world’s memory.

One thing I’ve realized from a decade of watching the fractal world is this:  I think the fractal world understands the art world to the same degree that the art world understands the fractal world.  That is to say, very little.

We can laugh it up all we want about work like this but someone thought this was worth exhibiting in an art gallery.  I wonder what they’d think about our fractal artwork?

The fractal art world as a whole is as eccentric as the math and programming that goes into creating the imagery.  Arvinder Bawa is one of us because he’s found something in fractals worth looking at and drawing other people’s attention to.  I can’t think of a better definition of “artist” than that.

…Plenty of room at the Hotel Fractalfornia

~Click on images to view full-size on original site~

bilding by ZZZ_spb

Just a neon sign, cloudy sky and moon, but what a transformation.  A number of 3d fractalists refer to having an “architectural style” and here you can really see what’s meant by that term and why it is such a natural one in the world of 3d fractals.  Nice and subtle addition to an otherwise average mandelbox.  ZZZ_spb really shines at this sort of thing.

Encapsulation by MarkJayBee

Another example of subtle but powerful.  This is not a terribly exciting mandelbox but the clear box Mark put around it and especially the way he’s colored and textured it’s surface has transformed the simple image into something fascinating.  I don’t think Mark was really trying to make something noteworthy here, just experiment with this inclusion feature of the program. But the final result is great.

Handshaking Buds by Kali

Made in Fragmentarium, a bold new program by Syntopia for making weird, terrifying things like this.  Although, like Mark’s image above, I believe this image is something of a technical experiment rather than an attempt to create art in the strict sense of the word (and what does that mean?), the result is something quite unique and almost humorous as well.  Humour in fractal art?

The power of fractal recursion to repeat things on smaller and smaller scales works quite an artistic effect here in the little shaking hands in the mid-foreground (bottom, center).  You might need to view the hi-res version to really appreciate it.  Next they’re all going to buy the world a Coke…

Growing Phantasma by lxh

Is this what ZZZ_spb’s hotel looks like in the morning?  Well, it’s by lxh, another screen name I’ve been unable to decipher.  Maybe’s that the idea behind these screen names.  Someone ought to compile a list so we can at least decode them from time to time.

Lxh says this about the image on the gallery page:

Description: This might be what we see – a foreign city or complex – but in fact it’s the virtual manifestation of thoughts, ideas and efforts of the fractalforums scene and at least stage of my personal fractal journey.

Greetings to all you fractal travelers and explorers out there. May the shape be with you. And many thanks to all the gurus who made my journey possible: Daniel White, Jesse, Tglad, Kali, DarkBeam and all the other genius behind. You are my heroes …


DURING the whole of a dull, dark, and soundless day in the autumn of the year, when the clouds hung oppressively low in the heavens, I had been passing alone, on horseback, through a singularly dreary tract of country ; and at length found myself, as the shades of the evening drew on, within view of the melancholy House of Usher.

(excerpt, The Fall of the House of Usher, by Edgar Allan Poe)


On a dark desert highway, cool wind in my hair
Warm smell of colitas, rising up through the air
Up ahead in the distance, I saw a shimmering light
My head grew heavy and my sight grew dim
I had to stop for the night

~lyrics, Hotel California, by the Eagles


Menger on the beach by SaMMY

Made in Structure Synth by SaMMy.  He says this:

Description: I tried to build the mengerbox in a chaotic style – i hope you ENJOY  embarrass

Created in Structure Synth ( ~96000 Objects),
rendered in Vue Xstream ( ~9,5 Mill. Polygons, global radiosity),
little corrections in Photoshop.


Nice, California look.  The sunlight reflects off the water and off the ceiling of the middle cavity; nice touch.  It resembles those 3d Bryce images that incorporate obviously artificial elements and yet have been seamlessly wrapped in the environment around them as if they grew out of it –right there.  In fact, this menger sponge structure looks like a ruined or dilapidated tropical building.

Crumbleton by FractalJam

“Her mind is tiffany-twisted…”  I see this as an extremely unusual coffee table and of course, the sort of thing that would only reside in a rather wealthy, luxurious kind of place.  It’s an interesting “thing”.  Made of glass; too delicate to be used and thus… tiffany-twisted.

Her mind is Tiffany-twisted, she got the Mercedes bends
She got a lot of pretty, pretty boys she calls friends

~Hotel California

ExoExhibit by MarkJayBee

Mirrors on the ceiling,
The pink champagne on ice
And she said “We are all just prisoners here, of our own device”

~Hotel California

You know, if they had 3d fractals back in 76 when Hotel California came out, then they would have used them for the album cover.  I’m assuming you know what an album cover is.

Mark’s image here uses reflection very well and creates images within the image –of itself!  “Prisoners… of our own device”  As always, if you want to get all the thrills this image has to offer, you need to click on it and see it full-size.  Or check out the mammoth version in Mark’s Deviant Art gallery.

Xenotransplantation by “aka FLUX” (on Flickr)

If you look closely you will see the rough, bud-like points of the mandelbulb.  However, this is not really a 3d image as you might have guessed and has been creatively layered and other things to produce this beastly looking creature.  (Pressed mandelbulb?)  As the title suggests, it’s a combination of various animal tissues –transplants.

From the Flickr gallery page:

Xenotransplantation (xenos- from the Greek meaning “foreign”), is the transplantation of living cells, tissues or organs from one species to another.


A continuing concern is that many animals, such as pigs, have shorter lifespans than humans, meaning that their tissues age at a quicker rate…

I like the symmetry.  Symmetry can give a surreal feeling implying this macabre concoction has morphed into a coat-of-arms symbolizing authority and pride instead of revulsion and fear.

And in the master’s chambers,
They gathered for the feast
They stab it with their steely knives,
But they just can’t kill the beast

~Hotel California

Autumn colors1 by Pauldelbrot

Nice coloring, interesting “zipper of the infinite” content, as well as the old “fractalscape” endlessness that is always eye-catching and reminds us that fractal art is playing with power –graphical power.  Which recursion to follow?  Paul’s next image in the series zooms into the green area, which looks small in this view but expands into the infinite in the next.  So many places to go…

Last thing I remember, I was
Running for the door
I had to find the passage parameters back
To the place I was before
“Relax, ” said the night man,
We You are programmed to receive.
You can check-out log-out any time you like,
But you can never leave! ”

~Hotel California

Album cover, Hotel California, by the Eagles, released in 1976 just a year after the term, “fractal” was coined by Mandelbrot (and playing ever since in endless recursion and perfect self-similarity).  Click to view back cover, inside, record sleeves, etc…

Simple album cover; just a neon sign, hazy sunset and some colonial architecture.  Computers have changed a whole lot since then, but art is still the same.

Plenty of room at the Hotel California
Any time of year (Any time of year)
You can find it here

~Hotel California

Listen to the Original song on YouTube

“Some dance to remember, some dance to forget”