Rebooting Fractal Art: Part 4

Pixel Art vs. Parameter Art

In my preceding three parts I have dealt with what I see are the limitations of fractals for making artwork.  To put it simply, the geometric imagery called “fractals” has a natural bent towards the decorative and design type of art work.  Artists who attempt to create more serious kinds of artwork with fractals have an overly optimistic view of their artistic potential and a view that at this late stage in the development of the genre is no longer justified.  Fractals are objects of sometimes intense graphical beauty, but frustrate even the greatest efforts at intellectual expression.  They are a source of simple graphical imagery whose “message” is never anything more than a strange new beauty born of mathematics and computer science.  Trying to present them as anything more refined and articulate is just pretentious.

At the core of all this is the way fractal art is made.  Fractals are made from geometric formulas and other graphical algorithms that give them their visual appearance.  These algorithmic origins are both the strength and the weakness of fractal art.

Strength:  Fractal algorithms quickly generate wild and incredible panoramas whose size and scope is literally on a galactic scale.

Weakness:  Algorithms are rigidly deterministic and we interact with them only in those aspects of which the parameters are adjustable.

What I want to talk about now is two different approaches to making fractal art.  One is what I call Parameter Art and the other is what I call Pixel Art.  Parameter Art is made entirely within a fractal program while Pixel Art only begins with the imagery a fractal program makes and extends the creative process by transforming it in a graphics program like Photoshop.  The two methods of making fractal art have been around for quite some time although Parameter art is by far the most common type today, while Pixel art, referred to as “post-processed” art in the past, has almost disappeared from the fractal world.

Different File Types

Images made entirely from parameters are similar to vector images which can be drawn at any size because the “image files” are not really images at all, they’re the stored blueprints, the instructions for drawing the image.  Common image file types like jpg, gif or png are bitmaps and simply store the pixel pattern that you see on your computer screen.  They’re no different than a screenshot or photograph of a fractal and contain no fractal formula or any other kind of rendering information.  A bitmap is derived from a fractal formula, it’s no longer connected to it –the end product.

Parameter files are used to generate fractal images in a fractal program while pixel files are just a bunch of colored dots (pixels) stored as a map just like a huge digital mosaic.  There’s a fundamental difference between these two types of files when it comes to working with them.  With parameter files you can alter the elements of the image and change it’s structure and other things.  With parameter files you work with the underlying algorithms that draw the image but with pixel files all you can do is alter the little pixel tiles in that big digital mosaic called a bitmap. By way of illustration, pixel files become a group portrait of a crowd of people while parameter files contain the actual people.

Parameter files can be more complex and incorporate other algorithms.  With the latest version of Ultra Fractal, one of the most popular programs, a great many more algorithmic things than ever before can be combined and tweaked like a graphical orchestra of algorithmic instruments.  But jpgs and other pixel files are one time deals that can only be adjusted and worked on in pixel based graphics program like Photoshop and many others.  You can only work on the pixels because that’s all that pixel files contain.

Parameter files = algorithms = fractal programs
Pixel files = pixel dots = graphics program

Obi wan Kenobi and the Post-processing Jedi Knights

Long, long ago in a galaxy far, far away… fractal artists used to argue about something called “post-processing”.  That was the processing of fractal generated pixel files in graphics programs after (post) making them in a fractal program.  It caused considerable controversy back then (c 2000), but today one hears little of this sort of thing in fractal circles.

The controversy was never resolved; what happened is that over the years fewer and fewer fractal artists post-processed their work (apart from minor enhancements like sharpening or anti-aliasing, which don’t really count) and so the post-processing debate just faded away.  Today almost all fractal artists create fractal art by adjusting and transforming the parameters of algorithms in fractal programs and not by transforming the pixel patterns with graphical effects in a graphics program.  Today’s fractal art is a parameter-based art form, not a pixel-based art form.  The final image is produced by a parameter file in a fractal program and not by processing in a graphics program.  The creative work is all done in a fractal program.

The great benefit of working entirely within a fractal program with parameters is that you can regenerate the exact same image at huge pixel sizes for printing out in high quality and you can rework those algorithm collections with new additions and collaborate with others in the ever popular, online “tweak-fests”.  It’s an aspect of fractal art that makes it unique –a sophisticated, programmable drawing machine.  This sort of technical power of high resolution rendering helps to give parameter art a more professional reputation among some.

But working solely with parameters is also an aspect of fractal art that limits it’s creativity and homogenizes its style.  Parameter art is algorithmic art and algorithmic art is limited only to those aspects of the image for which options are available.  No big deal, right?  Think of all the different things that can be altered in a multi-layered, complex fractal formula made in Ultra Fractal.  Plenty of room for creativity there, you’d probably say.  And many will agree.

Yes, but what one fractal artist can do to change a parameter, almost (almost) any other fractal artist can also do.  And the huge number of options available doesn’t mean much because unless one drastically changes the coloring and other rendering options, as opposed to simply the formula options, everything comes out looking like a variation on a theme because it’s all rendered in the same style.  You can get 50 different fractal images but they’re all made of the same stuff and rendered the same way.

I once stumbled on an online gallery made by someone who used the same fractal program I did.  They had a few images that looked very much like ones I had made and for which I had posted online along with the parameter files.  At first I was certain they’d “tweaked” my parameters and produced a “new” image by zooming in on some other part of the image created by my parameters.  But as I studied the image I began to see aspects of the coloring and general rendering that weren’t quite the same.  Finally, despite the general appearance of the image I decided that it was quite possible that they’d stumbled on a very similar rendering mixture all on their own.  They probably had never even seen my images or played with the parameters.  Why not?  Engineers often accidentally stumble on previously discovered and patented processes all on their own.  It ought to happen even more in the world of fractal software.

Yeah, I know.  “Think of all the variables involved and all the different ways layers can be merged or masked in Ultra Fractal.”  If you think all those parameters are an infinite creative playground for fractal artists then why does so much fractal art –and I’m talking about the better examples of it–look so much the same?  Or better yet:  Why do fractal artists not have identifiable styles?  I’ll tell you why: because fractal artists don’t work with the pixels.  It’s because they don’t post-process their work and avail themselves of the thousands of weird and not so weird graphical effects and filters that transform images much differently than the standard ways fractal programs do.

Parameter art tends to converge on a few successful looking rendering combinations (like my online rival did) while pixel art tends to diverge from those few styles because graphics processing provides many more options and they can have such a radical effects on the image.

Essential differences

The essential difference between parameter and pixel art is the difference between making fractal art entirely within a fractal program and instead using the fractal program as the beginning of a process that ends in a graphics program.  The output of a fractal program, although, strictly speaking, a pixel-based, bitmapped image, can be stored as a parameter file and that’s it’s defining quality: fractal program art–parameter file art.  The output of a graphics program although it can also be a multi-layered file format, is essentially a pixel thing, a bitmap.  In fractal programs one works with parameters and in graphics programs one works with pixels.

Despite the fact that both processes are “art with fractals” the characteristics of the two processes are quite different and diverge from each other in terms of final results.  Parameter art is restrictive and standardized, while pixel art is almost unlimited and produces more individualized results.  Pixel art therefore has greater creative potential and subsequently is the path that creative fractal artists ought to pursue.  Parameter art, with it’s deterministic, predominantly rule based methods of generating imagery appeals to people who enjoy the technical challenge of working with formulas and algorithms more than making weird and novel kinds of imagery.  Their perspective on fractal art I suspect is different from the post-processors.

A natural development for fractal art

Pixel art is a natural extension of fractal art for the graphically creative, while parameter art is satisfying only to those who are technically creative.  They see the confines of algorithms as a creative challenge of its own kind in the same way that designing better machinery is a creative puzzle that requires one to work within the limitations of the materials, laws of physics, and functional goals of the desired machine.  Or like the rules and boundaries of a sports game which one must master and respect if they want to play the game successfully.  Parameter art is an engineer’s kind of art form.

It’s not like one is art and the other isn’t; or one is better and the other isn’t.  It’s the results that one should evaluate and not the methods.  But I’ve observed that parameter fractal artists consistently produce the kind of work that would be expected from such confined methods while the post-processors produce work that is more individualistic and varied –as would be expected from a more divergent and wide ranging set of graphical options.

The Sciences and the Arts are both valued aspects of civilization.  Progress in the Sciences is measured in making discoveries, while in the Arts progress comes from creating new things.  Both are highly challenging fields but one is the challenge of discovering what is there but not previously known while with the other the challenge is to make things that never existed before.  I see connection between parameter art and scientific discovery and a different connection that joins graphical creativity to pixel art.  Most of the people engaged in fractal art today are of the science group and they make the sort of artwork that impresses their colleagues.  I’ve never been able to understand why more fractal folks don’t experiment with graphical filters.  But now I do:  To them that’s something completely different.

Formula in; Formula out

Fractal art is primarily parameter art today and that has given fractal art it’s distinctive look: formulaic and standardized.  Working solely within a fractal program with parameters is not going to allow artists to distinguish themselves or produce stylish, individualized artwork.  The parameter art method is homogenizing fractal art.  But it’s a natural outcome for fractals and not the fault of the artists, unless of course one can blame them for working entirely within a single program “dedicated” to fractal art.

Dedicated, yes; but not to artistic creativity.  A fractal program’s dedication is to generating fractal imagery.  It only becomes a limitation when one choses to make it the limit to fractal art.  It will greatly expand the creative horizon of fractal art to step beyond the boundaries of fractal algorithms and the simple in-house processing that fractal programs allow.  Furthermore, it begs the question, “Why is processing a fractal image, even to the point of distorting its shape and degrading its details, considered to be a different kind of fractal art when the multi-layering and masking abilities of Ultra Fractal produce similarly altered images?”

The answer is that UF processing is done entirely within a fractal program (i.e. working with parameters).  If you find that answer to be lacking in substance, then I think you’re beginning to see things more along my lines and are putting graphical creativity ahead of fractal algorith-mity (high five).

But in defense of the parameter artists, working entirely within a fractal program like UF (for example) allows you to produce artwork that can easily be rendered large enough for good sized, quality prints.  Actually, for any sized quality prints.  This in turn allows one to produce clean, smooth fractal structures in the same slick way that vector artwork looks sharp and crisp.  Once you start working with pixels you’re restricted to the current image size in your graphics program.  Unless you repeat everything over again starting with the same fractal image generated at a larger size.  But that sort of thing is hard to reproduce.  That’s why pixel art is so unique: often the artist can’t remember everything they did (or is it just me?).

But you can’t really say that Photoshop lacks the ability to produce large size, print quality images?  I process almost everything I make from fractal programs and I work at a resolution that is, at the most, slightly smaller than my monitor’s screen resolution.  But that’s just because it’s easier and I’m not interested in producing prints.  My favorite size is 600×600 pixels and it looks just great on a computer screen.  But that’s not where it’s at these days.

Pixel artists can produce big work, they just have to plan it out ahead of time.  In fact, there are some processing “syndromes” I’ve discovered that actually look better when you scale up the final image.  That goes against everything we’ve known about fractal art; scaling down (anti-aliasing) is what makes images look better.  Perhaps this is an example of how the creative options can be much larger and more unpredictable in the pixel world.

Your fractal art is missing something

I’ve often exalted the creative powers of purely algorithmic, “machine-made” art.  Algorithms create things that no human mind would ever make or conceive of.  But I’ve come to realize that because processing had become second nature to me, I was unaware that I was always talking about processed algorithmic art.  Fractal programs often produce neat looking things and they don’t need any help in doing it …but I’ve always gotten “better” neat looking things from adding the second machine, the graphics program.  On a technical basis one can easily call this something different than fractal art, but from an artistic perspective the results are simply enhanced and perfected rather than distorted and degraded.  Fractal artists I believe have for too long made the assumption that fractal art is art made with a fractal program.  Such a belief is not only the creative castration of fractals as art, it’s a purely arbitrary convention.

Graphical, non-fractal, processing takes place in all fractal programs at the very beginning of image creation.  There is no such thing as a pure fractal rendering as fractal formulas do not produce visible images (visibility is important in art).  All they produce are big, very detailed sets of data points.  Think of a gigantic bulletin board with pins stuck into it according to the direction of a formula.  How you choose to decorate that thing is what is called “rendering”.  Rendering options are the choice and provision of the program author and the selection of the user.  For instance, there is no standard or “natural” image for the famous mandelbrot set.  In almost every program the image you see is different in terms of colors and particularly in terms of the style in which it’s colored.  It’s a purely arbitrary choice: compare various programs, there’s no such thing as a “natural” fractal rendering.  (I’m a non-technical person and even I’ve figured this out.)

So you see, all fractal images are to some degree processed or arbitrarily enhanced.  I say “degree” because the sort of rendering that goes on in fractal programs usually serves to expose and make visible the details of the fractal formula rather than to color over or do something transformative with it.  Although layering (depending on how complex and heavy it is) is something quite different, that is, it’s results are not algorithmic unless merging the results of two fractal formulas can be seen as “mathematical” creation.

Fractals that aren’t fractal

What then does fractal art “lose” when someone transforms it in a graphics program?  It can certainly lose some of it’s details and fractal structure, but doesn’t that happen when one layers and masks in UF (and layers ten or twenty times?) and produces the sorts of images I wrote about in a previous posting, Sheets in the Wind and Rings of Gold?

I guess it’s not fractal art if you can’t recognize any fractal structures in it?  Like if you really process it into something unrelated to what you started with?  But like I said about Sheets in the Wind and Rings of Gold, images like that are already by-products of fractal formulas, features contributed by the non-fractal rendering methods, and have diverged as far from fractal art as anything created purely in Photoshop.  Whatever fractals can lose in being processed, images like those never possessed in the first place.  Even a chopped-up or lens distorted fractal image is more fractal than they are.  It appears that UF is fully capable of producing plain old digital art as well as fractal art.  For reasons like that, we ought to have a looser, more inclusive definition for fractal art.  In fact, a strict definition is not really possible if the varied rendering styles (and layering features) of fractal programs are considered.  Processing has been programmed into fractal art from the beginning.

Pixel processing doesn’t follow the cow paths of fractal algorithms and gives stale old fractal imagery some fresh options.  The label, “fractal art” might not even necessarily apply anymore.  But then many of the layering and other fancy features of Ultra Fractal create imagery that defies a simple definition of fractal art.  But Ultra Fractal is a very simple and scaled down post-processor, probably because it was designed to incorporate only the subtle, enhancing types of post processing.  Much more powerful post-processing can be done in freeware graphics programs, especially those that utilize Photoshop compatible plugins and filters.  Most fractal artists probably don’t see Ultra Fractal’s graphical features as post-processing because they’ve come to accept them as a natural part of making “fractal” art.

Real artists get itchy

So if the old, post-processing thing is such a quantum leap in creativity, then why don’t more artists do it?  It’s simple, really:  Because they’re not artists.  Artists don’t conform to standards or keep working on the same old things like the old craftsmen in the fractal art world do.  Artists crave novelty and are inherently drawn to create; and “to create” means to make new things, not polish the old stuff up or tweak to perfection imagery that lacked style in the first place and only possesses technical merit.  Fractal programs are the comfy home of the technical “artist”.

(Like I said in my comparison of science and the arts: one pursues discovery while the other pursues creativity itself.  Some fractal artists deny the label artists altogether and describe themselves entirely in technical terms like programmer, mathematician; and describe their innovative work as “test renders”.  There are two different mindsets at work in fractal art and the results they end up with are categorically different.

I’ve given a number of reasons in my last posting, Part 3, why fractal artists don’t deserve to be called artists and how their belief in a “serious” fractal art form is nothing more than a collective fantasy perpetuated by their own isolation and the avoidance of criticism and external standards.  But now I say that the biggest reason that fractal artists fail as artists and their art form fails to evolve into anything other than decoration or neat designs, is because they’re more comfortable doing what they see others do than doing what they don’t see others doing.    They’re more comfortable doing what has been done rather than doing what hasn’t been done.  They’re a small clique of imitators when they ought to be a more loosely knit group of experimenters and innovators; repelling as much as attracting each other.  Artists are the classic iconoclasts, radicals, eccentrics and non-conformists in any society.  But in the fractal art world, the artists are lapdogs and sheep.  Maybe art was never part of their equation?

Fractal artists who stick to just fractal software are not really artists but rather just fractal buffs.  They have, perhaps unintentionally, defined their domain so rigidly as to make it a closet with respect to creativity.  Fractal programs alone do not have enough graphical options to satisfy creative people.  Fractal software exclusivity is why the “fractal” art genre is advancing only on the technical front and producing new work only of technical merit, while artistically the genre stagnates.  If fractal art is defined only as imagery made with fractal software then it will only be composed of work that has technical interest.  It will continue to be a craft rather than an art form, possessing artistic potential but never realizing it.


Fractal algorithms, that is parameter art, is a cul-de-sac; it’s a nice quiet place to settle down, but a dead end for anyone trying to go anywhere.  Fractals have been called abstract art but that’s not really the best description.  Abstract art, the hand made kind, is much more creative and open to a wide range of imagery.  Fractals, and all algorithms, as I’ve been saying, aren’t like that.  Although they aren’t realistic, obviously, they’re not abstract either, they’re better described as geometric.  But this means they lack both the attributes of realistic as well as abstract imagery.  Geometric imagery can be wonderfully ornate and, like all algorithmic art, easily made, but each new algorithm just forms another short cul-de-sac in a neighborhood of similar, pretty but dead-end streets.  Fractals look like fractals: real mathematical constructions, which are neither realistic or abstract.  That’s another reason why fractal art isn’t just another artistic medium but is instead something that requires more a careful consideration and a second look.  Fractal art is something new and unique in the graphical realm.

I believe the reason why fractal art has failed to attract any serious artists or art talent is because any reasonably skilled artist can see how rigidly deterministic the process of creating fractal art is.  Fractal programs are not the sort of thing that a serious artist looking to make innovate work and establish a distinctive graphical style would chose as a tool.  Similarly fractal artists will only begin to break out of the creative cul-de-sac they’re in when they extend their tool set to include graphics programs and not just fractal programs.  Even if that fractal program is the great Ultra Fractal, deluxe, feature rich and all that.

Venture beyond the walls

Fractal artists need to start looking at fractals as the start of the creative process and not the final result.  What comes out of a fractal program is too raw and immature as far as computer art goes.  At the very least one needs to experiment with color!  Good color is the one ingredient that always makes me take a second look at a fractal image.  Color is almost a language and art form all its own.  But fractal programs just paint the algorithmic structures, they need to work on the whole pixel canvas.  At any rate, experimentation is what is needed and what ultimately leads to more creative results.  There’s more to color than just changing the palette.

Bad art is a self-limiting disease.  If any of what I’m saying is true, then fractal art as it is today will not develop any sort of audience beyond it’s own practitioners and the occasional curious onlooker because it only indulges their own narrow interests and narrow set of rules.  We might like fractal art because it’s fractals, but why should anyone else?  We need to make artwork that engages an audience not just our friends.  The fact that it was “made with fractals” might make it an interesting conversation piece, but it doesn’t mean much in a wider, artistic context if the images are boring.  Fractal art will never be much more than synthetic nature photography without broader graphical experimentation.  Fractal art needs to incorporate graphical as well as algorithmic experimentation.

And if the results aren’t truly fractal? and can’t quite be called “fractal” art?  Well, I’d say worry about that later and first try to make more appealing artwork with more of a sense of style and individuality.  Frankly, much of what has been exhibited at the Benoit Mandelbrot Fractal Art Exhibitions blurs the boundary of what is fractal art and what is just computer art.  The fact that most of those images were made in Ultra Fractal doesn’t mean that what they’re displaying is the product of a fractal algorithm.  And yet they all lack artistic style.  They embrace the acceptable processing of UF but block the full featured processing of pixel art with arbitrary requirements for huge, scalable (i.e. parameter) images.

Joining the Digital Art world

There are more things you can do with pixels than with fractal algorithms.  I remember reading a comment made online by Garth Thornton, the author of XenoDream when responding to a thread that was trying to come up with a definition of what fractal art is.  His response was that fractal art ought to be trying to move into the larger realm of digital art as a whole and not trying to limit itself to some self-prescribed box.  At the time I thought he was conveniently dodging that perennial, “what is fractal art?” question, but now I see the wisdom in what he was saying.  Moving more into digital art means graphical –pixel– processing, not more refined algorithms and fractal parameters.

Pixel art is an easy and uncontrolled kind of graphical creativity.  Combining and recombining a series of effects and developing new “syndromes”.  It allows one to take apart the process and rebuild it by applying effects in different orders and with different starting points.  Fractal algorithms easily produce a high quality raw material for such graphical processing especially as they can create non-compressed, cleam bmp format imagery.  Applying graphical effects to heavily compressed jpgs often serves only to accentuate the compression gradients.  (In fact, jpg compression is something of a graphical effect of its own.)

Well, I still have one more part in this series planned.  It’s all about the road ahead, what’s next for fractal art.  I intend to talk about what I think all this stuff I’ve said in these first four parts means for the future of fractal art.  I think I’ve gotten a better grasp of what fractal art is, and isn’t, and the art form is more exciting now.  I think it’s more exciting because the pretense and expectation of making fine art has been done away with.  Fractals are free to just be the simple but strange things that have been since the beginning.

2 thoughts on “Rebooting Fractal Art: Part 4

  1. “Fractals are objects of sometimes intense graphical beauty, but frustrate even the greatest efforts at intellectual expression. They are a source of simple graphical imagery whose “message” is never anything more than a strange new beauty born of mathematics and computer science. Trying to present them as anything more refined and articulate is just pretentious.”

    One day long, long ago in a uni math class we were studying a famous theorum. I don’t recall which one, but I do recall how that experience literally moved me to tears as I experienced its incredible beauty. This wasn’t an ‘intellectual’ experience, it touched my heart, my soul, it moved me deeply.

    My classmates thought I was a bit strange, but after the class the professor called me up to the front and just hugged me. We shared that profound experience of beauty. It wasn’t ‘strange’, but it was very ‘refined and articulate’, and anything but pretentious.

    Unfortunately not many people can appreciate that beauty, just like most won’t appreciate the sublime beauty of the late Beethoven string quartets.

    There is an innate beauty that can be found in fractal mathematics. Some of it may even be deep, profound. As a fractal artist one can perhaps find those jewels and make them visible to a viewer who may not be able to appreciate the pure mathematical beauty.

    “Art does not reproduce the visible, but makes visible.”
    -Paul Klee



  2. I’ve been following this series, waiting with anticipation, to see how it would play out. Initially the first two posts rattled my cage. That is a good thing as it helped define my own position and opinion. Once I was aware of that, it freed me to investigate your proposition. This post has helped refine and consolidate my definition of fractal art and surprisingly (or not) we are in agreement, so far. Technical proficiency preceeds creativity in my workflow. A mastery of the medium and tools creates a comfort zone to venture in and out of.

    Looking forward to the next post!

Comments are closed.