Are atomic explosions a type of fractal art?

Yep.  They sure are!

See if you can guess what fractal program made this one:

U.S. shot MIKE of Operation Ivy, 31 Oct 1952

Oh.  You guessed wrong.  But that’s understandable.  You see, the entire fractal generator that made the explosion was destroyed in the making.  Fast rendering time!  –but it only works once!

The Ivy Mike "Sausage" device before detonation.

I think they called it “Ivy Mike” because they weren’t sure if it was going to be a boy or a girl.

Sunsets are a cliche, aren’t they?  It’s the sort of art that beginner painters and beginner photographers make on their summer vacations.  Well, at the beginning of the Atomic Age, we were all beginners.  Here’s a nuclear sunset:

U.S. shot KING of Operation Ivy, November 15, 1952

This one reminds me of Monet.  Maybe it’s better than Monet.  It could sure blow Monet’s lilies right out of the water!

So hot and yet so cool!

Painted on black velvet; I love it! This one's going in the living room.

We don’t think of atomic weapons testing as fractal art because it’s not made with a computer.  But there’s been as much tweaking done to them as anything on the Ultra Fractal mailing list.  The early artists wouldn’t recognize today’s nuclear weapons.  They don’t look anything like the fractals made on the old Amigas.  Things have really changed.

The Past is sending signals

I like to go back to the old days and ask, “What if?”

What if… the biggest fractal ever made left a radioactive hole so deadly that even today we can only look at it from Space?

What if… I showed you a sunset so huge and fiery that it just blew you away? you'd say, "Wow!"

~photos from Wikipedia Wikimedia Commons Operation Ivy

Cellular Automata Escapes from the lab!

~Click images to view on original site~

Textile Cone Snail (Conus Textile)

Doesn’t this just freak you out?  I’ve actually held a few seashells like this in my own hand and seeing that computer art pattern on such a natural and living thing is just deeply weird.

We’ve all seen fractal patterns in broccoli, pine cones and spiral snail shells but for some reason those things just looked natural.  I guess fractals patterns are just plain natural looking while cellular automata is quite distinctively artificial and machine made in appearance.  Except for these seashells, of course.

Some living things use naturally occurring cellular automata in their functioning.

Patterns of some seashells, like the ones in Conus and Cymbiola genus, are generated by natural CA. The pigment cells reside in a narrow band along the shell’s lip. Each cell secretes pigments according to the activating and inhibiting activity of its neighbour pigment cells, obeying a natural version of a mathematical rule. The cell band leaves the colored pattern on the shell as it grows slowly. For example, the widespread species Conus textile bears a pattern resembling the Rule 30 CA described above.

-from Wikipedia, Cellular Automaton

Here’s what that “Rule 30” CA looks like:

Rule 30 CA pattern generated from's online generator

Here’s a whole family, a taxonomic family called conidae, with other CA rule 30-ish patterns:

Conidae family reunion sporting characteristic CA-30-ish patterns. Photo by "Pet" on Wikipedia CC-SA

In addition to Cellular automata, these seashell patterns also remind me of those old dot-matrix printers that back in the old days would have been used to print really cheesy looking graphics (back when ascii art was cutting-edge stuff).

But hold that thought for a moment; that’s the way these CA patterns are made: one line at a time.  Or rather, one row of cells at a time.  The shell pattern is the printout from the row of pigmentation cells and thus the shells display a matrix of dots –dot matrix CA printing.

Conus bengalensis

Conus aureus

Maybe you have to be as excited as I am about CA patterns to feel the enormity of all this.

You know, if they ever drop the bomb and civilization as we know it disappears and there’s no more electricity and computers and internet, we can still have computer art galleries made of Cellular Automata from these kinds of seashells.  In fact, considering how durable the material they’re “printed” on is, they may be the only kind of computational art around in the distant future.

A Journey to the Center of the Mandelbox

~Click images to view on original site~

Professor Trafassel leads the way

A new and wondrous discovery in the land of 3D fractals has been made by a veteran Fractalforum member, Erp Trafassel (trafassel).  You can read the soon to be famous thread on Fractalforums.  Daniel White (twinbee), who sparked the original 3D fractal quest for the “Holy Grail” that resulted in the Mandelbulb had these remarkable words to say about Trafassel’s recent discoveries:

Amazing stuff trafassel. This is surely much closer to what I originally envisaged for the real 3D Mandelbrot than we’ve ever seen before. We’re seeing all kinds of designs, giant 3D connected networks, tunnels, arrays of tentacles, intricate satellites, foamy materials, shapes we’ve never imagined, and of course, the return of the spine also! (closer to what I thought the 3D spine should look like). I love the zoom near the end of your video too.

If I were to give the Mandelbulb rating of how close I thought it was to the holy grail, say, 5/10, I would give yours perhaps 7 or maybe 8/10. I still think there are subtle and not so subtle things which prevent it from being the holy grail which I’ll try to elaborate on soon. In particular, there’s a feeling that many of the shapes have a somewhat IFS feel to them (over-smooth or chopped up spherical surfaces etc.), and of course the overall shape is not what we might expect.

…which I’ll try to elaborate on soon”  Sound like the game is “afoot” as Sherlock Holmes often said when discovering an intriguing new challenge.  Trafassel posted two YouTube videos in which he conveniently compiled a series of images documenting his latest discoveries as a video slide show.  This is as much a scientific and technical discovery as it is an artistic one, so look carefully for new structures and imagery.  It’s just like a space voyage or the photo stream coming back from a probe sent off to explore a distant planet.  Like Tom Lowe’s (Tglad) initial Mandelbox images, many of Trafassel’s images here are quite spectacular to see as well as to appreciate for their technical achievement.


I quoted Daniel White just to give you a quick idea of the great significance of what Trafassel has achieved, but it seems to me from reading the thread that Trafassel stumbled on all this entirely on his own while exploring various new parameter settings for the Mandelbox formula.

It all started on September 21st, 2010 with Trafassel’s very brief and humble opening post to his new thread, Inner view of the Mandelbox:

The Mandelbox, but seen from the Inside. This means a voxel is visible, if and only if its coordinate is no element of the Mandelbox set.

Screenshots from tell the story better:




Trafassel then goes on to share the parameters and explain them.  Which raises the obvious question in most readers’ minds,  “What program is he using?”

Much or all of the 3D fractals currently are being created using Krzysztof (buddhi) Marczak’s Mandelbulber and Jesse Dierk’s Mandelbulb 3d, and also Ultra Fractal with Dave Makin’s MMFwip3D formula.  I can’t really tell by just looking at the images to say what they were made with and I don’t actually use any of them myself, either (I’ve been too busy watching what everyone else is doing, lately).

Maybe I’m wrong about this, but it seems to me that Trafassel’s Journey to the Center of the Mandelbox has been made exclusively in a machine of his own design and manufacture?!  Yes, there seems to be even more software spinning off of the Fractalforum’s talented group of developers: Gestaltlupe 0.9 available for Windows developed by Herr Trafassel himself.

He describes the program, hosted on, as “Representation of tomographic data. This tool can be used to explore the mandelbulb fractal. Sounds rather scientific but then this is a machine that’s just gone where no one else has gone before.  I feel like I’m living in a vintage pulp sci-fi story or, of course, a Jules Verne novel.

Greater sights than this await you in the Inner View of the Mandelbox

In the past the pictures illustrated the text, but now the text is merely footnotes to the pictures.

Yes, as many of us know, fractals can be just as much voyages of discovery –computerized voyages– as they can be a way of creating interesting graphics.  There’s no better example that I can think of than Trafassel’s recent discoveries here of “inside” the Mandelbox.

Fractals are still a growing and expanding realm of imagery and science.  A place where fresh parameter strings can open the door to another world.

ASCII: Wild Fractal Typewriter has come to be the new and thriving venue for fractal software development.  I go there every day and I always find something worth writing about even though I rarely understand what’s being discussed.  If you’re interested in developing fractal software, or just listening in on enlightened conversations about it, then is the only place to do that these days.

Or you can just look at the pictures, like me, and see the results.  There’s been the birth of new programs like Krzysztof (buddhi) Marczak’s Mandelbulber and Jesse Dierk’s Mandelbulb 3d, and also the expansion of older programs like Ultra Fractal with Dave Makin’s MMFwip3D which incorporates, thanks to Dave’s persistent efforts, current 3D fractal innovations into UF’s existing repertoire.

So it wasn’t a surprise for me to stumble over this new and interesting program “yFractalExplorer” by “yv3”, a somewhat cryptic screen-name.  Yv3 had this to say about yFractalExplorer, his new program:


I am proud to present you the alpha version of my realtime fractal rendering tool that i called yFractalExplorer. Damn it took me more than a year to complete the engine from 3rd scratch and then implement the Text User Interface and OpenGL Fractal rendering :)

– Unique and intuitive ASCII-Mode Text User Interface for all nerds out there that liked the old Fractint software
– Fast OpenGL rendering engine with hardware accelration to draw the final fractal with it. You can set them with a single key command as a wallpaper or save to a huge file to print them out in perfect quality as your own art
– There are not much Fractal types yet but yFractalExplorer provides already tons of Mandelbrot variations with its unique realtime fractal modification and random settings. There is no saving of fractal parameters to ensure that every time u use yFractalExplorer you will find a unique Fractal. Its not a typical fractal application, its art ;)
– Psychedelic Old School realtime color cycling in graphics mode
– 145 Palettes


You can download it at my Forums ( or directly from

Make sure you install it to a folder with admin rights (better installer will come soon). Please share your opinions and suggetions with me. have fun.

Screenshots?  He’s done better than that; he’s made a video:

I like the ascii “graphics” but I’m not enough of a “nerd” to have enjoyed using Fractint.  Here’s another ascii fractal example by another artist using different software, this time in black and white:

What I like about ascii art is the way your mind switches between text and graphics mode.  There’s words and then there’s the words forming pictures.  You can see both at almost the same time.

I know it’s kind of a cheap gimmicky thing, but some presentations of the ascii render are more effective than others so you need to check out a wider variety of ascii works before you (no pun intended) write it off.  I think the key to the art form is to view it close enough to see both the letters and the graphic they collectively render.  Viewed too far away and the image is no different than any regular, pixel-based image.  The ascii characters are really just bigger “pixels” and form, like pixels, a mosaic.

What’s interesting, and very apparent in the above video, is that ascii renderings are even more impressive as moving images.  I generally find that the best fractal art and even the best photographic art is found as still images.  Perhaps video is a more narrative art form and things which are graphically impressive (look good) don’t gain much by being animated because they don’t tell a story so much as they just make a statement.  Or maybe video is just a harder medium to work with?

Anyhow, ascii seems to gain something when animated.  Maybe it’s the changing gibberish of the letters?  There’s a sort of verbal effervescence that takes place as the image changes which adds to the show.  Sand animation is the same too,  suggesting that maybe renderings made up of particles like letters or sand take on an extra dimension, a flow, when animated.  Other things ooze, but ascii flows.

I wish this one was clearer because it really shows the “particle shower” effect but it’s still impressive.  Scibot9000 in the notes to this video says:

I was digging through my files and folders from high school when I found this thing.

I dusted off the code a bit and recorded the results, then added some music that I also made in high school.

The video is not the best, but please note that this was all html that only worked in Internet Explorer. Jittery animation is to be expected.

Technical details:
All the code was written in class, using notepad and IE7.
The total render time for that animation was close to 13 hours.
Each frame too between 0:40s and 3:15s to render.
The coordinates are (-0.7491245002453,-0.043015050302) if you want to see it on a better-rendered Mandelbrot. :)

Is this the beginning of an ascii art revival?  Well, the technique does lose some of its excitement after a while.  But I think ascii rendering is going to be a perennial technique in the hands of computer artists for a long time because it’s just plain stylish.  Even for those viewers who’ve never seen or used a computer in text-mode, ascii still looks neat.  It’s outgrown it’s humble (and old) origins.

Attention all passengers departing Munich airport!

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

From, where "Cheers!" is more than just a digital signature and "Prost!" needs no translation

I actually got a good look at the (new) Munich airport back in 1993 when I was on a British Airways flight to Istanbul.  The pilot announced that passengers were welcome to come up and look around the cabin (pre-9/11 days),  it was a clear day and when I was up there one of the pilots pointed over to the left and said,  “That’s the new airport at Munich”.

He's not joking; Eching is just down the road from the airport

Well drown my sorrows!  Hermann is none other than the Hermann of  I’m familiar with Wackerart because I bookmarked a particularly nice example of the Burning Ship formula a few months ago from that site.  It’s a special image for a number of reasons.

Burning Ship by Hermann Wacker

The burning ship formula is nothing new, but I find in today’s fractal art world it’s all about style now and not technology.  This image has a special style to it.

You can see the ship in distress on the horizon and how the “flames” reflect the windows and woodwork of the stern of an old sailing ship.  The top of the flames is even a chimney-like shape.  It’s a glowing, LED-red seascape and in dreamlike fashion the smoke from the ships rises up as surreal towers forming a forest of bare trees on a winter’s night (or maybe that’s just me).

The other reason this image is special is because it links directly to a java applet where you can explore this actual image by clicking on it.  Hermann’s fractal gallery is actually an interactive one; the images are just starting points for your own exploration.  (There’s an enormous amount of work on Hermann’s site including watercolor paintings.)

This is “java gallery” is a very nice way to introduce people to fractal art.  It shows not just how it’s made but also where it’s made.  The interactive image becomes merely one snapshot of the fractal “camera” and an example of how the final image is derived from the raw source of fractal imagery created by the software.

The coloring is fairly simple, but as I was saying, it’s not about technology so much anymore as it is about style.

Here’s another very stylish and yet deceptively simple image:

Spikebar 04 by jwm-art (on

Pretty simple fractal image in some ways and yet the bright but plain color scheme really makes the fractal patterns and structures become electric.  It’s like something out of a circus, but a very stylish circus like Cirque du Soleil.

Here’s another one by jwm-art:

Spobar 01 1000 by jwm-art

Simple shapes and simple colors again, but like all little things when they’re multiplied instead of added, the results are huge and categorically different.  That’s the difference (no pun intended) between the effects of technology compared to the effects of style on artistic impression.

I like the little Space Invaders shapes and especially, like in the previous one, the round, eye-like shapes in the central part of the image.  Also there is a certain phosphorescence to some of the elements in the image like the blue outer background and the green little shapes sailing on it.

Jwm-art had this to say about these two images of his in the original thread on

I’m quite pleased with how these two turned out. I’m trying to familiarize myself with tuning with zooming into the M-set. I’ve been spending quite a lot of time over the past few days exploring these things and am starting to see the patterns so to speak. I want to discover new constructs but am not sure it’s possible – I recently came across a page of Mandelbrot constructs created around the year 2000 which blew me away (sorry I can’t recall how I got to them).

(Unrelated to all this is an interesting and extremely realistic rendering of a mandelbox detail here on jwm-art’s site.)

Jwm-art is, if I’m reading the threads on correctly, currently writing his own fractal program, MDZ.  I believe these images I’ve shown here come from prototypes of that program he’s developing.  I just can’t get over how many multi-talented programmers have congregated over on  It’s like the Athens of fractal art to which I am nothing more than a tourist.  Fortunately for people like me, you don’t have to speak Greek to look at the pictures.

I just discovered from reading the Readme file of mdz-0.0.9 that jwm-art is James W. Morris.  I kept thinking it had some connection with Joe’s Window Manager but no, it’s unrelated.

I don’t know if some of the graphical qualities of James’ images are a product of his program, MDZ, and that MDZ just lends itself to these styles of rendering.

Well, in closing I’d just like to suggest that I think it only appropriate that Fractalforums adds another smiley to their vast repetoire of emoticons in honor of Hermann’s hospitable invitation:

Mixed Media Fractals

Although some fractals today can look extremely realistic, rendered in three dimensions and having an appearance as photo-realistic as any photograph, I find they don’t usually mix well with photographic elements used as backgrounds or when embedded as repeating pictures in formulas.  There’s no technical reason for this, computer-made imagery like fractals just seems to clash aesthetically with imagery from the real world.

But just recently I discovered a few examples of just the opposite; harmony and synergy in a image mixing fractal and non-fractal imagery.  Up until now most attempts to combine the two haven’t looked so great and even now these images shown here are still quite unique in that they combine two different kinds of imagery with successful results.

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

Cherry Blossoms by BrutalToad (

This is by far the most effective use I’ve ever seen of blending photographic imagery with fractals.  I think this is exactly the kind of sinister, predatory plant that John Wyndham imagined in his classic science fiction novel, The Day of the Triffids.

Note the subdued and sweet “cherry” flavored color in the blossoms on the trees in the background and also carefully mixed into the fractal “blossom”.  I’m assuming that was intended, but even if not it’s a very nice touch, a sort of wolf in sheep’s clothing theme; camouflaged fractal predator.

The mandelbulb object seems to almost have a grimacing mouth and squinted eyes.  The low, worms-eye-view perspective (looking up) suggests a large, looming creature.  I don’t think a professional artist could have done any better with this mandelbulb image than Mr. BrutalToad has.  It ought to look out of place with the photographic background but instead it merges into it naturally and the two complement each other perfectly.

Influence of Close Encounters by Fiery-Fire

Another superb combination, this time of a mandelbox fractal with an image of at least differing origins if not entirely photographic and real.  I’m not absolutely sure if the image of the sky which forms the background is a photo or not but it’s clearly not part of the mandelbox.  On her Deviant Art page Fiery-Fire refers to it as a “beautiful nebula by Ali =casperium“.

The two go together so well I’m sure Fiery-Fire took a great deal of care in selecting and positioning the background to get the great effect it has.  Perhaps that’s what makes mixed media fractals so hard to make: you need multiple skills and multiple programs.  But when it’s done this well it looks easy.

The exploding nebula dust-sky is of course an overcast one and this matches the diffuse light in the fractal image.  Furthermore, the “camera” position in the fractal image is looking up at this towering clump of fractal shapes whose composition leads our eye right up the clump to the one at the top and into the strange, alien clouds.  It’s not a fluke; Fiery very carefully crafted this image.

Many great fractal images are simply found while exploring a vast fractal generated panorama, but if you want to incorporate other kinds of imagery, particularly photographs, into a fractal image then you’re going to have to work a little more and you’re going to have to juggle two often opposing mediums.  Brutaltoad and Fiery-Fire have achieved some really great results in the two images shown here but I think their success is rare and not as easy as it may look.

Guido Cavalcante has pursued a mixed media style of fractal art for  some time now.  I have not one, but four of his images here.  Three of them are 3D fractals like Fiery-Fire’s and BrutalToads.  All of them were made in Ultra Fractal, sometimes with a little help from Photoshop and sometimes just UF and its versatile image importing features alone.  Guido’s style is different but his methods and tools are the same as any fractal artist who pursues mixed media.

Archimedes 5 by Guido Cavalcante

Wouldn’t you rather live in a computer than the real world?  Of course there’s more than one real world to chose from.  Here’s a golden mandelbox with a third world slum in the background.  It’s not an image that requires a lot of explanation; the golden computer temple is contrasted with the bleak, B&W misery of the slum world.

There’s more: each is a highly detail edifice; the individual slum houses merge into a single, organic-looking multi-celled organism.  The mandelbox is equally detailed and yet the expression of just one formula with three dimensions: length-width-depth; food-clothing-shelter.  It’s a very clever contrast and done so simply.  Golden fantasy vs. concrete reality (no pun intended).

The Hanging Garden by Guido Cavalcante

It’s the cow that “makes” this one for me.  But perhaps the movement of the tangoing couple accentuates the simple pastoral calmness of the grazing cow.  I don’t know about the airship, but it does give some depth and perspective to the great, mossy mandel-palace.  Old dance halls used to be distinguished by their many pillared rooms.  They were built at a time when the strength of structural materials was not as great as it is today and therefore had many more vertical supports.

One can make up a million stories for images like this but to me it’s instantly a palatial dance hall in decay like a wonder from the ancient world.

The Fall of Syracuse by Guido Cavalcante

Alright.  Where’s the mixed media?  All I see is a mandelbox overlayed with a texture and given a torn paper drop shadow border.  But together, mixed together, they create a papyrus fragment depicting the fall of Syracuse, an ancient city thought to be impregnable (secure) but conquered by some sly ancient Greek (better check that).

I like the coloring too.  Looks like a hand-tinted engraving out of a Victorian book (ripped out of a Victorian book).

No Way Out (9) by Guido Cavalcante

Fractal?  Where’s the fractal art?  I know what you’re thinking: it’s all made with Photoshop.

“No way out” is an entirely UltraFractal processed image – the astronaut was rendered with the the image Importer “Sprite” (Mark Townsend´s freeware). The image belongs to one of my obsessions, which is death in space

And the space station, grey cylindrical thing? A quaternion?  The planet in the center looks like a fractal image mapped to a sphere.  UF is the photoshop of fractal art and Guido’s image here is a great example of those features.

I like the space theme; fractals often lend themselves to fantastic, extraterrestrial contexts.  It’s like a graphical voyage or graphical exploration of space: not a real, but a mythical space.

You can see more of Guido’s work on his blog, Fractalmix.

Mixed media fractal imagery can be very expressive when done well like it has been in these six images.  It’s a graphical twilight zone where the virtual meets the real.  But some just call it digital art.

Why Image files are very different than Parameter files: Derivative Works!

From Last Week’s Episode…

If you’ve been reading the comments to my last two postings:  Can you really copyright an Ultra Fractal parameter file? and;  Is it too late to patent your fractals?; you will have probably come to the conclusion that Ultrafractalists see no essential difference between a parameter file and the resulting image file that it creates.

Samuel Monnier thinks so and he’s a veteran Ultra Fractal user and very familiar with the way the program works, especially how it creates imagery using various techniques, many of them pioneered by himself.  Sam said:

There is absolutely no conceptual difference between a parameter set and a jpg image. Both contain data, that a certain algorithm can use to display an image on your screen. Displaying a parameter file just requires more computations from the computer, yet there isn’t any difference in essence.

Jock Cooper, another veteran Ultra Fractal user and pioneer in pushing the parameters of the program agreed with Sam’s categorization of parameter files as well as disagreeing that Ultra Fractal parameter files (UPRs) are patentable processes and said,

As the comments have pointed out, the UPR is a alternate form of the image…

And as far as the UPR being/defining a process, actually it doesn’t. No process is described by the UPR–those processes are described in the formula files. The UPR defines which processes to use (by naming them) and what numeric inputs to use.

Lessons Learned

So how has this expert advice changed my view on the copyright status of Ultra Fractal parameter files?  A UPR is probably something that can be copyrighted because it’s really no different than a computer script.  But even with the roaring search power of Google at my fingertips I couldn’t find a single legal case of copyright infringement of a computer script or even someone –anyone– on the internet who would say you can copyright a computer script.  But isn’t a computer script a subcategory of computer software?  And computer software can be copyrighted… so there, I guess the question is answered and done with.

Besides, isn’t a parameter file more of a creative work than even the image it renders?  What do fractal artists really do but adjust and explore fractal parameters?  When one works with Ultra Fractal they work with parameters; the image comes later, just like a print artist creates a printing plate and then only afterwards –after all the real work has been done– creates the print, the thing we call the image.  The fractal parameter file is analogous to a printing plate –a fractal printing plate.

No, that’s not right.  It’s a little different.  Let me put it in very cerebral, philosophical language: The parameter file is to a fractal image what the printmaker’s creative choices are to the printed image.  Ultra Fractal provides all the mechanical support: the expert engraver; inking; and pressing of the plate.  (Fractal artists never get dirty or lose fingers.) The artist’s creative “authorship” is contained entirely in its choices of: what formula; what rendering method; what coordinates to zoom to; what boxes to tick off; what numbers to key in; and of course, as a multi-layered program, what layers to include; how to merge them; and as you can see, choosing whatever can be chosen.

The Answers to Everything

A parameter file is a whole bunch of answers to a whole bunch of questions.  Fractal images have a whole lot of variables; parameter files define those variables.  I think this is what Jock Cooper was getting at when he said, “The UPR defines which processes to use (by naming them) and what numeric inputs to use.”

Anyhow, if you’re an Ultrafractalist you know all this already.  That’s why you may find all this copyright stuff somewhat pointless and of no practical importance.  But copyright is all about practical matters –all about what are you going to do?

For instance, speaking of Ultra Fractal parameter files, what are you going to do when someone makes something with your copyrighted parameters?  I don’t mean copies your parameters verbatim, I mean they make another image based on your copyrighted parameters.  I believe “tweaking” is the popular word.  Is it infringement when someone does this?

zn2 + c + mustache + beard

One small step for U-P-R; One giant leap for J-P-G

You see, as my co-contributor, Terry Wright suggested in his comment, image files (or sound files) react very differently to “tweaking” and it’s this difference –the way derivative works are made– that is the real practical difference between image files and parameter files with respect to copyright.  Un-tweaked or simply copied verbatim, parameter files and image files have, as Samuel Monnier said, “no conceptual difference”. (Assuming, as Paul N. Lee added, that they’re used with “the same version/release/mod-level of that application… each time, and the formulas and other criteria (transforms, gradients, etc.) not changing from the original coding”.)  If you copy a parameter file without any alteration, then copyright infringement is a very simple matter to decide.  Of course, the resulting, identical image would make the matter pretty easy to judge, too.

But what if someone changes something in your parameter file just a little bit? What if I take a “1” and make it a “10” and then start selling prints of the image online?  Are you going to send me a harsh email or see a lawyer about it?  Like I said, what are you going “to do”?  Copyright is a practical thing.  If you don’t care about infringement and protecting the commercial value of your work then there’s no reason to care about copyright or bother with it; that’s all copyright is good for.  That’s what I was getting at when I said the copyright notices in parameter files on the UF mailing list were “a little weird”.  What possible infringement scenario could they be hoping to protect their work from?

As every fractal artist who has ever inputed julia coordinates or any kind of number into the dialog box of a fractal program knows, tiny parameter differences can produce huge graphical effects.  Of course, sometimes tiny parameter changes produce tiny graphical differences and sometimes huge parameter changes do nothing at all to the image.  Derivative works are a violation of copyright unless you get permission to use the copyrighted material from the original artist.  You’re copying their work without making substantial, transformative changes to it.  Therefore, that portion of your new work that is their work, is protected by the original artist’s copyright and can’t be copyrighted by you because it isn’t your work.  Derivative works incorporate the copyrighted work of others and create works with dual, or even multiple copyright owners because there are dual, or even multiple –authors.

Unwritten laws of Fractaldom

This is the nightmare scenario that Gumbycat (alias Linda Allison) is hinting at in her online article, “When is it yours?“.  Well, maybe not exactly a “nightmare” or “doomsday” scenario, but if fellow UFers start to feel like you’re exploiting their work by using their parameter files and they see a pretty straightforward and simple legal recourse, i.e. an infringement lawsuit, then I’d say that’s a pretty grim environment to be caught up in.

Nobody wants headaches like that and in the interest of online happiness over the years certain unwritten rules have arisen regarding the proper use of parameter files that many have come to assume (mistakenly, I believe) are supported by copyright law.  Linda Allison (in case you don’t know) is a long-time Ultra Fractal user, so I think what she writes on this matter is worth reading even if it was posted quite a few years ago.  She also explains it quite well.

There are “UPR” files – parameter files. These files hold the data that is the final, sum total of the image you have created. Sometimes we post “UPR” files to the UF Mailing List. That doesn’t mean those images aren’t copyrighted! They are. Nevertheless, we may* expect them to be tweaked (altered slightly or greatly) or picked apart as a learning tool by other List subscribers. Sometimes the tweaks are posted back on the list. When the original images are altered slightly by another List subscriber, the resulting image cannot be claimed by that second person as his or her own image. When they are greatly altered to the extent that in all aspects the new image looks totally unlike the first image, the second person may claim that image as his or hers. When you are unsure whether you can claim the image as your own, contact the creator of the original UPR and work it out with her/him.

Yes, even way back then (I suspect long before that “2005” that appears on the bottom of the web page) the thorny issue of derivative works was anticipated and precisely because of what caused me to start asking these questions myself: posting parameter files to the UF mailing list.  Note that whether the tweak results in a new work or merely a derivative work is a matter judged by what the image looks like.  That makes perfect sense of course; how else would you compare the differences between two parameter files?  What would my suggested substitution of “10” for “1” result in if you can’t see the result?

Courtrooms and complex technology

You see the sort of confusion I’m suggesting will accompany any accusation of copyright infringement of a parameter file?  All a defendant has to do is show a judge or jury how many variables there are in a parameter file and how some of them can be changed from “1” to “10” and result in no changes at all and how others can be changed the same way and result in a total transformation of the original image.  After that a judge or jury (that’s grasped the concept) will most likely conclude that the only kind of derivative work that can really be recognized and argued for is the alteration of images, not the alteration of parameter files.

But that’s assuming you’ve gotten past the first hurdle in any lawsuit: convincing a lawyer that your case is worth taking to court in the first place.  I’m assuming in all these fractal art copyright scenarios that there’s money to be gained in taking legal action because that’s what seems to drive infringement lawsuits.  But currently there probably isn’t any money or at least not enough to attract any interest in a lawsuit.  But even if you were super-rich and wanted to sue someone for the sheer joy of revenge (another frequent, but not nearly as common motive) you’d have to bring the lawyer up to speed with all the intricacies of fractal parameters.  I can just imagine the conversation: “The imaginary values are real things –real numbers– they’re just not the real values, those are different.  You can’t have decimal places in an integer!  I told you already; infinity is the largest number theoretically possible: we represent it with a zero.

It’s in this context of a courtroom or a lawyer’s office and not in the context of an online fractal art discussion that I’m saying an accusation of copyright infringement of a parameter file isn’t going to go anywhere or present any practical legal reaction.  But if the infringement involves an image, then it becomes a simple matter of applying decades of legal precedence to what is just another case of copyright infringement of a visual work.  Viewed from that aspect –derivative works– parameter files and images files are categorically different.  Verbatim duplication of a parameter file, say, in an online repository or reposting without the author’s permission, would probably be easy to deal with too.  And in the event that one published the parameter file for a very popular and commercially valuable work (when there is one) the damages might be far greater than those involved with simply copying an image because with access to the actual parameters, now many people would be able to reproduce the image at any resolution and make derivative works without infringing the artist’s actual image.  Actually, the copies made from the parameter file could be better!

Will any of this ever matter?

It’s hard to say what the future of fractal art is going to be.  But if the creative use of graphical fractal renderings ever acquires real commercial value then these things we’re just discussing as hobbyists might take on a much more serious form and nature.  If you think your fractal art has or ever will have commercial value, then you ought to take a more professional approach to copyright and not just adopt the so-called community standards of the online fractal art folks.  They aren’t the ones who will be judging your copyright infringement case or representing you in court.

Is it too late to patent your fractals?

In a previous post, Can you really copyright an Ultra Fractal parameter file?, I questioned the validity of copyright protection for parameter files.  I based this on my observation that what parameter files do is categorically different from what  image files do and more in keeping with the types of things the US Copyright Office excludes from copyright protection.

Some of those kinds of things that are excluded like procedures, processes, and methods of operation, are handled by patent law and not copyright law.  The different legal context arises from the differing nature of those two types of things:  for instance, you don’t copyright a procedure, you patent it.

If Ultra Fractal parameter files fall under patent law and not copyright law then anyone wanting to protect their work will have to get it patented –copyright won’t mean a thing because UF parameter files are not “copyright things”.  But acquiring patent protection is quite a different matter from copyright protection.  Copyright protection is automatic and only requires formal (i.e. paid) registration in the event that you actually want to take someone to court for infringement.  Patents always require official registration and most importantly:  fast registration!

After a year of your parameter file being publicly available, the Patent Office will not allow it to be patented.  It is no longer patentable because you’ve waited too long; your opportunity to protect your work has now officially expired!  Copyright is vastly different than this and it simply requires proof that you’re the author should it ever be questioned at some point down the road.  Official copyright registration will probably prevent it from ever being questioned but it’s not necessary and copyright protection now lasts for the life of the author plus an additional seventy years –well over a hundred years in many cases.

But patents only last for 20 years and in the case of design patents (ornamental design of a functional item), the duration is a mere 14 years.  Interestingly, 14 years was the original length of time for copyright protection when it was first created back in the late 1700’s around the same time as patents whose initial lifespan was also 14 years.  Copyright has been extended to almost ten times its original length while patent protection has remained pretty much the same.

Does it change your perspective on parameter files to view them as “patentable things” rather than “copyrightable things”?  It should because it will cost you between $80 to $300 to patent your parameter file and you’ve got to do it quickly.  But copyright, as almost every fractal artist knows, is free, automatic and 24/7.

Internationally, and fractal art is very international, patents are also much different than copyright.  Thanks to Mickey Mouse and his Disneyland gang, fractal artists get to stand under a huge umbrella of automatic and near endless copyright protection held up by the ever-strengthening arm of Mickey himself and whole-heartedly agreed upon by almost every nation via global trade treaties.  Your copyrights will likely still be in force when your grandchildren are around and you’re long gone: “Thanks for leaving us all your fractals, Grandma.  What are they?”

But the one-year window of opportunity for registering a fractal parameter file only applies to a few countries.  In Europe you must patent something before making it public, and in some countries, like New Zealand,  software patents don’t even exist because they don’t qualify as something that can be patented.  Just like copyright exclusions, there are patent exclusions too.

So if you want to patent your UF parameter files, the best strategy I can suggest is to at least register them with the Patent Office before posting them anywhere or even showing them to anyone.  Then you can officially say “patent-pending” when you post them to the UF mailing list.  But don’t say that if they aren’t being registered because it’s an offense to label something as “patented” or “patent-pending” when it actually isn’t.  Patents are a whole different racket than copyright.

So what happens when you don’t patent your work?  It’s a completely different scenario than copyright:  unpatented work automatically becomes Public Domainfree for anyone to use for any purpose they want!

Something to think about next time you get that urge to post a parameter file with a growling copyright warning and the stern words, “On-list tweaks only!”  You just might be giving it all away and it’ll be too late for:

…yeah, you know what.

Can you really copyright an Ultra Fractal parameter file?


I’m not an Ultra Fractal user but I do follow the daily exchange of information on the Ultra Fractal mailing list, an email group anyone can join.  Most of the time it’s just users sharing what looks like big long paragraphs of jumbled letters and numbers.  When opened up in Ultra Fractal the scrambled text produces an image.  They call those pieces of text, parameter files.  I just skip over them since, like I said, I’m not actually a UF user, just a curious bystander.

The actual parameter code contained in the emails mean nothing to me and probably can’t be deciphered even by an expert, but there is one little bit that I often see in them that I understand quite well and is intended to be read by everyone who looks at it –a copyright notice.  Up until recently I never thought anything of those copyright notices but after giving myself an award winning internet education on copyright, I’ve begun to feel that those copyright notices on UF parameter files are …a little weird.

Why weird?  Because indecipherable text is not the type of thing that most people would think of as even qualifying for copyright protection.  The US Copyright Office says this about what kinds of things can be copyrighted:

§ 102. Subject matter of copyright: In general28

(a) Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device. Works of authorship include the following categories:

(1) literary works;

(2) musical works, including any accompanying words;

(3) dramatic works, including any accompanying music;

(4) pantomimes and choreographic works;

(5) pictorial, graphic, and sculptural works;

(6) motion pictures and other audiovisual works;

(7) sound recordings; and

(8) architectural works.

(b) In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.

Here’s an example of what a UF parameter file looks like:

An example of what a UF parameter file looks like

Now ask yourself: In which of the eight categories listed by the US Copyright Office would you put the above UF parameter file?

None, of course.  It doesn’t fall under any of the categories, although “(5) pictorial, graphic, and sculptural works;” is probably where most Ultrafractalists would say it fits.

But I don’t think that’s right.  The reason it’s not a graphic work is because it’s not a picture of anything, it’s a text file.  Of course it will create an image once it’s opened up in UF and that image would qualify as something that can be copyrighted, but the parameter file itself is really just a set of instructions or method of operation to make the program draw the image.  It’s not a piece of literature or a poem or even a news story, it’s just a set of written instructions or what would be better described as a procedure or algorithm.

If you look at the last paragraph it says, “(b) In no case does copyright protection for an original work of authorship extend to any idea, procedure … method of operation … or discovery, regardless of the form in which it is described…”

I think a parameter file is a “procedure” and although it comes in the form of a text file just like a piece of writing would, it’s still a procedure and not a really far-out, avant-garde poem or other kind of textual work that can be copyrighted.

Now the US Copyright Office says, “Works of authorship include the following categories:”.  They aren’t limiting the coverage of copyright to just those eight.  There could be others, I suppose, that they haven’t included.  Would you expect the US Copyright Office to have considered or even known about fractal parameter files?  The wording is vague and open-ended because human expression comes in so many forms and formats.  So maybe another category could be added or proposed and it would be suitable for parameter files and other, “original works of authorship”?  But are UF parameter files “original works of authorship”?

Sure, they are.  But if they’re procedures or processes or methods of operation, then they are clearly excluded from copyright protection.  That’s because those sorts of things are covered by patent law and not copyright law.  UF parameter files look more like algorithms than the sort of “works of original authorship” that are covered by copyright.

Algorithms, even computer algorithms, can be patented.  Not in all countries, but they can be in the U.S.  The GIF file format contains a patented algorithm, the LZW compression algorithm.  Unisys caused a great deal of anxiety among software developers some time back when it acquired ownership of the LZW algorithm and was going to require everyone to buy a license to use GIFs.  But getting a patent is different from getting a copyright.  Copyright is something that occurs automatically today, but patents require formal registration with the Patent Office.  You can’t just slap a “Patented” label on a parameter file like you can with those, one size fits all, anywhere-anytime, 24/7, copyright notices.

If I’m right that UF parameter files can’t be copyrighted, then there are some ramifications to that.  For one, there would be no restrictions on copying or publishing UF parameter files.  That means anyone wanting to set up a repository of parameter files could do so without worrying that they are infringing anyone’s copyright —there would be no copyright. Those notices would just be mistakes written by parameter file authors who have misunderstood what copyright really is.

I don’t expect those notices to go away anytime soon though.  In the words of Colonel Kilgore:

"I love the smell of copyright on my parameter files. Smells like --Victory"

Hold on to your mind: Lloyd Garrick’s little video project

Known as JackOfTraDeZ or FractAlkemist and probably a few others, Lloyd Garrick, a name he rarely goes by, has made a sizable collection of fractal videos using Fractint and some very interesting musical soundtracks.  In fact, the music almost adds an extra dimension to the fractal visuals and the combination of the two transforms them in the same way adding a third dimension makes everything come alive in 3D imagery.

As is so often the case with me these days, my discovery began with a humble link from a thread about something unrelated at

Famous videos?  I didn’t know there was such a thing in Fractaland.  After clicking on the famous videos link and visting the Ultimate Fractal Video Project site where his many videos are available for download, I went to his YouTube channel.  And all this before I’d even finished my morning coffee.

The title image for the BuddaBrot video caught my interest right away…

I generally “listen” to videos with the sound turned off.  That’s because the musical accompaniment usually doesn’t accompany the video.  So I “listened” to this one muted as well.  It wasn’t until I’d viewed a few more that I began to wonder what sort of soundtrack, if any, there was.

Like I said, the music combines with the imagery to take the video to a whole new level of creativity and alive-ness.  In BuddaBrot the gritty golden noise actually seems to be moving with the beat of the music.  It’s like it’s dancing.

Lloyd says this about Mission to Mars on the video’s YouTube page:

Use your imagination! You’re a rich space tourist on a mission to Mars. You approach the red planet from deep space, descend into orbit, then make planetfall into one of the large canyons known to exist there. You rocket above and over the surface looking for a smooth place to land among the sand dunes and mountains. … And you wish you had hired a better pilot …

Lloyd’s got a sense of humor!  I don’t think I’ve ever seen comedy in a fractal video before.  Also; did you notice that the video is nothing more than a “deep-deep” zoom?  Lloyd’s got a way a making everything new.

Note how the acceleration of the car’s engine is matched by the changing imagery in the video.  This is really a very well planned bit of animation.

Fractint stuff looks pretty retro doesn’t it?  And the soundtrack is –what? It sounds more like a machine than a piece of music.  But together, they create something I find very impressive.  This is the secret of art: it’s not what you use, it’s how you use it.

Ultrafractal makes some very smooth and advanced fractal imagery, but it’s no different than Fractint when it comes to making art.

Lloyd goes even further and makes this comment on Cathedral of Chaos (not included here): “Tweaked Mandelbrot LAKE animation. You can do things with FRACTINT like no other freakin program out there!”

I chose Dancing Dragon not because it’s one of Lloyd’s best videos but because it’s probably the best example of his skill in combining fractals with sound.  The fractal imagery alone is really nothing too exciting.  As cool as this julia of the mandelbrot set might have looked the very first time we discovered it, it’s a pretty cliche theme in any fractal art venue now.

And yet!  And yet, the soundtrack floods that old worn-out image with a golden grandeur and makes us feel we’re watching the awakening of  some great golden dragon.  We can all learn a thing or two from Lloyd here.  Or should I say, Master Lloyd?

StarGate uses a soundtrack from 2001: A Space Odyssey, Stanley Kubrick’s famous, and very freaky, science fiction movie.  Kubrick really raised the bar for science fiction movies, maybe even a bit too high since no one’s been able to even touch it since then.

Lloyd is right when he says, “Too bad fractal animation wasn’t available when 2001 Space Odyssey was made in 1968 but it’s available now so how come noone’s using it?”  Lloyd’s simple fractal imagery fits in quite well with what I think Kubrick was trying to do in the Star Gate scene from his movie (which is something everyone is still trying to figure out).  But I don’t have to tell you; the power of YouTube allows me to “quote” from 2001: A Space Odyssey. You don’t have to watch the whole 10 minutes; some people find Stanley Kubrick boring.

Back to Lloyd, the Stanley Kubrick of fractal art.

Profoundly minimalistic; that’s what makes this one so good.  The silvery, bubbly fractal image is quite elegant and has strong design characteristics.  The music is really nothing more than a background “theme” (musical texture?) with a single shimmery chord.  The fractal drifts in and then out in a single, simple crescendo.

Well, I could go on but all I think I’d end up doing is embedding everything Lloyd has ever done into this blog post.  Check out the rest if you like what you’ve seen so far.  Holding on to your hat is not the same as holding on to your mind.

Max Ernst: Fractal Art’s Imaginary Link

~ Click on any image to view a larger version on the original site ~

Sahelanthropus tchadensis by Didier Descouens CC-SA

Although the works of Max Ernst (1891-1976) might exhibit a pronounced frontal brow on their foreheads, closer examination reveals startling similarities between them and the contemporary fractal art that now inhabits the same landscapes they once did.

Europe After the Rain by Max Ernst 1942

Ernest employed a technique of squished paint.  Touched-up obviously and with some additional hand-painted elements, but what a fine way to represent the airborne decay of the European urban landscape in the early days of WW2.  The abstract, unrealistic imagery of paint squishing (decalcomania) has real similarities to the algorithmic renderings produced by aerial bombardment.  Ernst’s image is a better expression of that because it works even worse thoughts in our imagination.  It also, perhaps, served as inspiration of Ernst himself to produce the work he did.  The same imaginary effects that work on the artist are felt by the audience too.

The Entire City by Max Ernst, 1936

If you will forget for a moment the central theme of Ernst’s work here, you will undoubtedly recognize a proto-mandelbox in this image.  Seriously, Ernst is portraying a single, monolithic image of a “lump” as an iconic image for a city.  But wait, what came first?  Was it Ernst’s idea to portray a city this way, or was it Ernst’s creation of an interesting “lump” that triggered the concept of The Entire City in his imagination?

Again, the imaginary workings of Ernst’s imagery conjure up a twilight zone where abstraction and realism meet.

Fishbone Forest by Max Ernst, 1927

Did he make that circular Sun-like object in the sky by pressing a pop bottle into the canvas?  Artists like Ernst are sometimes shockingly creative.  Of all the skulls we’ve unearthed here, this one displays the fractalopithecus family characteristics the best:  Abstract imagery used to imagine an alternate but legible reality.

It’s an example of what fractals can sometimes do because fractals are primarily abstract but can sometimes be found in naturally occuring formations where they suddenly suggest realistic themes.  I call this neither abstract nor realism but instead: imaginary.  It’s already cropping up here and there because fractal artists sense something of interest in their imaginary scenes but they fumble with the terms for it because the currently used terms don’t apply to this artificial “realism”.

Fleurs sur Fond Jaune by Max Ernst, 19-something

Unfortunately I can’t find a larger version of this image (or the year it was made).  Perhaps it is perennially new because every viewer interprets it differently.  It’s more than just a study of popcorn; the flowers have transcended their real forms and become vivid imaginations of what they once were.  We will not see flowers like this anywhere in the world, and yet we will recognize them when we do.  The same imagination is present in both graphical experiences, real and imaginary.

Hommage a Rimbaud by Max Ernst, 1961

The Birmingham Museums and Art Gallery site says this about the above image by Ernst:

The most inventive prints by the surrealist Max Ernst were arguably produced after the Second World War in collaboration with the master etcher George Visat. This is from a series, developed in the early 1960s, on the theme of the ovoid or egg shape. This most essential of natural forms is here conceived as a constant spiral, half-submerged in a web of textural irregularities. In this ‘hidden’ vision, Ernst appropriately pays homage to the symbolist poet Arthur Rimbaud (1854-91).

Inventive / theme of the ovoid or egg shape / hidden vision / symbolist” I’m not the only one to see modern things in this pre-fractal artifact.

Imaginary art opens it’s mouth but it doesn’t speak –it sings.  The title can be part of the work and not merely some stuck-on thing; an iconic utterance as ancient as Adam naming the animals.  It doesn’t stick; it protrudes from the image.

The Forest by Max Ernst, 1928

Forests don’t look like this, but some do feel like it sometimes.  There is a forest like this somewhere out in the world, undiscovered by us, and this image prophesies it.  Imaginary art slips past our eyes and makes a direct appeal to our minds by conveying, in secret alphabet, a message our eyeball gatekeepers would have turned away.  It’s a parable or metaphor: more real than the real thing.  I can’t think of any better way to define what “art” is than that: art is what you think of when you’re looking at it.

There are great expressive possibilities for fractal art.  But first we have to accept, like I believe Ernst accepted with his own work, that we are better off letting it direct us than we are in trying to direct it -being the directed rather than the director. How can one make imaginary things?  They can’t, of course.  But we can look for them and decipher their names.

My Oort Cloud Vacation

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

Untitled by tohu777 (on Flickr)

Comment posted to the above image on Flickr

In defense of Valerie, tohu777’s image fooled me too.  I thought it was an art installation out in some desert somewhere.

Even now I’m not so sure it’s not a real photograph.  But of course, what difference does it really make?

It makes a difference.  For some reason it’s just different when you find out an image is not made from what you thought it was.  But in this case, because the image is so incredibly realistic (would the real thing would be more vivid?) and also because the image has such great artistic interest, I can’t look at it without seeing something real and as relevant as the real world.  It has become real.

Good art invents itself.

What is artistic about it?  A lot of hyper-realistic 3D imagery is boring when placed in a non-technical context.  In itself, realism is a rather empty goal because reality is common.  I said similar things in a previous post, Reinventing the Real.  But this image doesn’t merely attempt to fake the photographic look, it presents something that’s interesting and thought-absorbing regardless of its graphical origins.

  • Arctic
  • another planet
  • crash-landed ship or protruding alien city tower?
  • the highly fabricated mesh around the tower makes me want to check what I’m standing on
  • the sun (or whatever) is setting and it’s going to get cold
  • what was built first? the tower or the bent superstructure around it?  Was it designed to look bent?
  • no one has been here for a thousand years (or since the last heavy snowfall)
  • such intense human activity punctuating such a vast expanse of emptiness
  • on most days the sun is the only viewer
  • I hope this wasn’t the rescue ship I’ve been waiting for
  • there’s got to be a door in there somewhere

Untitled by tohu777 (Flickr)

Not far from the first one, in Flickr-land, I stumbled on this.

Flotsam on a remote space beach?  When an asteroid cleans out its pockets, it  all ends up somewhere.  Are there hurricanes in space?

Check out tohu777’s Flickr photostream for more scenes transmitted from a distant star.

Liquid Canvas Abstracts by Richard Todd

Liquid Canvas Abstract by Richard Todd

A “liquid canvas abstract” is a floating painting — an artistic expression of color and form on a liquid “canvas” using oil-based pigments. The evanescent image is preserved photographically in high resolution.

No digital construction is involved.


Liquid Canvas Abstract by Richard Todd

I had the idea for a liquid canvas about 20 years ago, but I was too busy with other projects to do much with it. Fortunately, a good idea lives on. Two years ago, I came back to this one. And now I’m excited to share the results with you. So far, the response has been more than I could have hoped for. Adjectives like “beautiful,” “stunning,” and “fantastic” have inspired me to work in this medium with ever greater depth of purpose. The paintings are a combination of artistic technique and the uncontrollable physics of fluids in motion, creating a unique cacophony of form, light, and color. The paintings are so ephemeral that they last only seconds. I use fine art photography to give them the permanence they deserve.


Liquid Canvas Abstract by Richard Todd

Richard really describes his work well and very concisely, too.  But still, there’s a few things I’d like to add: The Confluence of Ancient and Modern.

Yes, if I understand what he’s describing properly, he’s doing a variation of the ancient marble paper making technique.  What’s different is that he’s using photography to capture the imagery rather than laying a sheet of paper over the painted matrix.  The result of this, if you think carefully, is to produce a 3D version of the marbled imagery instead of the flat, paper version of the ancient method.  Photography captures the paint that is below the surface as well as on top of it.

But then he prints the photos out using high quality methods:

I’m pleased to be able to offer a level of print quality commensurate with the paintings themselves. I doubt there’s a better printer than the Epson 9900. Combined with Moab’s Entrada Gloss paper or Innova’s Ultra Gloss canvas, the resulting images are truly beautiful.


It’s an interesting digital twist to an ancient artform: the results of both methods are a flat, very ornate, long lasting image.

There’s many more to look at in his Galleries and Collections section, as well as in the flash applet on the home page.

Ebru Sanati: Turkish Marbling

We follow the Western footsteps that brought the technique for making marbled paper back to Europe from Istanbul in Turkey…

We are soon invited in to have tea with a friendly turk.  What do you know?  On the television is a show all about the Turkish art of painting on a gelatinous surface.  Fortunately it’s a very visual demonstration so our inability to speak Turkish is not a problem.  Art is the universal language.  Tea is pretty widely understood too.

Looks pretty easy doesn’t it?  Apophysis is even easier though.  Here’s a more sophisticated example which incorporates the actual painting of an object in the paint film and not merely the creation of an ornate background.

I find Richard Todd’s work interesting not just because it looks so good, but because it’s an advancement of an ancient art.  Not only that, stop me if I’m wrong, but I think fractals can be considered a new technique for dripping and swirling paint.

A special thanks to Paul N. Lee, the veteran fractal archivist, for alerting me to Richard Todd’s Liquid Canvas Abstracts.

Prince Johan …and a few others

I have a few rules of thumb I like to keep to when it comes to reviewing fractal art.  One of them, if it were boiled down and expressed as a revolutionary slogan painted on a flag, is “Art, not Artists”.  It’s not a hard rule to follow in the fractal art world where the work of most artists is eclectic by nature and varies quite widely.  Expressed another way: There are no good artists, only good art.

I go looking for good artwork and the name of the artist is just part of the frame.  Lately the art trail keeps leading back to Johan Ason’s Mandelwerk Castle, his Deviant Art gallery.  I think there is such a thing as a talent for working with fractal software and other algorithmic machines to make artwork.  It’s like a talent for taking photographs.  It’s different than a talent for painting or sketching but, like all visual art, the final result is something you look at.  The process is different and as such it favors a different skill set and a different talent that directs it.  So maybe there is a such a thing as a good fractal artist.

Johan (aka Kraftwerk on seems to have that talent for fractal software.  And there’s a few others.  Let’s take a look.

~ Click any of the following images in this posting to view full-size on the original site ~

Hommage to Benoit Mandelbrot, by Johan Ason (Mandelwerk)

Most of the time, natural imagery like sunsets and clouds clash with computer generated fractal imagery.  For that reason alone, Johan deserves an special award for this one: the natural sky and the fractal landscape fit together perfectly.  And as a salute to the recent passing of Dr. Mandelbrot it’s even more appropriate:  I can’t think of a more realistic, while at the same time fantastic, rendering of what an alien planet might look like; a world created by fractal geometry.

Someone on commented on the excellent composition of the image also.  The eye is naturally and effortlessly guided through the image first from the structure in the left foreground, across that barren stretch in the middle to the distant hill and finally to that fading sunset.  Painters can make these sorts of compositions happen deliberately, but photographers and fractal artists have to hunt them down and capture them in the wild.  (With a little help sometimes from a graphics program.)

13th Secret of Cathedral Woods by Johan Ason (Mandelwerk)

You really need to click on this one to see the great detail in the full-size image.  The “tree trunks” themselves have some strange secrets to tell and the glowing glass canopy of “leaves” is even more spectacular in the larger version.  Cathedral and Woods makes for a good title and I like the mysterious sound of the 13th Secret.

Do you see the strange face lurking beside the tree trunk in the right corner?  That’s not an evil troll waiting to skin you alive in a full moon ritual, that’s the artist.  I’ve seen artists try to get creative with their signature/watermarks but none have looked as good as this.

Finest signature/watermark I've ever seen by... Johan Andersson!

Well, drown my kittens!  It’s Andersson, not Ason.  I noticed that his first name didn’t seem to be spelled right on his Deviant Art page, so maybe I should have been more careful.  Don’t believe everything you read on the internet or just guess at stuff you’re not sure about.

That’s his picture (I’m guessing); the squiggle on his shoulder is his actual autograph; there’s an email address and a nifty, euro-company name: KONSTPRODUKT.  All that in a single color image; that’s better identification than a passport.  Very classy.  Apparently konstprodukt is Swedish for artifact.  I think I’m getting close to unraveling the next secret of the Cathedral Woods.

Anyhow, Johan has constructed a very creative as well as effective signature for his work.  The email address is a great idea.  Assuming that shadowy figure hasn’t scared you off.

Seventh Secret of the Forest by Johan Andersson (Mandelwerk)

Johan writes: “Inspired by Jesses;sa=view;id=3447 and Rrrolas images of negative scaled boxes I went ahead and found a surreal forest…”

I would never have thought such an image could come from the mandelbox, but then, it hasn’t even been around for a whole year yet, so maybe there’s lots more to be done with it.  A very different style of image from the usual 3D fractal graphics.  It would make a great Yes album cover.

Dark Secret of the Moon by Johan Andersson (Kraftwerk/Mandelwerk)

Apart from the awesome panorama in the top left of the image and the shining cliff face that forms part of it, what I find equally interesting is what’s going on in the right hand side.  The incredibly lifelike and very graphic imagery on the left slowly changes to very plain, geometric and much more abstract imagery on the right.  It’s almost like a diagram or chart showing a range of something.  I find it gives the image a very surreal quality because the two very different sorts of imagery are connected and flow from one to the other.  It’s a sort of dissolving reality; a face slowly morphing into a landscape or a landscape gradually melting into a geometric shape.  It reminds me of one of those many Salvador Dali abstracted sequences.

Under Desert by Jesse

This is the image referred to by Johan previously.  As he said, it’s a variation using a negative scale parameter setting.  The results, as you can see, are these elegant, almost vector graphic images.  The title is a very good one; a desert cave or tunnel with some glowing light source.  Again, such a different style from the gritty, weathered stone surfaces that most mandelbox images have.  It sure pays to explore the whole range of parameter settings.  When you set off to boldly explore the mandelbox formula, this is the sort of treasure and new worlds you may find.

Statics by Jesse Dierks (Jesse)

This one is absolutely incredible, isn’t it? not just because of the innovative needle like structures but also because of the range of imagery and the incredible intertwining designs.  Note also the interesting recursion of the design we see in detail in the top and left as it iterates into infinity in the bottom and right.  The color is perfect; from the gold/orange of the cathedral like spires to the fish bone needles in the mid-ground to the red/green clay surface that lays exposed in the top right.  Jesse deserves not just an award for this image but for creating the program that made it.  He’s a real multi-talented individual.

Mandelbox add rotations 2 by Krzysztof Marczak (buddhi)

The full size is worth the click.  I found this one via Johan’s list of Favs on Deviant Art.  I see an alpine scene; something up in the mountains but grass covered.  That smooth golden patch in the upper right is a (fractal) alpine meadow.  And from that meadow you can see the distant tops of other mountains, but, just kind of twisted and spun around.  I can’t explain the smooth cave structures in the bottom right, but sometimes dreams get mixed into the formula.  Click on them, and they’re gone…

Emerging by bib (Jeremie Brunet)

What the tomb saw, before the archaeologist entered.  Is that a mandel-light-bulb glowing and emerging from the crypt?  Perhaps this is what light sources look like up close in the mandelbox programs?  Anyhow, I like the Egyptian tomb look to this: the ornately carved wood furniture and the decorated walls.  It’s both ancient and decayed while at the same time elegant and well, emergent.  Something is coming out and it doesn’t look any worse for wear after a few thousand years of lying entombed in silence.  There looks to be two other burial things there in the foreground.  Empty?  Or robbed?  It’s a mistake that the emerging thing has allowed you to see this much and live.  Be thankful for that oversight and start running.

"mandelbulber_03_10_2010_sauermann_b" by Jotero (ID on

Jotero?  A new face on  And he’s got his own unique style too.  Who else makes 3D fractals that look like this?  The coloring here is special.  It creates an electron micrograph look.  That’s a photograph taken through an electron microscope.  If you had really good eyes and they worked with electrons instead of photons, this is what you’d see when you looked at a mandelbox.  From the title I’m assuming he used the Mandelbulber program by buddhi (Krzysztof Marczak), a free program for Windows as well as Linux.  (Not to be confused with the Mandelbulb 3D by Jesse.)

"mandelbulber_06_10_2010_b_sauermann" by Jotero

Magnificent detail.  This is a royal mandel-palace.  And it’s virtually monochromatic and yet looks great.  The single color tone probably heightens the visual impression that all those intricate details make.  Very subtle lighting and shading makes for a very vivid 3D image just like a scanning electron microscope does.  The best fractal images are discovered, not constructed, in my opinion.  I’m sure we’ll be seeing some more great work by “Jotero”.  (Some connection with this site and this one, too.)

I’ve got more.  Lots more.  My fractal fishing net is still full.  There’s just so much good stuff out there since the Mandelbulb and all the rest of the 3D fractals crashed onto the scene.  So I thought I’d make a start by emptying out my net here; starting with Prince Johan …and a few others.

Copyright and Fractal Art: If a tree falls in the woods…

Kellerwald by Willow (Wikipedia) Published under a Creative Commons Attribution Share Alike license

If a tree falls in the woods…

…and no one hears it, does it really make a sound?

If a tree falls in the woods and it doesn’t cost anything, does it really make a sound?

If someone violates your copyright and it doesn’t cost you anything, should you be making a sound?

Does copyright have any purpose or meaning in situations where the artist’s commercial interests are not threatened?

Purpose of Copyright

The US Constitution, Article 1 Section 8 (powers of Congress) has this to say about copyright:

To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

The World International Property Organization (WIPO – an agency of the United Nations) says this about copyright on their website:

The purpose of copyright and related rights is twofold: to encourage a dynamic creative culture, while returning value to creators so that they can lead a dignified economic existence, and to provide widespread, affordable access to content for the public.

“To encourage a dynamic creative culture while returning value to creators so that they can lead a dignified economic existence”.  In other words: to make money from their work so they can make more of it.

Copyright was invented to commercialize the production of cultural works so as to benefit those who produce them.  Copyright granted a monopoly to the artist for the commercial exploitation of their work.  Copyright then, is a legal device which attempts to promote the production of creative cultural works by making them economically self-sustaining.  Profit, that great economic motivator which dictates the careers and daily routines of most people, can now be harnessed for the production of culture via the mechanism of copyright.

Moral Copyright?

So getting back to my analogy of the tree falling in the woods, one ought to first consider the commercial ramifications of those copyright trees that fall in the woods before “listening” to them, because that’s really what copyright is all about: commerce.  Long before I ever started reviewing fractal artwork on the internet I became aware that most fractal artists saw copyright as the exclusive right to say, “Hey!  That’s mine!” whenever their work popped up somewhere they hadn’t put it.  But that sort of “moral copyright” is something that:

  1. Was never intended by copyright law
  2. Makes an actual lawsuit totally pointless
  3. Serves no purpose in fostering cultural works

So far there is no commercial market for fractal art in the form in which it appears on the internet.  Images uploaded to the internet at best serve the commercial purpose of low resolution samples from which potential customers can go to the artist to buy prints.  It’s the high resolution files that have commercial value because only with them can you produce prints.  If you just want to look at the images online, that’s free of charge, but if you want to look at them offline like as a print hanging on a wall, you have to pay.  You have to pay because you need access to a high resolution file and you can’t get that on the internet.

These low resolution images posted to the internet allow artists to exhibit and share their work, for the large part, so far, as a hobby and in the context of an online social network.  They don’t allow artists to make money merely by posting them to the internet; to do that they’d have to charge admission to their online gallery and simultaneously restrict access to it.  There is no commercial loss to artists when their images are reposted elsewhere on the internet because no artist anywhere charges merely for viewing their work.  In fact, if a proper link is provided, one can argue that reposting artwork serves only to benefit the artist commercially by increasing online access to it and thereby increasing their audience and subsequently the potential market for their work.

Links can be good for art sales

Most commercial enterprises on the internet pay people to link to them.  Amazon, for example, has a very sophisticated and well established system for paying people to review their books, post the (copyrighted) cover art, and link to the page on Amazon that offers the book for sale.  Here’s a screenshot for those of you who never click on text links:

Amazon Associates Referral Program by Oct 19, 2010. Click to visit site.

Web browsers = Virtual Squirrels

Images posted to the internet are in an environment where copying is not just easy, it’s trivially easy.  In fact, copies of them are made by the viewer’s web browser for everything they look at and stored in their browser’s cache automatically, whether they want them there or not.  I said, “for everything they look at” but if you look through the file folder used as your browser cache you’ll probably also find some images you didn’t even notice while you were browsing; that’s how trivial and common the act of copying is on the internet.

I don’t know of anyone who actually sells the low-res digital images they display on the internet; I don’t see anyone actually trying to do this.  I do see other types of digital images being sold and it’s theoretically possible for fractal art to be sold that way too, but I’m not sure how much success fractal artists (or any artists) would have selling desktop wallpaper images or stock images for websites or electronic publications.  Outside of print sales, which require high resolution image files that are rarely posted to the internet, fractal art images found on the internet have no significant commercial value and therefore the copyright protection which they hold is virtually meaningless (no pun intended) in such a non-commercial context.

Money is the backbone of copyright.  Without it, copyright literally can’t stand up.  Instead it becomes some misshapen and dysfunctional thing squirming about on the floor making strange gurgling and terrifying noises (so to speak).

Don’t let your artwork surf naked

Did your mother ever tell you to put your name on something before you take it to school to show everybody?  Well, she’d probably tell you to put your name on your fractal images before publishing them on the internet.  That way you’ll always be assured of attribution and at least a “visual” link by which interested viewers can google your name and find your site.  Large images might be resized so consider making your name large enough that it will still be readable if the image is reduced to a size in the neighborhood of 300 to 400 pixels.  Cavemen didn’t sign their art; but if they were alive today they would.

Early attempts at uploading. (By Abdullah Geelah - Creative Commons-SA license)

Copyright is slowly getting acclimatized

Although the internet may not seem like a new thing to anyone anymore, it’s still developing and is only gradually becoming incorporated into the deeper structures of our culture and society.  Laws are probably one of the most complex aspects of our culture and the medium in which politics and social power are most intensely expressed.  Even stupid laws are the result of very careful complex social and political negotiation.  Small changes to the social and political environment of any country often results in changes to its laws or in the creation of political pressure to make those changes.

The internet has brought about many changes to the world and nowhere have these changes been as extreme as in the area of publishing.  Publishing is done differently on the internet and naturally laws which were designed for an offline publishing environment won’t always achieve the same intended results when applied online.

Continuing my analogy… when trees fell in the offline forest (i.e. they were copied) the event was almost always one of commercial significance because offline publishing is expensive (print, television) and almost always had to revolve around making money in some way, if only just to exist.  But today, when trees fall in the internet forest, the event rarely has any commercial impact because a good deal of internet publishing (posting, uploading) is for fun or other non-commercial, amateur purposes.  Sure, there’s people on the internet cutting into the profits of film and music companies through file sharing, but if you look at what goes on elsewhere on the internet it’s a completely different situation because all of that internet activity is happening outside the context of any potential or actual commercial market for what is being viewed, up- or downloaded.  Accusing people of stealing amateur internet content makes about as much sense as calling your insurance company to tell them your car has been downloaded.

Copyright takes on a different meaning when it’s applied to amateur, online communities like the fractal art world.  Traditional copyright law was drawn up for very different situations.  It doesn’t make sense to respond the same way to seeing our artwork on someone else’s website as we would if it was being used for the cover of Time magazine.

Copyright and Fractal Art: Crimes of the Century

In my previous post, Copyright and Fractal Art:  What the law really says,  I quoted from the US Copyright Office what their definitions of copyright privileges and fair use exemptions were.  Fair use is something that is always a matter of argument and degree, but some scenarios make for extremely simple arguments –against fair use.

The examples I am going to mention, fortunately, have all disappeared.  I can’t link to them or post screen shots because they’ve either gone offline or literally, changed their address.  A few are still online but I don’t want to link to them because it’s not really necessary and besides, they are real examples of copyright infringement.  As a result, the contents of this posting will have to take on a rather anecdotal style.  The actual facts of the infringement aren’t that important anyway as they merely serve as examples of realistic, online situations involving copyright in the fractal art world.

The Case of the Cell Phone Wallpaper Salesman
If you’ve hung out on Deviant Art for any length of time you will have heard about this one and maybe know more about it than I do.  A well known fractal artist discovered some of his fractal images on a website being sold as part of a collection of  images to be used as wallpaper for cellphones.  He noticed the work of other fractal artists and posted his discovery which is how I came to know about it.

Is is fair use?  Of course not, but let’s go through the four factors that the US Copyright Office gives for determining fair use and is the format which Columbia University’s analysis of (attempted) fair use examples also follows.  The four factors are: Purpose; Nature; Amount; and Effect.  (For an official explanation of the four factors, see 107. Limitations on exclusive rights: Fair use from the US Copyright Office website.)

  • Purpose: to make money selling the artist’s work.  This weighs heavily against fair use because the purpose is purely commercial as opposed to educational, informative or commentary and review.
  • Nature: the copyrighted works were creative in nature and taken from a site where they were also available for sale, although not as cell phone wallpaper.  Factual works, like photos of natural scenery or say, illustrations of mathematical formulas, are more likely to be fairly used because they have obvious educational and informational applications.  Works that are entirely the product of a person’s creative expression need a stronger argument to be fairly used.
  • Amount: although there would have been some reduction in resolution and resulting image quality to display it on the cell phone screen, the images as sold for download were identical to the originals taken from the author’s website.
  • Effect: the copyright holder’s original images are used partly to solicit sales for high resolution prints and are already available for anyone to use as a cell phone wallpaper if they have the technical knowledge.  Lack of attribution for the artist however, would prevent people from buying high resolution prints and frustrate one of the artist’s purposes for freely posting the images.

Is there anyone who would not say that this is a clear case of copyright infringement?  I think the main factor is that the use is purely commercial and has absolutely no criticism, comment, news reporting, teaching , scholarship, or research aspect at all.  There doesn’t appear to be any commercial harm to the work though if you really look at it, and, in fact, the infringer is only offering a use for the original images that is already available without restriction, although that use (saving the image to your cell phone as a wallpaper) would also be copyright infringement as well, strictly speaking.

The Case of the World’s Greatest Artist
This one is actually pretty recent, but from what I’ve heard it’s something that’s been cropping up every so often for quite some time.  A new user appears on Deviant Art or Renderosity and is suddenly in possession of a “personal” gallery of what is nothing more than the greatest hits of Deviant Art’s fractal art section.  A few prowling Deviant Artists soon discover the gallery, are immediately outraged, break the safety glass and pull the nearby Copyright Alarm.  The moderators have day jobs, however, and they also have to go through a lengthy checklist before removing the offending user’s account, but before all that they need to check it out because there’s some disbelief in their own minds because “why on earth would anyone do that?”

  • Purpose: Social prank.  (Apparently) non-commercial.
  • Nature:  The copyrighted works are creative artwork.
  • Amount:  Entire images at the same resolution (image size) as the originals –identical copies of digital files.
  • Effect:  Artists would not have profited from any sales of images bought through this bogus gallery and possibly suffered some damage to their reputation from buyers who might have received low quality prints (the bogus artist would not posses the necessary high resolution files to make proper prints).  Furthermore, the true authorship of an artwork is confused when it’s displayed without the artist’s name and especially in this case, when it’s displayed with another artist’s name.

Artists have a legal right to attribution even if they sell their copyrights to an image (see 106a).  It’s easy to laugh this one off because it’s pretty hard to put up a bogus gallery on a place like Deviant Art without a huge and immediate public outcry (or do anything else).  But the possibility really does exist of selling prints and therefore the commercial exploitation of the copyrighted works and their potential customers also exists which could result in damage to the real artists’ online reputations.

Most examples of this sort of thing are just pranks, but in a similar way, today’s real-life threat of computer viruses started off years ago also primarily as pranks; the criminal potential of bogus galleries is something that could give this type of copyright infringement a much more serious outcome if the artwork has significant commercial value.  Printing your name on your images is perhaps something artists ought to consider if they see their work as having commercial value and they engage in business on the internet.  Just like having a burglar alarm sticker on the front door of your home, it might just be enough of an annoyance to dissuade anyone who has criminal intentions.

In case you’re still wondering, I think it’s safe to say this is a case of copyright infringement.

The Case of the Really Bad Musical Slide Show
An adoring fan has visited your fractal gallery.  He just loves your stuff.  He loves music too.  He plays cultural match-maker and weds your wonderful fractals to Mozart.  He then uploads the resulting video to YouTube.  He’s got your name in the video so people know you made the artwork, but there’s no link to your site or anything else that might direct fresh fans to the original source.  Somehow or other you find out, but not before some time has elapsed.  You email the fan because he’s got a contact address posted…

  • Purpose: To (attempt) to create a beautiful thing just for fun and without commercial intentions.
  • Nature: The images used are creative works.
  • Amount:  He used the whole image, and several of them are ones considered to be your best but they’re so small and YouTube’s compression has smudged them so much they’re hardly a substitute for the originals and would probably send interested viewers to your site if there was a link.  The main feature of the video is your work, the music (albeit Mozart) is commonplace and merely a background.
  • Effect: Not likely to have much effect on the commercial sales of your artwork although, possibly, some interested viewers might google your name and find your website while others write you off entirely as the “Painter of Sludge™”.

This is not fair use because the purpose is merely to exploit the aesthetics of the artwork.  The use is not “transformative” as it doesn’t use the artwork in a way which is different, and therefore, non-competing, with the the original.  You can’t simply take copyrighted work and display it because you’ve got a “great” way of doing it.  For that you need to either own the copyright or get permission.

Furthermore, the work is displayed as a poor quality reproduction, although perhaps not intentionally (YouTube’s compression can really produce bad results sometimes), and this can present a poor impression of the artist’s work and subsequent reputation which is also a violation of copyright law (see 106a again).  Fans like this aren’t doing you any favors.

The Case of the Caring, Sharing Customer
I don’t know if this has ever happened, but I suggest it, hypothetically, because it could well become “the end of the world as we know it” with respect to copyright and make all the other crimes look like petty annoyances.

You put together a really nice DVD of high resolution artwork (but not print grade) and even spend a little money to give it some professional features.  One of your customers buys a copy, transfers the entire disk to his hard drive and then uploads it to Pirate Bay because they think it’s great and want to share it –with the whole world.

People who consider your $20 price tag to be “ridiculous” and who are accustomed to ripping off big, money-stuffed media companies while they sleep, download your DVD and highly recommend it –on Pirate Bay– not at your online store.  After a year or two, sales have never really taken off for your nice DVD project although you’re always selling a few, but it’s just your first and you’re half way through making the second one which you know will be much more impressive.  But the business angle doesn’t look so clear anymore because online “file sharing” has a better price tag and faster delivery and how can you possibly compete with that?

  • Purpose: To make it possible for people to get your DVD for free.
  • Nature:  The works are creative.
  • Amount:  An exact duplicate of the entire work.
  • Effect:  It makes buying the original from the copyright holder unnecessary and thus potentially destroys the commercial value of the original.

I just put those four factors up for the sake of consistency.  This one loses the fair use test for every single factor but that’s not surprising because the sole motive for this kind of activity is to sidestep copyright altogether so consumers don’t have to pay the copyright holder for a copy.  That’s precisely the sort of thing copyright was made to oppose.  The only redeeming quality here is that the pirates aren’t trying to sell the “shared” files.  But then, even if they did, I guess someone would post them somewhere else and destroy their (illegal) business.

File sharing is a crime.  It’s a complete renunciation of copyright law.  Some people get philosophical about it and play up the pleasant feeling associated with “sharing” and it’s kumbaya qualities, but what they’re really saying is they don’t believe in the legitimacy of copyright at all.  It’s obvious how copyright law views such things:  the two are arch-enemies.  It’s not so obvious however, which one will win in the long run.

Well, there’s the fractal art copyright crimes of the century.  The way things go on the internet though, the next decade could be a whole new century.

Copyright and Fractal Art: What the Law really says

Copyright: the word that launched a thousand fairy tales!

Let’s see what the US Copyright Office says about copyright:

§ 102. Subject matter of copyright: In general28

(a) Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device. Works of authorship include the following categories:

(1) literary works;

(2) musical works, including any accompanying words;

(3) dramatic works, including any accompanying music;

(4) pantomimes and choreographic works;

(5) pictorial, graphic, and sculptural works;

(6) motion pictures and other audiovisual works;

(7) sound recordings; and

(8) architectural works.

What it means for fractal art: graphical works are protected by copyright

Here’s some more from US Copyright Office:

§ 106. Exclusive rights in copyrighted works38

Subject to sections 107 through 122, the owner of copyright under this title has the exclusive rights to do and to authorize any of the following:

(1) to reproduce the copyrighted work in copies or phonorecords;

(2) to prepare derivative works based upon the copyrighted work;

(3) to distribute copies or phonorecords of the copyrighted work to the public by sale or other transfer of ownership, or by rental, lease, or lending;

(4) in the case of literary, musical, dramatic, and choreographic works, pantomimes, and motion pictures and other audiovisual works, to perform the copyrighted work publicly;

(5) in the case of literary, musical, dramatic, and choreographic works, pantomimes, and pictorial, graphic, or sculptural works, including the individual images of a motion picture or other audiovisual work, to display the copyrighted work publicly; and

(6) in the case of sound recordings, to perform the copyrighted work publicly by means of a digital audio transmission.

What it means for fractal art: only the creator of an artwork has the right to make copies of it.  Only they can sell or distribute them.  This is what is meant by “copyright”.

There’s a few more rights for artists:

§ 106A. Rights of certain authors to attribution and integrity39

(a) Rights of Attribution and Integrity. — Subject to section 107 and independent of the exclusive rights provided in section 106, the author of a work of visual art —

(1) shall have the right —

(A) to claim authorship of that work, and

(B) to prevent the use of his or her name as the author of any work of visual art which he or she did not create;

(2) shall have the right to prevent the use of his or her name as the author of the work of visual art in the event of a distortion, mutilation, or other modification of the work which would be prejudicial to his or her honor or reputation; and

(3) subject to the limitations set forth in section 113(d), shall have the right —

(A) to prevent any intentional distortion, mutilation, or other modification of that work which would be prejudicial to his or her honor or reputation, and any intentional distortion, mutilation, or modification of that work is a violation of that right, and

What it means for fractal art: Artists have the right to have their name displayed with their work so people know they made it.  They also have the right to prevent their work from being used in ways that harms their reputation.

And now for something, completely different:

§ 107. Limitations on exclusive rights: Fair use40

Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include —

(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;

(2) the nature of the copyrighted work;

(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and

(4) the effect of the use upon the potential market for or value of the copyrighted work.

The fact that a work is unpublished shall not itself bar a finding of fair use if such finding is made upon consideration of all the above factors.

What it means for fractal art: It is not a violation of copyright to use an artist’s work for the purpose of criticism, comment or news reporting; it is actually considered “fair use”.  But in order to qualify as fair use four factors must be considered and therefore determining fair use is a matter of degree and argument.

Well, that’s what the law really says.  Surely quoting the documents of the US Copyright Office is the best antidote to myths and misunderstandings about copyright?  Or, at the very least, it’s the best place to start.  As you’ll see in future Orbit Trap postings on copyright, there’s more to know about all this.  But those other things are minor compared to the weightier stuff presented here.

A few of my own personal comments regarding fair use:

Fair use is complicated because fair use, as described by the US Copyright Office, is something that needs “determining” and involves “factors” to be “considered”.  This fuzzy quality to fair use is probably because the range of materials that can be protected by copyright –anything that can be “fixed in a tangible medium of expression”– and the widely varying circumstances in which they can be used makes a simple set of rules inappropriate (impossible?) for determining what is, and is not, fair use.

There’s writing, music, visual art, photography, film, dance and other types of media, and they can be quoted, critiqued and collaged and it can take place in newspapers, radio, television, advertising, online, public performances, and in a hundred other ways and finally, it can be for commercial or non-commercial purposes or even non-profit, charitable purposes or for purposes that are educational, entertainment, informational.  And then there’s examples of parody, making fun of something which can result in the creation of a completely new work which itself will be protected by copyright in addition to making claims of fair use of other copyrighted works.  And let’s not forget the future:  in the future there will likely be fair use scenarios we can’t even imagine today.

Copyright is pretty simple but fair use is not.  Copyright is simply about who made what and when, but fair use is about: 1) what exactly are you doing and why;  2) the uniqueness and eccentricities of the medium;  3) what is the core substance or essence of the copyrighted work and how much of that “thing” are you actually using;  and  4) what effect will the sum of those three factors likely be on the commercial value or potential value of the copyrighted work.

Legal precedence is the past judgments of actual court cases and has a great influence on future judgments because it creates standards by which those future cases are compared.  But with fair use, the cases that have actually gone to court and received a verdict often create very little precedence because those cases are so unique that they’re only partially applicable to the ones that may come after.  One needs to compare judgments for scenarios that are as close to their own intended fair use case as possible to be relevant.  But they’re hard to find and if they involve internet use, then they’re very hard to find.  All this makes for conflicting expectations between copyright holders and those who engage in fair use activities.

Anyhow, here’s a good copyright guide from Stanford University, albeit primarily from an educational perspective, but clear and easy to read.  There’s also some more resources from the US Copyright Office website.

Fractal Universe Calendar 2011 – Spot the duplicates

Cornelia Yoder was true to her words: the Fractal Universe Calendar 2011 is made up exclusively of her images and retains the traditional name although the publisher has skipped like a stone from Avalanche to Lang to Perfect Timing.  She has also kept up the time-worn tradition of adhering to that tested and true style that, in the words of one editor, “just works”.

Cornelia’s had quite an act to follow; over a decade of lush fractal bouquets, turned this way, turned that way, some with ribbons, some with none at all –but all of them radiating that, je ne sais quoi, that has made the Fractal Universe Calendar a cult favorite and engendered today a very cultish following despite more than a decade of progress in fractal art software and artistic style within the fractal art world.

But I sense the worshippers of this Fractal Universe Calendar style are coming to the end of their creative spiral.  I can see a good number of images amongst those published throughout the years that bear a close resemblance to each other.  Is this the coalescence of a new sub-genre? or the inevitable genetic collapse after so many years of inbreeding?

Some of the images to me look to be minor variations of the same parameters.  For instance: compare 2007-4 and 2009-7, counting from the left to the right.  Now there’s a twisted family tree –one too many “Julias” in that one!  Imagine having no in-laws.

Look carefully; can you spot any other slightly modified duplicates?  A little shift of the hue?  Something spun the other way?  Old tire, new tread?

Can you see any?  Or is it just me?

Fractal Universe Calendar 2011 and past years thumbnail gallery. Click to view larger version at publisher's site

What the Fractal Universe Calendar did for Fractal Art

What has it done for fractal art?  It’s brought publishers to the realization that fractal art can be bought in bulk like any other stock imagery they already use.  The years of contests, editors, sorting, sifting, short-listing and final cutting are over; just find someone who knows how to make the stuff and order a dozen.

While Cornelia Yoder might be “flabbergasted” over her recent rise to fame, laying claim to what used to be a highly contested and multi-artist production, I see this sudden development as a sign that the calendar publishers have gotten wise to the over-inflated view that fractal artists have of themselves and their cliche artwork.  Publishers don’t need “artists”, they just need one person who can perform the fractal equivalent of a flower arranger.

Flower Arrangement 2 by Craig Hein Design

Now I know some of you like the kind of fractal art that the calendar features (year after year) but that’s okay because there’s many people who love looking at flower arrangements and they have about as much variety in artistic style as the calendar’s “fractal arrangements” do.  I’m not interested in pointing out what is “good art” and what isn’t, I just want to point out that “fractal arranging” has become a very common skill which is easy to acquire and needs only a little “tweaking”, as they say on the Ultra Fractal Mailing List, to enable one to produce work that can be considered individual.  It wasn’t that way back in the 90s when these delightful, shiny ribbon things first burst onto the fractal art scene, spinning and sparkling in ways fractals had never spun or sparkled before.

Easy and Efficient Online Floral Arrangement Ordering from FTD

I have a funny anecdote to tell: back a year ago when the Fractal Universe calendar was going through some changes and looked to be closing up and then to be producing one last issue without a contest, I thought they had made a new calendar out of old images from previous years.  So I went to the calendar site and compared the latest calendar’s set of images with the archives.  Immediately I was sure I spotted some duplicates!  I searched the archives to find what image and from what year they’d taken it –but I couldn’t find them! The ones I thought were reprints weren’t reprints at all it seemed.  But it was hard to be sure so I went over each year again because I was sure I’d seen a few images from the new calendar that matched ones in the archives.  Finally, I had to go through the process really slowly and carefully: I would look at the new one I suspected of being reused and then look at a single archived image and then look back at the new image again and then repeat the process with every archived image.  It took a while but I was certain I’d find proof that they’d rehashed old calendars.  It was like in the old cop TV shows where they have a witness look over the mug shot books again and again because the detectives can’t believe none of the criminals in the book match the person the witness saw.  Then it dawned on me:  These fractal images are all so similar that they have no distinguishing characteristics –They all look the same!

So, is it any surprise that the calendar publishers have come to the same conclusion?

Publishers now believe that…

  • Fractal art is a type of craft, not a type of art
  • Fractal art is anonymous because it lacks the personal style that traditional art, like painting or even photography has had, and which gave its creators name-brand recognition
  • Hundreds of artists can make those “flowers in a blender” fractals and it’s a nice, safe style for mass consumption because the wall-calendar buying public is primarily looking for decoration and inoffensive gifts, not the latest cutting-edge fractal art
  • There’s no reason to pay more than a token fee for fractal art because artists have been lining up year after year just for the thrill of getting offline attention and online bragging rights
  • If they ever get into the paper plate business, they’ve got enough fractals to put off hiring a design department for a hundred years

So the next time you hear someone trying to defend things like fractal art calendars because they “introduce fractal art to a mainstream audience”, just tell them the story about the great Fractal Universe calendar and what it did for fractal art.

The only way fractal art will ever become mainstream is by becoming mainstream.

Smudge-ism: Blurred to Perfection

We’ve all heard of blur.  It’s one of those basic graphic effects that every graphics program, and even some fractal programs, automatically include.  Most of us though are probably more familiar with the sharpen effect which does the exact opposite which is to get rid of, or at least reduce, blur.

Few digital artists, and for that matter, few artists of any kind, would deliberately blur an image, especially an entire image.  Fewer still would do it again and again pursuing on a large scale such a passive, mild-mannered effect which is usually only employed on a small scale.

I should point out that the images here are not digital works.  They’re combination prints which are photographs made by combining negatives to make a single image.  It’s just like layering, in fact it is layering in it’s original, literal sense.

The artist who made all of these images is José Medina and they come from his Transitions series of combination prints made this year.  I found these images at and since they are all displayed in a flash applet along with the works of many other artists it’s impossible to link to them.  Strangely, they don’t appear anywhere else on the internet except as these small thumbnails in the flash applet; perhaps they are unique to Medina’s work at the CRAM collective.  I first saw the images in a Niagara Region (as in Niagara Falls) travel magazine and was immediately impressed with their strong artistic qualities and unique style.  Like the Mandelbox, they just looked so incredibly cool.  I Googled the artist’s name and found some more wondrous examples on the CRAM site.

About CRAM:

CRAM was founded in February 2006 and is located in the heart of Niagara on the second floor of 24 James Street in downtown St. Catharines, Ontario, between Christopher’s Magazine & Smoke Shop and The Office Tap & Grill. The CRAMplex is home to Canada’s smallest art gallery, CRAM Press, and Marinko Jareb’s DJ Service, Fine Art & Design Studio & Collectible Designer Toy Shop.

CRAM Gallery showcases a collective of professional artists with ties to St. Catharines and Niagara who advocate regional ideas from outside metro and international centres.

CRAM Press was established as Canada’s smallest independent print workshop in 2009 by Co-Directors Tobey C. Anderson and Alan Flint with the installation of Harold Town’s old etching press. In August 2010 the CRAM Press was expanded to accommodate an American French Tool etching press and, while no longer Canada’s smallest print studio, it remains Niagara’s only print facility.


Like I said about the blur effect, it’s hardly new and exciting but these images are new and exciting.  Like Colombus, I think Medina just sailed a little further than the rest but it was sailing over the horizon.  Now, of course it all looks so simple because he’s shown us where we too can go.

Digital or not, we can all relate to work like this and learn from it.  Or just appreciate it, “stumbling in the neon glow” as Aristotle would say.

José Medina 2010

“Less is more.” You’ve heard that I’ll bet but here you’re actually seeing it.  That’s the minimalist trick.  On the other hand less can also be a lot less and even nothing, but done carefully the object in the image become a mystery (mist-ery, ha, ha,) and it’s no longer something we recognize, it’s something that may be, or something almost imaginary.  Blurring can be transformative –in a good way.

I assume this image above is a lighthouse but that’s mostly because the next image is obviously a lighthouse and most artists work with themes.  But it doesn’t matter because the object is interesting even if I can’t say for sure that it’s not a concrete parking barrier or a lawn ornament.  And that black crackly thing on the right is almost fractalish even though I suspect it was placed there deliberately to balance the composition which would otherwise be somewhat empty on that side.  I think the distant hills in the middle foreground are, ironically, more distinct than the top of the lighthouse.  And how about the way the lighthouse dissolves into the sky?  It’s almost like a detail view of an old renaissance oil painting with its subtle but careful features.

José Medina 2010

This one has it all: dream-like details; dissolving boundaries; ghost-like horizons; colors that drift across the spectrum; and a few smudgy mysteries.  I particularly like the little window halfway up the lighthouse below the balcony railings.  I think it’s been deliberately not obliterated.  Good artists cheat like that.  Photoshop filters never do.

Although the method used is composite printing, Medina’s images here use that particular method to achieve a strongly blurred style of image.  Other composite prints look like normal photographs, crisp and in focus.  They just combine features and imagery in the same way we layer images in a grpahics program.  But Medina’s composite prints are characterized by a heavily blurred artistic style and that’s the effect that impresses me the most with them.  You could say they’ve been post-processed in just the same way we would make a fractal image and blur it in a graphics program.  Although, of course, most of us wouldn’t blur a fractal, we’d sharpen it.  It might be worth trying the blur thing if we could get results like this.

José Medina 2010

I’m guessing this is the CN Tower, Toronto’s great claim to fame for many years which has subsequently been overshadowed by even taller, free-standing, feats of engineering like the Burj Khalifa in Dubai.  But how many of those have been immortalized like this?  Yes, greater than that great icon is this new icon by Medina.  Towers of art will never be topped.

José Medina 2010

I don’t think a digital filter would produce such irregular blurring here.  In places you can make out brick work and in other places the edge of the building itself has dissolved away.  This is what I mean about the selective, hand-made blurring effect seen in these images.  The rooftops have been quite obviously, for lack of a better word, gaussian blurred as we know in the digital world.  I didn’t really notice it until I looked more closely at the edges of the building.  Or maybe it just came out this way?

José Medina 2010

A word about Craquelure.  Not the French candy, the cracking that old, hundreds of years old, paint in paintings do.  It gives an old, worn look which in this case accentuates the blurred, renaissance, faded, dissolving look.  I’m sure there’s a filter that does that too, but here there are some finer touches to it.  Note the dark “crack” in the lower mid section of this one and the 3D appearance to the other cracks.  It’s subtle, but then blurring is all about subtlety.  Subtle subtlety.

José Medina 2010

Well done blurring is hypnagogic.  We are seeing the image as it slips away into sleep.  But no, it’s us, the viewer who is dissolving away.  I say, “Well done blurring” because blurring is a tricky thing really.  It’s hard to straddle that ideal twilight zone of majestic illusion without falling off completely into total attenuation and pigmentary nothingness and at the same time not playing it so safe that we stay well within the everyday realm of legibility.  Blurring is a fine art and I show these images here because I think they’re the finest examples of it I’ve seen.

Is this image a palm tree?  Maybe.  But the regularity of the branches suggest something possibly mechanical.  Maybe an amusement park ride that spins around with swings hanging from it’s arms.  The swings are outside the picture and the chains that connect them are too small and thread-like to show up.  Look more closely and I think I see a roundish trunk and the slight presence of sunlight coming from the right hand side.  Some wind too.  Voices?  Sounds?  Asleep again…

José Medina 2010

I think blur is a kind of minimalism; it’s the transition zone between the usual, detail-driven and intelligent focused artwork that most artists make (and most viewers look for) and the incoherence of things like painting with white paint on a white canvas.  We can make out water and by deduction coast, possibly sand, a sandy beach, and a few dark objects along it, possibly rocks which would suggest those dark areas inland are trees and that this is a remote or more remote place or is that green haze in the right foreground a well-mowed lawn in a public park?

José Medina 2010

“Stumblin’ in the neon glow.”  That’s the sort of thing I mean.  And “purple haze” is not too far off either.  They’d make great names for filters that do this.  Neither of the authors would object to the use of those titles, I’m sure.  Does Jim have email?  Or Jimi?  What?  Jim and Jimi?  That’s almost a verbal blur.  “Grasshopper!  Now do you see it?”  “I see nothing at all master!”  “Good, good.  You have done well, Grasshopper.”

Again, I see water and from water comes shore.  The strange shapes in the foreground are rocks and since they seem to clash with the shore I’d say they’re part of a breakwall or shore project to reduce erosion.  The trail in this urban project looks familiar and I’m thinking that maybe I’ve even been to this place.  Medina is based in St. Catharines which is only 2 hours from where I live and since he seems to have included a photo of the CN Tower it’s possible that he visited the city and took this photo at one of its many lakeside parks that are characterized by these urban garden-isms.  On the other hand, it could easily be Cuba.  Blurring gives anonymity to things and yet the result is we claim them as our own.

The Master and his Iron Photoshop, José Medina

Sure, it’s an Iron photoshop.  Just look at the roller in his hand.  I think there’s a roller tool in Photoshop.  I’ve never used Photoshop actually.  I’m guessing that it’s the same as the Gimp and it has a roller tool and a smudgy finger tool and of course, several kinds of blur effects.  Gaussian is nice, but it’s not as sophisticated as the blur effect in the images here that I suspect have been done by hand, selectively, more in some areas and less in others.  Of course you can do that too in a graphics program.  You’re just using numbers instead of using your hand.  Not as much fun as working with the Iron photoshop, but then you’re not working with zero levels of undo like they are in the Iron world.  (And when have you ever gotten your clothes stained with fractal ink?)

The Jumping Spiders of Oklahoma, and elsewhere

Is DNA an algorithm?  Can its renderings be presented as Algorithmic Art?  Will they jump down off the wall and attack the well-dressed gallery patrons?

Consider the humble jumping spiders of Oklahoma:

Jumping Spiders of Oklahoma composite from the work of Thomas Shahan on Flickr

As always, click on any image to view it on the original web site or in full-size.

It’s easy to define (and limit) fractal art to the renderings of fractal formulas, but then that also focuses our attention and our consideration on just that kind of imagery.  That makes a lot of sense at first because really, aren’t insects and weird microscopic creatures a completely different sort of visual thing than computer rendered fractal formulas?

On the other hand, we raise no objection to the inclusion of the complex creations of layering and other graphical manipulations when they’re labeled as fractal art even when their (assumed) fractal formula qualities are hard to recognize.  (Well, they at least started out as fractals.)  Perhaps the boundaries of any genre start to look arbitrary and fuzzy when we try to defend them.  Maybe visual imagery is more about what it looks like than how it was made?  In that case:  what does “fractal” mean?

After attending every live concert ever given, this Grateful Dead fan was spontaneously transformed into a hairy spider and now waits patiently on a tree leaf for the End of the World.

Aztec Flying City by arias on

Yes, arias combined the products of several formulas to create this very natural and stylish image.  This is a masterpiece of layering, and not the usual monstrosity that often results.  Check out the high resolution version (6000 x 2326 pixels) and you can marvel at the rich detail in this well composed image.  Note especially the mandelbox details near the middle edge on the right.

Arias is Bernard Bittler, has a professional art background and I believe lives in France.  I’m sure he’ll be making many more 3D fractal images because he’s obviously very good at it.

Cube Guardian by bib (Jermie Brunet)

This one is also even more impressive viewed full-size.  I like the subtle, blue-gray coloring and of course the velvety texture of the “clock faces” or “drums”  that are silent and yet ever-watching this tiny mandelbox neighborhood.  I might have titled this one “fungus clocks”.  It looks very natural and is proliferating with the growth of these round clock faces that to me resemble the smooth velvety surfaces of some tree funguses.  The fine detail to the left and right of the main Cube Guardian is a great presentation of the endless recursion of fractals.

Fractal forest by Power 8

It’s hard to put my finger on exactly what I find so captivating about this image.  There’s some surreal mood to this image and the title, Fractal Forest, is a good one as it really has the look of a strange, but forested, place.  The red-green coloring is very creative and works well despite being so unusual and unnatural for such a suggested “forest” scene.  You’d never guess this was a mandelbox (and I’m guessing) but it just shows how powerfully creative fractal art can be when you’re ready for the unexpected.  There’s a old, oil painting, Renaissance feeling lurking around down there.

Caves by Prokofiev

This image I found in a thread on discussing the “Hausdorff dimension of the Mandelbulb”.  I have to confess that although Fractalforums is an extremely rich environment for the discussion of all sorts of concepts and technical matters related to fractals and their rendering, all I mostly do is look at the pictures.

Perhaps this image was not intended by Prokofiev (a screen name, I assume) to be a powerful work of fractal art but rather merely to function as an illustration of some concept or technical issue?  Well, in that case it succeeds at both.  I’d like to title it, “Unzipping Infinity”.  Art doesn’t have to be lavish and complicated, it just has to push a few buttons in your mind.

Method by Far

A cellular automata triptych (three panel) made in Ultra Fractal.  Although cellular automata aren’t anything overly complicated to render, I didn’t know UF could render CA images.  I like the triptych style; it suggests something carefully made and designed to be set over top of an altar —sacred renderings.  Click on the image to see the cosmic details as well as things that cannot be explained.

CA have some interesting fractal and not so fractal qualities to them.  For one, there’s always a large scale structure to the image as well as a myriad of small, tiny scale structures.  This gives CA both a macro as well as micro appeal.  CA are the busy ants of the fractal (or something) world and this set by Far is a reminder that the creative possibilities are far from over for them (no pun intended).

Time for a movie.  Here’s an excellent fly over of a special area of a mandelbox that Kraftwerk (aka Mandelwerk on DA, aka Johan Ason) has been exploring recently.  This fly over is particularly well done and much more engaging than most I see because there is a specific subject or point of interest in it, that being the “Cheops” collection of structures which are also particularly interesting as still images in their own right.  Much more of “Cheops-ville” can be seen at Mandelwerk’s Deviant Art site (aka Kraftwerk).

Champion Graveyard Sound

Macro photography and fractals have a lot in common.  I don’t know what that is, but I just sense that they have a “family resemblance”.  Imagine you’re trying to put together a jig-saw puzzle but someone has accidentally thrown in another puzzle with it.  While looking for the pieces that match up with the ones you’ve already put together you’re also picking out the ones that belong to that other puzzle that don’t belong in the same box.  But you also keep coming across pieces that, while they don’t fit in immediately with the small part you’re already assembled, you sense they’re part of the larger complete picture and you want to hold on to them and not put them aside with the pieces of the other puzzle because they look, in some vague and hard to describe way, similar.

Calliphora vomitoria Portrait by Noodle Snacks

Haven’t we all zoomed into something like this in a fractal program?  This fly’s head reminds me of many of the formulas in Sterlingware.  Flies are purely a nuisance when seen at a regular scale but they are both magnificent and terrifying when seen up close.

Housefly on a leaf by Muhammad Mahdi Karim

I got these two fly photos off the Wikipedia.  This second one here is really a work of art.  I like color and I think color almost has a subliminal thought-inducing language and quality all its own.  What an incredible machine the common housefly is; no spaceship or aircraft a human could design will ever look as superb as this housefly.

Haze of Time by jesse

10 Million Year-Old Fractal Found in Antarctic Ice! According to a recent article in the Scientific American, some ancient species of molds when allowed to grow slowly and undisturbed for millions of years, grow and develop in patterns that are identical to those formed by iterating fractal formulas with a computer.

I just made that up, but that’s what I thought when I saw this image by Jesse in the gallery.  Great images just make me want to say great things.  The facts come later.

Assimilation by lenord

The mandelbrot inside the mandelbox!  But it seems only natural to find a mandelbrot man inside a mandelbox 3D fractal formula.  He lives there.  Just like a pearl inside an oyster and it’s shell.

I’ve looked at this image quite a bit and I can’t decide if it looks more like the mandelbrot is being absorbed by the mandelbox, as I think the title by lenord is suggesting, or if the mandelbox is actually growing out from –and growing off of–  the mandelbrot just like a plant grows out of a seed.  Lenord’s got some other ones like this and they have the same interesting combination of old and new fractal designs.  Apparently it’s all from the same formula and not from layering or some sly photoshop trick.

Kractal by tatty

New people are always popping up over at Fractalforums.  Fractalforums seems to be where all the action is lately.  I don’t know who any of these people are (and they don’t know me) but I don’t really need to know them when I can just look at their work and judge it for itself.  Tatty has really come up with something new here.  So much detail and such variety of it.  But it doesn’t look like a mandelbox or mandelbulb to me and yet it has that 3D look to it.  Could there really be some new thing called a “Kractal”?

Box 1 by tatty

Another by Tatty.  Already she’s developing some noticeable style just in these two images.  There’s a wide variety of shapes and yet they complement each other instead of clashing or looking pushed together.  Subtle and with good coloring too.

Box 1? If this is just the first she’s off to a great start.  Tatty has a good eye for the sort of pleasing organic shapes that fractals excel at.

The Last Dive by janetino

I followed a link from Mandelwerk’s Deviant Art page to these incredible mandelbox images by Janetino.  Janetino has such unique color palettes.  I’ve never seen any mandelbox images with this sort of coloring that looked so good.  Nice use of the foggy perspective effect here too.

The Laughing Cliff by janetino

This one is really something.  So ornate and such unique color.  The blue haze suggests sky and sunlight streaming into this ornate temple or ritzy spaceship.  I’ve got to look around Deviant Art more.  It’ll be worth it if I find another artist with such unique and well done work as Janetino.  She’s up there with the other top “Mandelboxers” in my opinion.

Hirgrnd1 by Seizo Yamada

Here’s an interesting photo for two reasons:  First, because it has such a dreamy, visionary, summer night, sky full of imagination and wonder look to it.  Second because it’s actually a photograph of the Hiroshima atomic bomb explosion taken, not from the air, but from the ground several miles away by a civilian who just happened to be in the right place at the right time.  It dulls the golden glow of the photo’s dreaminess to know we’re also observing an event that killed over 100,000 people in less time than it takes to answer a ringing telephone.  I wonder how many other attractive things in our world would look less appealing if we knew what we were really looking at?

Texture by hermann

Texture was found on the gallery like many of the images here.  The gallery contains (I believe) any images uploaded to the forum for any purpose, either artistic or as examples and illustrations in technical discussions.  I can’t always tell what context the image appears in with respect to the forum postings, I just browse the image gallery in behind the scenes mode and comment on whatever catches my eye.  I like this one for it’s simple, classical fractal style.  Sometimes less is more and this is a good example.  This image has a real sense of style and stands out because of it.

Another World by Well En Taoed

Just like Texture this image features imagery that isn’t new and cutting-edge like the mandelbox or mandelbulb and yet has real style and focuses on the more classical fractal type of imagery.  I think this has an extra layer, a grid pattern over it and although that might seem rather simple the effect it has on the image is strong.  It looks like it could have been taken off a vintage pulp sci-fi cover and maybe the author thought the same thing when he named it.

Mandelbox Lobby by Buddhi

This image really has to be seen in full-size which you can do by clicking on it.  The mandelbox, like most fractals, is capable of producing a lot of imagery but it takes a good eye and some careful experimentation to produce something of interest amidst the deluge of images that pour out of the formula  This one has a surreal look to it.  Maybe it’s the ornate architectural appearance that makes the square “front desk” of the mandelbox lobby look real and therefore strangely out of place.  The fact that it’s sunk below the horizon and hidden from sight enhances the eerie feel.

Menger Borg Mother ship by Cyclops

I hear this Borg thing mentioned here and there but I don’t know what it’s about or what it’s from.  I find it odd that a Cyclops would be making 3D art, but maybe that’s just a screen name for L. Shone?  There’s an MC Escher look to this and I like the careful, repetitive metallic detail in it.  The hole in the center is a nice touch and shows us that the inside is remarkably no different than the outside.  It’s got an old, engraved illustration appearance that I like.

Ave by Agurkyz (AGUS)

Another one that I’d call “classical”.  I guess I’m referring to fractal imagery that is single layer and was much more common back before multi-layered programs like Ultra Fractal came out.  But… this one was apparently made with UF!  I’ve always liked the shiny tubes and other orbit trap kinds of imagery that have an almost collage look to them.   The abrupt transitions resemble cut paper but sometimes the tube forests stretch all the way to the horizon although they do look like the scissors lopped off their upper branches, swift and invisible.  There can be a lot to see in these apparently simple images.  Good art is like that.

Orion4 by Dominique Peronino

I check in on the gallery everyday.  When I saw the first of these Orion images I frowned a little because it reminded me of when I first started out making fractal images in Sterlingware almost a decade ago.  Later on, after seeing this one and especially the jagged, machine made elements surrounding it, I began to see the subtle but attractive style that these Orion images have.  This is pure digital vision; it’s all machine made and it shines with a technological glow like only some bold new discovery in a laboratory can.  The machine drew this and no human hand can imitate that cold, fractonic style.

Titan (moon of Saturn) from

One last one.  This is a real photograph of Titan, the largest of Saturn’s moons.  I think it’s made up of several shots taken by more than one pass of the space probe although it lacks the jumbled, collage look of a composite photo.  I’ve been using this image as my desktop wallpaper for almost a week, centered with a black background.  I keep thinking it’s the opening shot from some vintage, 1950s sci-fi film that’s about to begin:  Sinister Planet.

Anyhow, those are the pieces of the puzzle.  Maybe some of them don’t belong to the same big picture.  Or maybe this puzzle is a lot bigger than the 10,000 piece label on the box says.  We should have started building this on the floor instead of the table.

Frames, drains and hurricanes

Many people have a favorite sport.  Some follow soccer, others american football or hockey, basketball, baseball, cricket…  I follow hurricanes, the tropical storms or cyclones that form in the Carribean during summer and fall of every year.  There’s never a players strike and you can follow all the action over the internet.  In fact, you really don’t want to buy tickets to see any of these “games” live.  The American National Hurricane Center gives you the best seat in town, or out of town, rather.  There’s only one team but everybody loses.  And it’s impossible to cheat.  It’s a funny sport.

This year was supposed to be much more energetic, which was a great relief after the incredibly disappointing 2009 season.  I’m still waiting for a really big, Category 4 or 5, game this year.  Bonnie was so pathetic the NHC stopped talking about her before she even made landfall which, in this game, is ordinarily the main event.  She just went back to being a depression —tropical depression.

They don’t name them only after women anymore, they’ll use any name.  They ought to let the folks living in the path of the hurricane suggest the names.  But they’ve got more important things on their minds –hiding, dodging, staying alive.

Life is the sport of sports and art is its World Cup.  But that’s coming from a guy who thinks hurricane season is more fun to watch than the SuperBowl.

Back to fractal art:  here’s a piece of fractal artwork by Deviant Art member Sophiiiii that caught my eye just this week and also strongly suggested –hurricane– to me.  (That’s Sophi with five “eyes”.)

– Click on any of the images below to view them full size and on their original site –

Ghosty Frosty by Sophiiiii on Deviant Art

This image (by “Five-Eyed Sophi”) has a number of interesting aspects.  Although, from the title, she probably didn’t intend it to have a marine theme much less that of a hurricane, it fits well into this and I think she saw a similar terrifying weather theme from her choice of the word, frost.  But maybe the spider web is the terrifying theme here?

I guess that’s the thing with “imaginary” art: the image is open to a number of interpretations, each one arising from the personal context the image unavoidably becomes mixed up in when it engages the viewer’s mind.

It was made in Incendia and I suspect has a few other layers incorporated into it, such as the spider web and the cloudy, watery background.

As I was saying about hurricanes, they are “wrathful” creatures that arise almost out of nothing and quickly grow (within days sometimes) into massively destructive beasts.  They are also composed, not of a neat circulation pattern which we see in the simplified diagrams used to explain them, but of broken and winding bands of thunderstorms and sometimes tornadoes spawned by those thunderstorms.  Sophiiiii’s image here, although completely artificial, is an excellent example of such an “extreme weather phenomenon”.

And it looks good too.  Incendia seems to have this nice ability to make grainy images that are more characteristic of real world imagery than the slick smooth world of computers, but I think Sophiiiii has added a lot of her own artistic talent to make this one looks a well as it does.

Tulum, 1988, Acrylic and Pastel on Paper, 18 x 20, by Peter Alexander

Sure.  This one’s not a fractal.  But when you’re floating in the ocean off the coast of Quintana Roo where Mexico meets Belize and the rest of Central America, such things are incidental.  There is the hint of shore in the dark bottom we see through the water, but where is it?  This is the morning after the hurricane.  It’s beautiful.  Out there somewhere is your house, but take heart, there’s plenty of building materials all around you.  One of them must have hit you and knocked you out.

I read an anectdote about hurricane Hattie that erased Belize City back in the 60s.  The author, a young boy at the time, told about how his family had completely lost their house (built on the beach, incidentally) but then a week later his father and uncle were out fishing and found a better one that the storm had dropped off from somewhere else.  I’ll bet there’s a lot of that shuffling of property going on in the wake of hurricanes every year.

Westmoreland, 2009, monoprint, 12 7/8 x 14 5/8, by Peter Alexander

Obviously this isn’t a fractal either, but Peter Alexander has made palm trees into such a separate and well developed genre much like the fractal spiral is in fractal art that they deserve a mention.  Click on the image to see the whole collection.  Very colorful.  I had a hard time picking the best one because they’re all very interesting.  Monoprints are prints that are made with unique characteristics and thus not reproducible merely by making another impression with the plate.  (I’ll bet they sell for more too.)  I think the coloring here is very sophisticated and carefully done.  I don’t like a lot of contemporary art (of the paintbrush sort) but these palm trees are something completely different.  Better than Warhol?

Revived by Sophiiiii

This one is just fantastic.  Color, shadows, lighting, contrast; it’s like a carefully painted old master’s work, laboriously rendered and painstakingly perfected.  That’s what Incendia can do when the right person is clicking it’s buttons.  I guess it’s a bit like paintbrushes: what comes from them depends on who’s holding them.  This is sort of weird, but I think the real beauty of this work is in what the image is reflecting.  It’s the light source that we don’t see.  There’s something golden, shining and radiant in this image –off screen– and it’s all suggested by what we see in the image.  The question is not, “What is this?” but rather, “Where are we?”  This is a great place.

To me this image is sea shells and other sea debris caught in a tangle of branches on the shore after that world cup of storms –a hurricane.  Neatly collected, I see.  Apparently the best time to collect sea shells is right after a storm (the key word is “after”).  That might also be the best time to check and see if your neighbors are still alive, so you’ll have to chose between the two.  Of course if your neighbors are down on the beach… with the seashells…

Sophiiiii added a link on her Deviant Art page to the image she used as the background for this image.  It’s worth looking at too.

Colour Acrylic 20 by Tackon (Deviant Art)

I find it interesting how the background complements the incendia image.  It may seem trivial, but the background layer, even just a colored texture like this, just like the frame on a painting, is part of the artwork and contributes to the viewer’s general impression in ways which I suspect can be quite strong even if they may appear subtle at first glance.  Speaking of frames…

What came first?  The Picture or the Frame?

Flickr’s thesmartestfish (Sophia Brueckner) said “experimenting with some vintage round picture frames I bought on etsy. I was thinking it would be interesting to have a series of paintings in round frames. not sure if I want to keep going in this direction though.”

( apparently is a website that describes itself as “Your place to buy and sell all things handmade, vintage, and supplies.”)

Thesmartestfish really is pretty bright.  Not only is she a Master of Fine Arts student, she also works with javascript to create generative imagery using the Processing platform; a nice combination of skills we could all use.  From this I suspect she either printed and embellished by paintbrush the images in her round collection (similar to monoprinting) or just painted them freehand using their simple but characteristic, generative look as a guide.  Either way she’s produced something quite appealing.

Here they are; nicely photographed, too.

Round Painting Collection by smartestfish (Flickr)

Untitled Round Painting by smartestfish

Untitled Round Painting by smartestfish

Untitled Round Painting by smartestfish

Untitled Round Painting by smartestfish

Javascript-photoshop1 by smartestfish

The round paintings look hand-painted but the bottom image the author describes as “shapes generated by javascript + photoshop with a scanned watercolor background.”

It’s a strange dynamic between frame and picture but there’s more dynamism going on.   Consider the interplay between the digital imagery of the javascript-photoshop process and thesmartestfish’s own hand painting skills.  Thesmartestfish created the javascript which in turn produced the snakey tendril imagery.  But that computer generated imagery in turn went on to inspire the hand made images in the round picture frames.  From such well defined and synergistic rotation often comes a powerful hurricane.  But it has to stay well out at sea, away from land, and feed on  warm waters and also avoid the vertical shearing forces of interfering ridges and troughs which dissipate the force of that rising energy coming off the sea.  Hey, some people like to talk in football or baseball analogies.  I prefer hurricanes.

Finally, everything flows back to where it came.  Solomon remarked on this very thing almost three thousand years ago: “All streams flow into the sea, yet the sea is never full.  To the place the streams come from, there they return again.  All things are wearisome, more than one can say.”

Ouch.  Here’s a fine illustration of that somewhat depressing/encouraging quotation.  It’s in the form of a video screen capture of a highly talented java applet rendering Fractal Drainage Patterns.  This is extremely fractal.  But I doubt it would have cheered up Solomon: everything is just sinking into the earth and if you watch the applet long enough at the original site, everything eventually fades into nothing.

Get the Flash Player to see this content.

I think they’re cool.  They’ve got a weird, sci-fi, Andromeda Strain replicating space-virus look to them.  I suppose epidemics and even wars have similarities to sports, just like hurricanes season does.  But hurricane season has a much more regular, reliable schedule than those other disasters even if all the hurricane game dates are impossible to predict ahead of time except by more than just a few days.  I should go check right now.  There’s a new update at the NHC about every four hours.  The next big one could be boiling away as we speak.

Surf’s up

I’ve been surfing.  From the noisey beaches of Deviant Art to the silent shores of guano islands.  Every one here’s a gem to me.  Each one gleamed in its own way when I saw it.

Remember this:  There are things that can be bought for a few glass beads in the South Seas that can be sold for a king’s ransom back in Amsterdam.  But remember this also:  there are things that can be bought for a king’s ransom in Amsterdam that are worth nothing more than a few glass beads in the South Seas.

Click on any of the images to see them full-size and on their original website where you can browse more works by the artists.

The Complex by David Makin

Dave seems to make a very wide variety of fractal imagery and works almost entirely, I believe, in Ultra Fractal.  I’ve never seen anything quite like this.  A city of dreidels?  The surface texture suggest some old kind of nylon material.  There’s a strange vintage radio tube feeling to it.  Nice, subtle coloring that reinforces the 20s or 30s Art Deco style (before the time of brightly colored plastics).  A rather unique image with a similarly unique style.

Daniel White Julia Mode by Bent-Winged Angel

Strange electronic vibes and I like strange electronic vibes.  Perhaps an unusual image to draw attention to, but who cares about the usual images?  I suspect this one was uploaded as part of a discussion, but that just adds to it’s exotic allure.  Maybe Bent-Winged Angel wasn’t trying to make a piece of art with this one, but she did.  It splashes like water but turns into grains of sand around the edges.  Far out.

Graffiti by Talfrac

Talfrac adds that the image was made with Fractal Imaginator.  This is a program by Terry Gintz that I’ve never tried.  I like the clean, solid, silkscreen rendering style that the image has.  Sharp, crisp colors.  Anyone familiar with fractals will recognize the common organic structure to the image despite it’s very untraditional –vector-like– blocky rendering style.  This looks more “art gallery” like than most of the smooth, millions of colors fractal images normally seen.

20091226-1 by Samuel Monnier

Full color or black and white, a good image is simply a good image.  Art’s funny that way.  Working with the most advanced and feature rich formats doesn’t guarantee anything.  Of course there’s nothing simple or retro about this image here by Samuel Monnier.  It’s another example of his sophisticated pattern piling technique that he’s been polishing over the years and developing with Ultra Fractal.  Click on the image to go to the original site where you can explore the vast algorithmic world which we are only seeing as a mere thumbnail here.  There’s  so many interesting things to see in this one.  It’s like a table of contents for a large anthology.

FRAC-tional Friction by Lenord

This is a mandelbox, I’m guessing.  Not your average type of mandelbox and not the usual style.  Strong design is what makes this one special.  Everything lined up and arranged in a careful display of shape, form and symmetry –but with the usual mandelbox variations and complexity to it.  Look closely, is it really symmetrical?  anywhere?  All an artist really does is help us to see the great scenes going on around us that us common folks don’t seem to notice.  I think that’s what Lenord’s done with this one: he’s helped us to see the simple shapes and the sophisticated patterns made in the mandelbox by cutting out all the usual distractions of surface texture and wild, vast perspective.  Yes, art is complex, but only when you analyze it.  Out in the wild it’s natural and instinctive.  But that’s why it sneaks past us so easily.

Pipe Organ "Klais ' by DeadZero (on Deviant Art)

What are those men doing in a fractal?  Believe it or not, this is actually a photograph of a very elaborately designed pipe organ somewhere in Spain.  Or maybe it really is a fractal and the author cleverly edited the image?  Never let your right eye know what your left eye is looking at.

The Eye of Silence by Max Ernst (1944)

I often feel that fractal art is not really about fractals but is instead about “imaginary” imagery.  In that sense, there are many “pre-columbian” fractals out there; meaning they are graphically similar although completely unrelated in terms of the way they were made.  Fractals just make it easier to create imaginary imagery.  I guess it depends on how you chose to define the art form.  The lack of a fractal formula naturally makes it hard to call  “fractal”.  Well, in the old days fractal artists worked hard.  Try doing something like this.

Incendia Sketch by Kaeltyk (Deviant Art)

This one’s for real.  I stumbled on Kaeltyk’s Deviant Art gallery somehow.  I forget how.  Maybe from a link in someone else’s favorites?  Incendia does some nice things, but I’ve never seen such a good combination of 3D and 2D elements like there is in this one by Kaeltyk.  And it’s black and white, too.  Black and white is a whole new kind of color.  The uber-color.  It’s often thought of as being being feature-poor as opposed to feature-rich.  But all the colors in the world can’t do what black and white does.  More strangeness.

Tilings II by Kaeltyk

This one by Kaeltyk was done in Ultra Fractal.  I just like these peaceful drifting snowflakes and the different landscapes they seem to be falling and dissolving into.  It’s hard to crop out just the right piece from among such a huge mass of repeating imagery like this, but Kaeltyk did a good job here.  Very professional looking.  It deserves a classy title and black frame.

Shells by Kaeltyk

I would have guessed Incendia for this one, but Kaeltyk’s notes for this one indicate it was made with Xenodream.  I know these sorts of spirally seashell/horns are common and perhaps even cliche now, but Kaeltyk has managed to create something interesting and appealing even in such a heavily picked over genre.  In Kaeltyk’s own words, “I like how it’s clean and almost carved.”  That’s why I like it too.  The coloring and surface texture adds a lot as well.

Sky by Marco Gervasio (Flickr)

According to notes for this image it was made by “two pictures of the sky that I merged together and then reversed”.  I guess the inverting created the yell0w-orange coloring from the natural blue sky tones in the original.  I include this because it’s another “mind-bender” that show that when we look at graphical imagery and ignore how it was made, we find “fractals” in places we wouldn’t have expected.  Although the shapes and structure of clouds really are a natural form of fractal rendering.  I guess that just reinforces my point.

Sphere by spanzhang (Renderosity)

“FMF + POV-Ray”  POV-Ray is a ray-tracing (ultra realistic) program, but I’m not sure what FMF stands for.  I like planetoids and this one’s got some cool coloring and texture.  Looks like ice cream that’s just about to start dripping.  Incidently this was chosen for a Fractal Window Weekly on Renderosity a year and a half ago.  I visited, the so-called Chinese Fractal Art Society and I think maybe Ferry Man Fractal is the mysterious “FMF”.  I’ve never heard of the program, so maybe spanzhang made it himself?

Rings and Wires by spanzhang

By spanzhang again.  He’s got a gallery at  This one’s made with Apophysis.  Nice design with repeating circular elements and good colors.

Onceinalifetimesingle by Anonymous

Yes, people used to dream of such imaginary, fractal-like imagery way back in the 70s.  But it’s not merely once in a lifetime today; it’s everyday and all the time.  Music’s gotten a lot cheaper now too.  Hasn’t it?  And who needs to pay to get great artwork for their album covers nowadays with all this computer made stuff around?  “And you may ask yourself…” how come nobody sings about having mental breakdowns and emotional decay anymore?

Seed Bead Fractals by Shala Kerrigan

Check out the nice set of instructions Shala has made to go with this example of Fractal Earrings.  “Fractals are geometric patterns that show self-similarity, they can be very complex and really beautiful.”  Doesn’t that statement by Shala answer the proverbial, “What are fractals?” question quite nicely?

You can also bead fractals. This is a pair of earrings that uses a very simple fractal pattern to create a delicate fringe or tassel that resembles some of the fractals you can see in nature like trees or the veins in your body.
The shape I used was 3 lines. Each time you add another set of 3 lines to the ends of the lines, that’s called an iteration.

For folks like myself such descriptions are more enlightening than those of the more technical type.  You’d think by now I’d know what a fractal is.  But I keep finding fractals that don’t fit the formulas.  Never let your left brain know what you’re right brain is thinking.

You’ll only end up slapping yourself in the face.

Art imitates Nintendo

The original Mandelbox?

I don’t play video games much; just an hour every day of Star Wars Battlefront (original one).  I have friends in Mos Eisley and although they always lose –horribly– they’re always asking me to come out and “play”.

My nephew loaned us his old GameCube and while I’ve never used it because all we have for it are Super Mario games, it’s been there on the floor in front of the TV for almost a year now.   I glance at it occasionally in between ferociously savage bouts of Battlefront ( Dark Trooper… Rhen Var Citadel…shotgun in the sky).

Since the discovery of the Mandelbox by Tom Lowe (Tglad) early in this year with it’s general cube formation and multiple grid and curved structures in it, I’ve looked at the Nintendo Gamecube differently.  They seem to be derived from the same formula.  Could it be true?

Mandelbox Edition: Nintendo GameCube -- no word from Nintendo yet regarding release date. Which one's the power button? (Image by MarkJayBee)

You can see the common structural elements from the GameCube here in this Mandlebox image. Nintendo GameCube: GoldBox Edition. (Image by Timeroot)

The Mandelbox has much improved and much more stylish ventilation ducts than it's predecessors. Does this mean they've added a huge amount of processing power, or is it just for aesthetics? (Image by Tom Lowe)

If Nintendo ever brings the Mandelbox GameCube into full scale production the first one ought to go to the Museum of Modern Art. (Image by Tom Lowe)

Exploring the graphical output of fractal algorithms should give you a floating feeling from time to time as you experience that “I don’t think we’re in Kansas anymore” feeling that Dorothy did when she found herself in Oz.  The world of video games is not so different either;  they’re as real as any movie you can see on your TV screen.  What we find in fractal graphics today would have passed for pure science fiction in the past.  What else?  3D fractals are the best game in town.

Anyhow, I just keep looking at that GameCube and can’t help but notice the resemblance to the Mandelbox.

Weird Scenes Inside the Goldmine

There’s actually a lot of goldmines out there in the outer reaches of our computer system.  None of us have been to all of them, but we’ve all been to some of them.  I don’t know where exactly this one is, but you can find all the scenes from it here.

This is what’s written at the entrance to the mine:

A gallery of large graphs

graph drawing of matrices in the University of Florida Collection

Graph visualization is a way to discover and visualize structures in complex relations. What sort of structures are people who do large scale computation studying? We can get a glimpse by visualizing the thousands of sparse matrices submitted to the University of Florida Sparse Matrix collection using sfdp algorithm . The resulting gallery contains the drawing of graphs as represented by 2328 sparse matrices in this collection. Each of these sparse matrices (a rectangular matrix is treated as a bipartite graph) is viewed as the adjacency matrix of an undirected graph, and is laid out by a multilevel graph drawing algorithm. If the graph is disconnected, then the largest connected component is drawn. The largest graph (Schenk@nlpkkt240) has 27,993,600 vertices and 366,327,376 edges. A simple coloring scheme is used: longer edges are colored with colder colors, and short ones warmer. The graphs are in alphabetical order. Use the “Search” link to find graphs of specific characters.


The computer awoke before dawn, he put his boots on

What page in a mathbook ever looked like this?

I should have been a bag of glowing mesh, gliding across the floors of silent seas

I argued with infinity. I wish I hadn't.

I just like it

Somewhere, this was the topic of an advanced technical discussion

It looks like this

And this too

Why? Why did it do that?

you don't know what you're digging, until it's been dug

1. I got a handle on it 2. I had a handle on it 3. What's a handle?

The machine is humble and efficient. It would draw another picture before it would ever sign its name.

Another picture

This could be a sub-atomic energy cloud, or a map of the universe

It all makes sense, the longer you stare at it

We know art doesn't have to be useful, but do we also know that art doesn't have to be useless?

It's perfect. What does perfect mean?

The elegant effervescence of electricity

It pretends to be a car, and slips away unseen

Can a prison cell be a work of art?

So little, so much

Thanks to but does it float for helping me find the Goldmine.

Bow the Knee to Blob!

Alien Ruins by blob on (click for full-size)

Such simple rendering and yet, such powerful rendering.  Remember, most of MC Escher’s great drawings were done in pencil, so there’s no reason why a grayscale or monotone image has to be dull.  Just look at the detail in blob’s image, how it’s all over the place in every nook and cranny and has such creative diversity.  This is the magic of great software and those who know how to get the most out of it.

It’s made in Jesse’s Dierks’ free program, Mandelbulb 3D 1.53.  The expression, “the proof of the pudding is in the eating” really applies to fractal programs: you can judge them by what users are able to make with them.  As you can see here, Jesse’s program is clearly top notch.  I’m really surprised that such high quality software continues to be made in the fractal world.  I guess the new 3D formulas have inspired programmers like Jesse to create these new things.

Here’s another in the same palette but with more of a carved ivory look to it:

Electron Microscopy by blob from (click for full-size)

Again, subtle rendering that magnifies the beautiful designs of the hybrid mandelbox/sierpinski formula.  The top left corner I find to be the most interesting, next to the large round cavity in the center.  Everywhere you look there seems to be something a little different.  I’ll bet one could get completely lost exploring this object and forget all about taking snapshots.  Makes the Grand Canyon look like a ditch.

Just to show some contrast in rendering styles, take a look at these two by Kraftwerk:

the Giant alien Generaator, by Kraftwerk

This is no pencil drawing, but the lavish gold and metallic emerald surfaces look good in this mandelbox.

In his own words:

This is just too much for me, found this yesterday evening, sitting in the garden sun, two different worlds…

These formulas really makes you feel that they are designs from another world… first time I feel that mathematics really can beat the human fantasy… mindblowing…

Thank you everyone involved in this @ fractalforums, I think the things you all found is bigger than anyone of us can imagine!


There’s more images like this by Kraftwerk to be seen on his Deviant Art page, they all come from the internal details of this intriguing mandelbox structure:

Alien Generaator Building by Kraftwerk (click for full-size)

I think the starry background has been added in, but it sure fits with this extraterrestrial space temple.  The coloring is really exceptional.  Kraftwerk has a real talent for that.  He’s made some of the best colored mandelbulbs I’ve ever seen.  He’s also using Jesse’s Mandelbulb 3D just like blob.  I find it quite interesting that both of them can use the same program and get equally good results and yet with such widely varying styles.  Fractal programs are bit like musical instruments: it’s not what you play but how you play it.

I can’t resist adding YouTube content to my postings.  So here’s a recording of the original Kraftwerk music group of “The Voice of Energy” which inspired fractal Kraftwerk’s title for this series of mandelbox images.  It’s in German.

7Up: The Un-Cola

What exactly does it mean to be un-Cola?  Cola drinks, like Coca-Cola, are dark-colored and contain caffeine.  The opposite would be light-colored without caffeine?  But both of them are sugary, carbonated drinks sold on the same shelf and dropping out of the same vending machine, or at least side by side vending machines (7Up is a product of Pepsico, Coke’s rival).

To those who like soft drinks and don’t like colas, then 7Up is perhaps very different.  Refreshingly different. But for those who are simply thirsty and don’t want to eat 10 teaspoons of sugar while trying to quench their thirst, 7Up and every other soft drink, including all the various members of the vast cola club, are all one thing:  cans of liquid candy.

Mosaics:  The Un-Fractal!

60s Scream, by Village9991

These mosaics, including the so-called mashups that are made of tiny images, are a kind of un-cola with respect to fractal art.  Their ingredients, like 7Up’s ingredients, are fundamentally different and yet seem to have all the same sweetness and fizz of regular fractals.

They look like fractals and from a purely visual standpoint, I enthusiastically declare them to be fractal art and insist they take their rightful place in that great vending machine –shining humming monolith of cold drink correct change worship– called fractal art.

And they’re cool to look at.  And maybe not so hard to make, either?  This one above I believe is a rendition of the screaming woman in the shower scene of Alfred Hitchcock’s Psycho.  There’s something called actionscript which does some really neat things like this.  Flash artists do similar things.  I have no idea how it works.  Wouldn’t it be funny if they used some type of fractal algorithm to scale the mosaic pieces?

You can view a whole bunch of them here on Village9991’s Mosaici page.  He’s Italian and lives in a small village in northern Italy.

Giant Peach by Jim Bumgardner

The full-size (1800×1800) image is here and is worth a look.  The details in this mash-up are quite appealing, unlike most which get ugly when you move up close.

Jim Bumgardner is a Flickr master and has done some prominent things:

I’m a computer technologist / artist / composer in the Los Angeles area. I blog about my various projects at

I’ve done a lot of mosaic art using the Flickr APIs, and co-authored Flickr Hacks, from O’Reilly, with Paul Bausch.

I’m a little obsessed with circles, radial symmetry and mechanical instruments.

* * * * * * * * * * * * * *
I work amongst an awesome collective of nerd/hipsters at Topspin in Santa Monica.

I did some mosaic posters for squared circle, and a day in the life, here on Flickr:

[see Giant Peach image above]

* * * * * * * * * * * * * *
One of the first things I did on Flickr was to make a number of fun-to-use Flickr Colr Pickrs. Check ’em out!

I also made the world’s first Flickr Chia Pet, an experiment in collaborative defacement.

– From Jim’s Flickr profile page

I made something similar once, using a photoshop filter called Mosaic Toolkit by Lance Otis.  Over here.

Pearl Glance by Village9991

Whaddaya know?  It’s the same guy as made the first one!  Well, I guess he’s got some sort of program to make these with because it would take a lot of work to draw these things even with a computer drawing program.

The woman, in case you don’t recognize her, is a detail from some very famous painting.  But here her image is made up of all the senseless words that people in art galleries have spoken while viewing the painting.  Individually, the words are gibberish and without any meaning.  But together they “speak” her image in a new but equally appealing way.  Some of the smallest comments are crucial details.  The other deep message in this image is: if you’ve got enough fonts installed on your computer you can do anything!

Time for another one:

Steal a Kiss by Village9991

Well hit my avatar with a digital two by four.  Same guy again.

He says it’s from a Pucca cartoon: YouTube Link.

The image has changed: it’s full of details that have their own (short) story to tell.

After watching a Pucca cartoon I now see the image differently.  I can clearly make out the two Pucca cartoon characters.  Nevertheless, the graphical effect is what makes this image interesting for me.  Those of you who are fans of the Pucca People you might feel differently.  Which is the greater art?

Blogging: The Un-Writing

I never intended to focus on the mosaic images of just one artist.  Incidentally, the way I review these things is a multi-step process and details like names often get temporarily lost in the shuffle.  First I wander around the internet and when I come upon an interesting image I bookmark the page.  This stores the link to the original (obviously) along with the image and any references to a title and author’s name.  Later on when I’m thinking of writing about something I go back to these collected bookmarks and I open up 10 or so from a single sub-folder bearing some (at the time) relevant name.  The folder names are often just dates like “June” or “May” or “3D”.  Digital art in general and fractal art as well is such an eclectic medium that meaningful sub-categories are hard to come up with.  And author names quite often aren’t the common ingredient in a particular graphical theme.

But sometimes they are. For me it’s all about art and not artists.  But you have to include the author’s name if for no other reason than readers want to know who made it.  Sometimes there are legal reasons such as attribution requirements.  Artists are less important in fractal art because individual accomplishment is more about the style of pushing buttons and operating the machine than it is about actually interacting with the canvas in the intimate way that painters do.  If you do what they did then you’ll “make” what they made.

Clearly, no one makes them like Village9991 does!

Fractal America

I’ve been looking at some mash-ups lately on Flickr ….and I was browsing around on Samuel Monnier’s site ….and July 4th, Independence Day in the States is coming up, …which is similar to Canada’s own national holiday on July 1st called Canada Day … I thought, “America Day” …and here’s two images of that great icon of America, the American Flag …and they’re both fractal, sort of …here’s Fractal America …the deeper you look, the more you see close can you get?

20091103, by S. Monnier

United State of Art, by qthomasbower (on

Click on either one to see a larger version with much more detail.  Samuel Monnier’s image leads to a page where you can view the image in enormous detail.  He uses a special flash applet that allows you to practically explore the image to the same degree you would be able to if you were viewing it in the original fractal program (Ultra Fractal) that made it.  If you haven’t seen one of these before, it’s well worth a look.

Can the image of a national flag (especially the American flag) be purely something to look at and not have political overtones?

No.  Absolutely not.   And why is that?

Because it’s a symbol.  Our minds just refuse to look at it as if we’d never seen it before.

In social situations, if you want to avoid controversy, “don’t talk about religion or politics”.  But the American flag is both  politics and religion to many people –and not just the Americans.

In Canada (where I live) you will probably hear much more said about Americans and America than you will in America and among Americans.  Canadians are funny that way.  And so is much of the world.  No one see America (and Americans) quite like foreigners do.  And no one seems to talk about them as much as foreigners do.  Canadians, however, see America in a more powerful way because we are both foreigners and yet, in many ways, very american ourselves.  I won’t get into it right now because it’s too convoluted and confusing, but suffice it to say that Canadians embrace America with one hand while at the same time trying to get in a punch with the other.  It’s very hypocrital and juvenile and, I’ll come right out and say it: it’s very colonial.  Colonial-minded peoples are afraid of independence —they think they’re going to lose something.  Americans, on the other hand, enthusiastically fought for independence –because they thought they would be gaining something.

And there, in a nutshell, is the difference between Canadians and Americans.  Canadians like to complain about the government and you can’t do that when you’re independent because you’re only complaining about yourself.  Americans like to fix the government and to do that you need independence and self-government.  America wrote it’s own constitution.  Canada was content to let the British Parliament do it for them.  As a Canadian I’ve always found it surprising that my fellow Canadians don’t seem to see this as a huge national embarrassment:  Canada is an act of British Parliament. America was a reformation of the acts of British Parliament (“new and improved”).

See?  Already things have gotten political.  I’m so glad that art doesn’t have to be that way.  Let’s talk about art instead.

Samuel Monnier says that fractal art doesn’t have to embrace social and political themes in order to be considered “serious art” and that if you browse through artworks of the past you’ll find many examples of good art in which these sorts of themes are not involved.  Maybe he didn’t say it exactly like that, but he’s right.  The works of Joan Miro and Paul Klee would be considered “serious art” and yet they (rarely) had any connection to what one would call social commentary.

Of course it would be a great compliment to fractal art if it also had some artwork that did engage in social commentary.  It’s not necessary (as Sam says) for fractal art to be earn the label, “serious”, but it would add another dimension to the genre.  And political themes can be quite engaging and thought provoking.

Back to the art:  Sam’s “pattern piling” version of the American flag is really without any sort of intended meaning (assuming that’s possible with the American flag).  It really is just an interesting, richly detailed, experiment with the geometric qualities that this flag possesses.  He does the same thing with the Swiss flag (Sam is from Switzerland) although the results aren’t quite as interesting because the Swiss flag’s elements are all right-angled and lack the variety that the stars of the American flag give to it.  And there’s an extra color in the American flag which in turn provides for more combinations and permutations when pattern piled.

Qthomasbower’s flag is, on the other hand, a deliberate attempt to provide social commentary:  A vast mosaic of many artworks forming (by overlaying an image of the flag) a diverse but united nation waving majestically in the wind.  I think the technique is easier than it looks.  Nevertheless the result is fascinating.  It really has the detailed and intricate wonder of an image made by the iterations of a fractal formula.

Qthomasbower has some more of these on his Flickr pages.  Unlike Monnier’s image, Q’s doesn’t look so hot when you zoom in.  It’s kind of like the “digital zoom” on a camera;  the picture just becomes chunkier and cruder as you move in.  I’m sure he’s not implying that the state of American art only looks good from a distance and when covered by the imprimatur of The Stars and Stripes.

Two of Arts by qthomasbower (on Flickr)

I find these mash-ups of Q to be very interesting because of the detail and texturing they give to the image when viewed at large.  I think almost any sort of half-decent image would look fantastic when treated this way.  It gives a large-scale and massive appearance to the image because of the non-repeating and highly detailed texture all the individual image “tiles” contribute.  The mash-up contributes really only a texture layer, but the effect, as I’ve said, is very impressive.

So.  Is America a fractal?  Does it have self-similarity at many levels?  Do parts of it descend down to zero while others escape to infinity? And why does a Presidential election with only two candidates take so long to render?

FractalWorks: One Smooth Machine!

The first time I saw an image made in FractalWorks it was in the gallery section of  I was impressed and yet, I couldn’t quite figure out why I was so impressed.  There wasn’t anything really special about it and yet there was something really special about it.  It was one of those “height field” fractals, a (somewhat old) trick to give flat fractals a 3D appearance.  They’re all over the place and have been for years, but this FractalWorks one was different: more polished and more stylish than I’ve ever seen.  It also seemed to have a slightly surreal and mysterious quality to it –a strange kind of silence.

Stone Path by Duncan Champney, Made in FractalWorks. (The first one I saw. I sensed something eerie; like an approaching Minotaur.)

A comment by Paul N. Lee, the veteran fractal archivist, lead me to Duncan Champney’s website and to the incredible discovery that not only had Duncan made other images like the first one I’d found, he also made the program, FractalWorks, that they were created with.

There’s a long tradition in fractal art of people performing the roles of both artist as well as programmer.  Duncan Champney joins that royal list and furthermore offers his excellent program free to anyone who wants to share his passion for exploring what his super fractal machine can do.  But before you head off to download it I should mention that it’s for Macs only.

3D view of Mar2310lma1c by schimkent, made in FractalWorks

From what I’ve seen the program’s forte is 3D fractals of the height field, or geographical terrain,  “relief” -variety.  However, as simple and plain as that might sound in these modern days of Mandelbulbs and Mandelboxes, FractalWorks does this one thing very, very well.  These sorts of old-style 3D fractals made in other programs can be rather kitschy to look at, but FractalWorks manages to achieve a quantum leap in rendering quality that gives this old technique a new and vibrant appeal.  But of course as with almost any kind of fractal program, it still requires an artistic eye and the relentless persistence that only an enthusiastic explorer can possess to produce really good work with it.

Ordinarily I’d just shrug off stuff like this as eye candy but FractalWorks has elevated this simple type of fractal to a new level of sophistication.  There’s something fresh and different here.  Like I said when describing my first encounter, there’s something special and captivating about these FractalWorks works.  Some have a fairy tale look to them and others suggest a landscape that is much more surreal and haunted.  Don’t let the fruity, frosty renderings fool you; there’s more to some of these FractalWorks images than mere graphical sweetness.

Duncan Champney wrote the program and started up a Flickr group to get people interested in it as well as to offer advice and encouragement (I’m just guessing).  Although Duncan produces some of the best images made in FractalWorks, I discovered from the Flickr group someone who also makes work that is equally good: schimkent! I think the proof of a really great program is in what the users of it can do and not just the super results the author can get with it.  Shimkent (and others) have shown that Duncan has created a very capable and creative fractal art tool in FractalWorks.  Even if it is only for those Starbuck sipping, sophisticated Apple computer users…  They ought to have at least one good fractal program, shouldn’t they?

Fractal Stimulus Plan, by schimkent, made in FractalWorks

Schimkent: I think his real name is Kent Schimke (hence, the clever screen name —schimke-nt).  Kent’s LinkedIn profile says that he is “…helping a developer create a fractal generating program called FractalWorks for macintosh computers.”  I think it’s pretty safe to say he’s the guy.

Kent’s got a really good eye for color and also seems to have a good grasp of what makes for a good 3D FractalWorks scene.  Both he and Duncan have made some very eye catching and interesting images.  I would never have thought such a simple 3D height field program could produce such a wide range of creative works but I guess, as Kent says, “You just don’t know what you can’t do.”  Well,  Kent seems to have excelled in pushing FractalWorks’ envelope and taking us to new places.

Touch of vertigo, by schimkent, made in FractalWorks --see what I mean by schimkent's great eye for color?

In addition to his own Flickr gallery, Kent has also recently had a wall calendar featuring some of his FractalWorks images published by Browntrout entitled, Chaos Fabulous Fractals 2010.  This is not the Cafepress, self-publishing, print on demand type of thing (the one at a time whenever someone buys one), but rather the traditional editor/publisher/press-run type of publishing.

Apr06wja1b, by schimkent, made in FractalWorks

Teed Up, by schimkent, made in FractalWorks. (I really like the perspective in the blue objects in the top area. Extraterrestrial garden.)

FractalWorks was released a couple years ago and since then it’s been upgraded a few times.  The most recent upgrade was just recently, May 4, 2010.  I’m sure the reason for such continuous development has been the impressive results users have achieved with the program.  That’s what usually drives fractal program development.  As the Flickr group message says:

FractalWorks is a free, high performance fractal renderer for Macintosh computers.
You can download fractalworks and try it yourself at the FractalWorks download site.

04 May 2010: Version 0.6.2 has expired. I just uploaded a new version, version 0.6.3 to the link above. Please upgrade to the new version.

-from the Flickr Group, FractalWorks site

I majored in Geography back in my university days and I think one of the things that drew me to that subject was all the imagery that one ends up studying, particularly the Remote Sensing images.  Perhaps part of the appeal that these FractalWorks images has for me is their similarity to maps and especially aerial photographs, something which the Wikipedia defines as “the taking of photographs of the ground from an elevated position“.

3D view of Aprwmc1a, by schimkent, made in FractalWorks. (It's autumn in fractal country.)

Fall Colors, by schimkent, made with FractalWorks

Another legacy of my geography days was the slowly developed ability to view stereo pairs of aerial photographs without the special lenses that make it easier for your eyes to perceive the 3D effect.  In digital art circles this special 3D imagery seems to be called “cross-eyed” stereogram.  I take it from this stereogram set posted on Duncan’s site, that FractalWorks is able to produce the paired images that produce this three dimensional illusion.  Here’s another also made in FractalWorks but slightly different in that you need red-cyan 3D glasses to view it (the old-style 3D movie glasses).  And here’s an even better one.  Wait!  This one too!  Go out right now and buy a pair of red-cyan 3D glasses so you can see this one!!!! (try the high res version on Flickr for an even biiiiiiger thrill).

FractalWorks produces a kind of high-quality imaginary aerial landscape.  Of course, that was always the intent I believe of the height field effect in fractal programs.  It’s just that FractalWorks has come along and achieved much better results than any other program that creates these kinds of fractal images, at least of all the ones that I’ve seen so far.  Although I’m sure Ultra Fractal or Chaos Pro could be programmed to produce similar smooth and richly colored images like this, no one seems to have attempted it yet (although there have been good examples of a mild form of 3D relief imagery created with them already).

3D view of Sep13lmb1d, by schimkent, made in FractalWorks. (This is the enchanted forest. Can you find Granny's house without getting lost?)

Well, three cheers for Duncan Champney for making this Mount Everest Machine of fractal programs and taking us right up to the top of it along with him.  And to Kent Schimke, his agile sherpa for showing us how great the views can be.

3D view of Jun16wmb1d, by schimkent, made in FractalWorks. (I know this is a pretty ordinary fractal, but what is it about FractalWorks that makes it look so cool?)

3D view of Feb12wja1b, by schimkent, made in FractalWorks. (If color was a flower, this is what it would look like.)

Well, I could go on and on doing this.  These FractalWorks images are really something.  Too bad I don’t have a Mac.  Oh well, we can still look at the results.  You can browse the entire Flickr group at this link.  And should you happen to own a Mac, why not download the free program and try it out while you’re sipping your Starbucks coffee and looking as stylish and hip as Mac folks always do?

Fractal Art: No Money

I want to talk about the money in fractal art.

Where in the fractal world is there any sort of commercial success?  I don’t mean someone making some trivial amount of money, I mean someone making enough money to, as they say, quit your day job, kind of money.

Is this the financial forecast for Ultra Fractal sales?

Of all the artists, programmers, publishers, online instructors and other types of individuals in the fractal world, who would you say would be the most likely to be making some serious amount of money?

My first guess would be Ultra Fractal author, Frederik Slijkerman.  Ultra Fractal currently sells for $69 US for the standard edition and $129 US for the full featured, animation edition.  It’s a very popular fractal program and has been for ten years or so and is an ongoing concern as they say in business circles.  But has it made Frederik so rich that he’s moved into a castle and spends most of his time in his counting house counting all his money?

I don’t think so.  As far as I can tell, Frederik spends most of his working time at a regular (non-fractal) programming job.  (His Linked-in profile) I’m sure he’s making something off his sales of Ultra Fractal, but even if there were 500 paid-up users of UF5, and I think that’s a gross overestimation, that works out to about $35,000 US.  But put that in “earning a living” terms and it’s not much of paycheck compared to a regular job.

So, Frederick, of all people in the fractal art world who I would guess to be in a commercially viable position is probably making more money at his day-job than at his “fractal-job”.

I wrote a post last year entitled Is The Name Of Our Hero Benoit Mandelbrot Being Used To Market Ultra Fractal?.  But now I’d say that even if anyone ever had the idea of attempting to promote UF via this contest (and why would anyone think that?) that now it’s obviously a waste of time.  There simply are not enough users of fractal art software to generate even a modest income on an ongoing basis.  In short, I think Frederik’s motives in creating and selling UF are more personal than commercial.  I’ll bet he could make much more money with the time he spends developing UF by putting it to use on projects of a purely commercial and straightforward business nature (i.e. his day-job).  The fractal art world would have to change considerably, such as grow significantly in size and become much more trendy for this to be any different in the future.  And who’s to say most of those newcomers wouldn’t opt for the freeware program ChaosPro?

More personal than commercial“.  I think this sums up all the rest of the fractal world from a money-making perspective.  But let’s look at online instruction anyhow, which, like UF,  is something that has had ties to the Benoit Mandelbrot Fractal Art contests via the judging panel.

No, there’s not much money there either!  Courses were about $25 US for a ten week course (two and a half months) and twice that for double semester courses.  Assuming you were a very keen instructor and you taught four course semesters a year and had a full class each time (not likely) what great pile of cash would you be rolling in at the end of the year?  Ten students a course, for instance, four times a year, and you (the instructor) get what?  Well, you wouldn’t get the whole $25 tuition, you’d have to split some of it with the online school who have their own administrative expenses to cover (and they want to get rich too, right?).  How about you get $20 per student at 10 students per semester and four semesters a year?  That would be (a whopping) $800 US per year.

Look before you leap --into the riches of online instruction!

Of course, if you’re trying to cover the rent  and buy groceries (you can’t get rich if you die on the way) then you might consider teaching more than one course.  Say you managed to teach 3 per semester.  3 x 800 is $2,400 US per year.  This is beginning to sound like a Get Poor Quick Scheme.  If money’s an issue then you need another job or you’d better just stay with a day-job.

Not surprisingly, none of the current or former judges of the Benoit Mandelbrot Fractal Art Contest are teaching online courses anymore.  Did they make too much money and decide to retire?  I don’t think so.  Their interest was, again, “more personal than commercial”.  I suspect they simply wanted to explore the option of teaching UF skills in an online environment.  Sure, there’s some money to be made, but it’s a token amount which might be some compensation for the instructor’s efforts but not a serious way to make a living or elevate one’s standard of living.  Would such a fractal-job income mean anything if you were applying for a mortgage? or a business loan?  Or how about bragging rights at a cocktail party?  “Hey, that’s nothing, man!  I’m a professional online fractal instructor and I made eight hundred bucks last year!”

Now how about selling artwork?  That ought to be worth something.  Hey!  Isn’t that how Picasso and Warhol got rich?  Ironically, I think this is probably the least profitable enterprise in the fractal art world.  And why would I say that?

Well, for starters, fractal art, like all digital art, is not collectible.  You can’t buy an original fractal print like you can an original painting.  You could print a limited edition of images and then (honestly say) you’re destroying the digital files (image and parameter files) just as print-makers destroy the original printing plate for art prints they sell after printing a numbered series of prints.  Throw in your (really famous) autograph into the package and then charge a bundle.

But the big problem with fractal art is that there’s so much of it around and it’s so easy to make.  People can shop around and find similar stuff for sale cheaper or even make it themselves. Can’t do that with Picasso’s paintings or Warhol’s silkscreens.  And of course fractal art isn’t as popular and as critically acclaimed as such traditional artworks are.  There’s probably money to be made in selling prints or fractal art for illustration purposes (book-covers, magazines…), but again, it’s some money, not enough to live on much less get rich at.  Yes, I think we’re back to the “More personal than commercial” aspect to things.

Alright.  Now I come to my main point in all of this:  Issues in the fractal art world are not taken as seriously as they would be if there were commercial interests at stake.

For instance: nobody really cares how the Benoit Mandelbrot Fractal Art Contests are run because winning or losing is purely a (temporary) matter of online status and has no impact on art sales or any other fractal commercial enterprise in any really significant way.  Maybe a few more UF licenses get sold because of the publicity, but I doubt it has any significant effect on anyone’s personal wealth or lifestyle.  (Actually, there is very little publicity generated by the BMFAC, isn’t there?)

I’ve seen artists advertising images on their websites as “Winners” in the BMFAC, but the real commercial opportunity would be selling prints right at the exhibitions themselves or at least taking orders.  Despite the other failings of the BMFAC, they have succeeded wonderfully in preventing the contest from becoming commercialized.  They don’t even sell a simple $10 souvenir poster or  wall calendar.  They could easily do this online from the contest site as well as from a table at the exhibition (hey, who needs a table? just stand by the door and sell them like newspapers).

Yes, the fractal art world is almost ascetic in it’s attitude towards fractal art and community events like contests.  We’re all in it for the art or for other things that have never had any commercial value like the social scene.  I believe that will change if fractal art ever develops a serious commercial side to it.  Until then it’ll continue to have the casual atmosphere of a community art club where even the big names are involved for reasons that are “more personal than commercial.”

10 Fractals and a Movie

Have I mentioned what a great addition to the fractal world is?  As someone who likes to review exciting new things in fractal art it’s really made my job much easier.  Before, I used to wander around Flickr or check out links on the UF mailing list or just stumble on something while surfing around.  I’ll probably have to go back to that again sometime, but until then I’ve got this alien planet filled with fractal treasure to report and review on.

It's more than a forum, it's a wild alien planet of the UNEXPECTED (image from

There’s been a lot of development in the area of 3D fractals and the results, as I’ve been saying lately, have been impressive.  But one can still create interesting 3D work with some of the older methods.  The Stone Path is a good example of one of the older 3D techniques called height field (or something) and gives the impression of perspective though a special rendering trick.  These sorts of images aren’t usually very interesting, but this one by the username, Duncan C is a tasteful combination of subtle coloring and a well chosen perspective.  It’s not a marvel of cutting edge fractal rendering, but that makes it even more of an accomplishment because Duncan C is using well established techniques to produce an image that is equal to the others in it’s overall impression.

Stone Path by Duncan C, 2010

Buddhi seems to have created his own unique style of fractals in these smudgy, glowing 3D creations.  If you look carefully you’ll see lines on the x or y or z or whatever axes.  It’s a nice, technical, lab-diagram, touch in an image with such strong artistic style.  I reviewed one of these types of images before.  They’re really stylish and not like anything else I’ve seen.

Trigonometric 3D Mandelbrot by Buddhi, 2010

Here’s an interesting Mandelbox by Dave Makin created in Ultra Fractal and titled New Rome detail.  The name I’m sure comes from the similarity the image shares with the ruins of the Colosseum in Rome.  The three dimensional details in this, and the excellent coloring which makes them stand out and look like such a carefully constructed and ornamented building is what caught my eye in this one.  It’s got amazing photorealism and shows how vivid and tangible these sorts of 3D fractals can be.

New Rome detail by Dave Makin, 2010

Elephant Canyon by bib, is another example of the older 3D style –or at least what appears to be the more traditional 3D style in fractals.  I think this is actually a “slice” of a Mandelbulb.  The contrast between the smooth, golden plain of the slice and the rough, craggy cliff of the edges is what gives this image its effect.  To me it almost suggests something about fractals themselves; that one often discovers things by accidentally falling off the edge or by traversing some huge empty plain and discovering at the horizon an abyss filled with rich and limitless detail.  This image was actually posted in a thread, Re: Problem replicating Mandelbulb power 2 and intended to be merely an additional illustration of the problem.  This comment by bib, accompanied his posting of the image: “Yes it’s always difficult to properly render the power 2, there too many chaotic shapes and calculation artifacts. When I saw this post I wanted to try again, so I did this image called “Elephant Canyon”. Nothing very original, but I like it smiley

Elephant Canyon by bib, 2010

Frozen in space. That’s what I think when I look at this one.  Another by Buddhi and having the same touch of the schematic style to it.  There’s an interesting structure formed by the repeating “bits” that form in a line off the major “pieces”.  Although this one is relatively monotone (one color), the lighting and surface texture effects are actually enhanced by the simple coloring.  That’s what makes art such a strange bird to capture and study: sometimes simpler things have a more powerful effect and sometimes they’re just simple.  The central core of the main object, back in the dark area, has an almost paint brushed appearance.  I guess that dark shadowed area is what draws our eye into it, but who can really say?  Trying to explain what makes an image impressive can often be futile as well as not being terribly exciting to read.

Hypercomplex Julia by Buddhi, 2010

I guess it wouldn’t be called Mandelbox castle if it wasn’t a Mandelbox.  Once again the title really catches the essential quality of the image.  I particularly like how the moonlight (it’s nighttime) shines on the floor under the arch in the area to the right of the center.  If you’ve ever played Prince of Persia: Sands of Time (video game) then you’ll probably immediately think of the part of the game where the Prince had to walk along the tops of stone walls, fight big birds and then get into the room above the gate where the gate opening mechanism was.  Or others.  There were so many nighttime scenes in that game featuring different parts of an Indian castle.  Maybe game developers will pick up on the Mandelbox and produce a game that actually takes place inside one.  You could change the castle just by starting the game with a new set of parameters.

Mandelbox castle by bib, 2010

A pretty unusual color palette in this one by Jesse entitled Teeth but it works really well.  I would never have thought florescent yellows and greens could look so natural.  This is the “S2 cube”, which I assume is a variety of the Mandelbox.  Reminds me of a man-made planet in a sci-fi story.  Here’s another one with the same coloring and looking just as natural and appealing too.  Jesse seems to make some of the most unusual and offbeat versions of these 3D fractals.  He’s obviously experimenting with more than just the coloring, although he’s done a great job just with that alone.

Teeth, by Jesse, 2010

Teeth by Jesse, 2010

This is another by Jesse taken from his Supercubes gallery section on  Have you ever seen such a freaky fractal and with so much bizarre and yet carefully constructed detail?  They’re like egg cannisters and they grow on the sides of the bigger egg things in strange patterns and all over the place too.  I remember back in my early days of using Sterlingware, I was zooming into a fractal that seemed to be made of red velvet curtains.  The “curtains” were quite intriguing but then while zooming in further I discovered shiny eggs growing under them.  All this makes it rather difficult to define what a fractal is or to explain to someone what fractal graphics look like.  There’s just too many freaky things to be found.  There’s fractals and then there’s “freak-tals“.

Birth by Jesse, 2010

Xenodream has not been left out of the 3D fractal craze here.  This one is by xenodreambuie and had the label, Triplex Z=rcosphi Julias.  I think a better title would be Catalog of the Fractal Brains.  They’re all very rich in well rendered, three dimensional details and colored well even though I think the method is a fairly basic one.  The numbers are in there for technical reference of course, but I think they add a nice artistic touch as well.  This would make a very appealing wall poster.  I’ll bet if you showed this image to people and asked them what kind of textbook it came from they’d all guess it was Biology and not Math.

Triplex Z=rcosphi Julias by xenodreambuie, 2010

Arch detail by Tglad (2010 Nobel Prize Winner, incidently) is interesting for the, well, details of this arch it shows…  Another great title.  See how the section in the lower right appears to be eroded away?  That’s all algorithmic.  The main arch structure off center to the left is interesting too with its floating triangle center.  The coloring gives it all the impression of being carved from wood or some sort of soft stone.  There’s always something new to see in the Mandelbox.  I think it’s going to be a popular formula for some time.

arch detail by Tglad, 2010

I said 10 fractals and a movie and here’s the movie.  I forget how I stumbled on this one.  I think I saw it amongst the entries in the current contest in the animation section.  However I didn’t actually view it right away (that’s a problem with animation, you can’t just take a quick glance at it).  I only looked at it for the first time while visiting subblue’s website (  For those of you who often skip videos if you don’t happen to like the title picture, this video features a very good soundtrack which straddles the categories of sound effects and slow paced instrumental music.  Also featured is some of subblue’s special, black and white, polished steel renderings of the Mandelbulb.  It’s some of the best video rendering of the Mandelbulb actually.  Anyhow, with good graphics and a smooth professional soundtrack, it’s worth taking a look at.

The music is actually not by subblue but by The Formula.  Here’s a link to subblue’s blog which has a larger version of the video and has a bit more information as well as a very long string of glowing comments.

The Formula from subBlue on Vimeo.

Well, there you go; 10 fractals and a movie.  And it didn’t even cost you 10cents like Tales of the Unexpected comic books did fifty years ago.  The internet is just a such a great and wonderful thing.  Let’s hope it stays that way.

A Knighthood for Knighty

I continue to dig through the treasure trove of fractal visions over at  In fact, lately it seems to me that the center of the fractal world has shifted to  It’s become the Paris/Milan/New York/London/Tokyo for new fractal fashions.  Is there anything new and exciting in the fractal world right now that doesn’t have its roots in

Sequence, by Knighty 2010

Although the obvious sequence of parameter adjustments is what this image is all about, and I think it was posted merely as an illustration in a thread on Kaleidoscopic (escape-time) IFS fractals (KIFS, for short), the color palette really makes this image much more than merely functional.  I think Knighty realized this too since he’s used this same palette quite a bit.  It’s one of the best I’ve seen on this new fractal frontier.

[Knighty starts this new topic, May 1st, 2010]

Here are some renderings of a class of fractals which I call “Kaleidoscopic IFS”. There is a big variations of shapes one can get with this method.
I began with this algorithm to get DE for symmetric Sierpinski tetrahedron:

[From, Kaleidoscopic (escape time) IFS]

Just like the early Mandelbox renderings by Tglad, the KIFS made by Knighty showed real graphical promise right from the first batch posted.  Here’s one that of the first few that received quite a bit of praise:

"last picture" by Knighty, 2010

[Knighty responds to the initial comments:]

There are many other known fractals that may appear from nowhere. I’ve already met the Koch curve, cantor dust and others I don’t know the name. The variation of possible shapes, from geometric figures to organic forms, still amazes me. The possibilities are infinite  wink, not only by changing the parameters but also by changing the algorithm.

What I’ve described in the O.P. is actually what I’ve explored so far. The main ingredients are the folding and the stretching, that is, kneading the space grin. Then add some salt and spice. Seriously! In the case of this class of fractals, folding are done about planes and stretching is an homothety. The rotations may be the salt and spice. I realize now that one can insert as many rotations between the foldings. In principle other transformations than a rotation can be used (but I may be wrong). The nice thing with rotation (and other orthonormal transformations) is that the distance estimation remains very simple and the generated distance field is continuous. I guess because they don’t add stretching.

I think the kneading process is what is done to generate escape time fractals in general… but this is a little bit off topic. I’ll start another thread.

PS: Most ideas behind these fractals were found in this forum. wink

[From, Kaleidoscopic (escape time) IFS]

If you read the forum thread you’ll see that many other people get involved.  In fact, according to Knighty’s remark, “PS: Most ideas behind these fractals were found in this forum” there’s been a lot of collaboration going on already.  The sort of group exchange of code and ideas which seems to be the hallmark on immediately starts to take place.  In addition to the regular 3D fractal enthusiasts, the venerable Jos Leys (of 3D Kleinian fame) joins in as well.  Only a truly great knight would have so many squires and inspire so many others to join in his exploits.  Is there an Order of Sierpinski?  An iterated knighthood?

Subblue charges forth with these surprisingly monochromatic but still very exciting renderings:

untitled by subblue, 2010

untitled by subblue, 2010

With more sublime renderings Knighty produced this family portrait of the Royal (3D)House of Sierpinski:


Tetrahedra-Sierpinski-family by Knighty, 2010

There’s more.  In fact, you ought to just go over to the gallery section of and view Knighty’s Kaleidoscopic IFS section.  But here’s two of the more interesting ones so you don’t miss them:

Pagode, by Knighty, 2010

Pagode is an interesting construction.  Although a higher resolution rendering would probably be even more impresssive, even this small version shows the sort of intricately detailed and vividly rendered imagery that Knighty has discovered with his KIFS fractals.  Like the Mandelbox, these KIFS are very creative in that they seem to have an almost endless number of variations depending on how one folds and twists the characteristics of the formula.

Pandora_seashell by Knighty, 2010

You know, I suppose if you’d seen this Pandora_seashell lying on the lawn in your backyard you might just think it was a rotting leaf.  But sometimes the “art” is in looking more closely at something that we’d otherwise, uh… step on.  Art is on the boot of the beholder.  Math is a very natural thing and for that reason I think it’s easy to make assumptions about mathematical, or algorithmic, imagery.  Such as assuming that it’s repetitive or predictable.  But I think Knighty’s recent discovery of these Kaleidoscopic IFS fractals shows that there’s still plenty of things to be discovered in this area (it only started at the beginning of this month, May 1st, 2010).  Maybe there’s no end to all of this and this is merely the beginning?

Well, it’s all happening over at, so stay tuned to that forum if you want to catch the next great event in the fractal world.  Perhaps some day all the rest of the fractal kingdom will be mere footnotes to  While Knighty and his other fellow members of the Round Table feast on roast boar and crash their flagons together in an endless round of toasts and heroic tales of fractal exploits.

Fractals Don’t Have to be Fractals

I often find myself preoccupied with justifying fractals (and other types of computational imagery) as art; trying to link fractals with the larger stream of visual art that has flowed and enriched (and provoked) our culture since pre-history.  I don’t know why it nags me so much.  I don’t think most fractalists are very concerned with what outsiders think about fractals or how they may label them.  Maybe that’s a more sensible attitude to have than the one I have which seems to keep wanting to write an Art Manifesto, Bill of Rights or a Declaration of Independence for fractals.

My latest inspiration to write a fractal Magna Carta occurred when I saw this Mandelbox image by Pauldelbrot (Paul Derbyshire, I think) posted at

Escher's Eiffel by Pauldelbrot, 2010

It’s weird, but I hear things when I look at this image.  I don’t really mean I hear audible sounds (that’s nuts!), but the image suggests to me the sound of icebergs bumping against each other underwater:  Great, massive objects in motion.

Or mountains.  Does this image not make you look up and see the distant, towering faces of whatever that smooth-sided thing is?  Is there a basement of the mountains, where the roots and feet of them are exposed and we see where they come from and what they stand on?

Yes, Pauldelbrot’s Mandelbox image here is every bit as expressive as a great Ansel Adams photograph or one of the Group of Seven landscape painters whose impressionistic and semi-abstract style displayed the raw, muscular beauty of the Canadian wilderness.

A few disjointed thoughts about fractals and art:

  • The images speak for themselves
  • They are what you see (and hear)
  • It doesn’t matter how they were made
  • They’re as much an art form as Paul Klee’s work is
  • They express themselves in a language of shape, form, color and pattern
  • They have a symbolic kind of expression
  • Good art is the stuff you keep coming back to look at
  • Design and ornamentation is visual music
  • Serious art is any kind of art you take seriously
  • Fractals are captured, not painted
  • Fractals are an abstract and imaginary type of imagery like Abstract Expressionism or Surrealism
  • Fractals are an interesting world just to explore; you don’t have to take your camera with you
  • Fractals don’t have to be fractals, they can be landscapes, sacred smudges or forbidden cities

Here’s two more by Pauldelbrot.

Moss by Pauldelbrot, 2010

The moss-covered stone ruins are a good example of the imaginary kind of themes that fractals seem to instinctively display.  It looks realistic, but the strange patterns in the stones are unreal.  Can you spot two cavities or spaces in the stones that look the same?  This shows the enormous creativity of the Mandelbox fractal: everywhere you look there’s something new.  That’s what creativity is all about: new things.

Trusses by Pauldelbrot, 2010

How about: Grendel trashes the mead hall? Amazingly photographic.  Note the glinting reflection of light on the truss in the foreground.  Would a professionally taken photograph of a ruined temple be clearer or more vivid than this?  There’s great imagination at work in the construction of these trusses and it all comes from a fractal formula (and an enormous amount of computing).  There’s a touch of the surreal in this image; its as if it was the illustration to one of those H.P. Lovecraft stories about million-year-old, pre-human temples of the cosmic elders.

Well, I haven’t finished my odyssey, but Pauldelbrot’s recent Mandelbox images posted to have certainly moved me on to the next island.  Actually, I don’t care if a voyage like this never ends.

2010 Nobel Prize for Fractal Art

For his work in discovering the Mandelbox formula of 3-D fractals, the winner is Tom Lowe, better known on as Tglad.

Now some might ask why Daniel White and the Mandelbulb Team weren’t this year’s Nobel recipients, but while the Mandelbulb discovery was truly the most exciting event in the fractal world this past year, and possibly the past two years, and has certainly received much more popular attention and interest, I felt the development of the Mandelbulb was an achievement of a more technical and scientific nature while the Mandelbox represents a development with a much greater impact and influence on fractals as an art form.

Paul Lee (Nahee_Enterprises on FF) recently made this remark here on Orbit Trap in a comment:

Yes, the Mandelbulb really became quite “famous” back in November, but the recent variation of the Mandelbox has added a lot more to the visual aspects on the current trend in fractal imagery. There are so many good examples to choose from that it is difficult to fully represent what can be done with the new set of programs and algorithms available.

There are so many examples because many others have noticed the potential of the Mandelbox formula and since these things have been so freely shared without restriction with other fractalists, the formula has been incorporated into a number of programs such as Krzysztof Marczak’s (Buddhi) Mandelbulber and Mandelbrot 3D by Jesse (I only know his screen name), both of which are freely available.  Furthermore, thanks to the help of veteran Ultra Fractal programmer, Dave Makin (alias David Makin on FF) the Mandelbox formula is available for UF as well.  In fact, I believe UF is what Tglad used for both his current and early renderings of the Mandelbox.

The Mandelbox didn’t exist until February of 2010, which means at his point it’s only been around for about three and a half months!  Like the the great Mandelbulb discovery, you can follow the development of the Mandelbox from it’s earliest form as an idea in Tglad’s head (inspired by a related group of 3D fractals) to it’s final incorporation in the three programs I just mentioned.  It all happened on and one can at least speculate that without and Christian Kleinhuis’ (Trifox) sponsorship and management of that online fractal forum, such advances in fractals may not have occured or would have been greatly hindered.  It’s also possible, I think, that the excitement and attention which the Mandelbulb event stirred up, also attracted and brought together the people who developed the Mandelbox.  I’m still reading through the archives of all these threads over at (and trying to keep the screen names straight) so I’m not as up to speed on these events as others who’ve been following them for longer may be (i.e. I could be wrong…).

Here’s the main thread about the Mandelbox entitled, Amazing Fractal.  It starts out, just like the Mandelbulb quest did, in a very simple and low-key way:

This is a new fractal that is member of the fractals described in

The formula is simple:

[ from ]

Even the very first examples of the Mandelbox were visually attractive.  Right away anyone can see the strong design qualities and rich variety to the Mandelbox.  Look closely and you’ll see very little of the self-similarity or repetition that most other fractals have.  This is a very un-fractal fractal, figuratively speaking.  Here are the first three posted by Tglad at on February 1st, 2010:

By Tom Lowe (Tglad) Feb. 1, 2010

By Tom Lowe (Tglad) Feb. 1, 2010

By Tom Lowe (Tglad) Feb. 1, 2010

Tglad has put together a small online gallery for the Mandelbox and it’s best for you to go there and read his explanations of the Mandelbox since the technical side of fractal art is not my forte.  One thing I can mention however is that the Mandelbox exhibits something which is a rather uncommon sight in fractals and that is a great amount of non-self-similarity.  This, of course, is what makes the Mandelbox so much more interesting (from an artistic perspective) than the famous Mandelbulb.  Tom has involved two features that I think I understand: Julia sets and Folding.  What it comes down to is that you don’t see the same shapes, forms and patterns everywhere in the Mandelbox just as you don’t see the same shapes and forms in every Julia set of the Mandelbrot formula.  Julia sets are one of the easiest ways to produce graphically appealing variations of the Mandelbrot set that’s part of the mix found in the Mandelbox.  The folding feature Tom has introduced just adds to the creative powers of the Mandelbox while at the same time maintaining it’s strong design qualities through rigorous and careful combinations of patterns (folded over on each other and rendered together).  How’s that for a non-technical description of the Mandelbox?

One other thing:  Like the Mandelbulb and probably all 3D fractals and other types of 3D graphics, the Mandelbox will make good use of all the processing and memory resources your computer has.  If you’ve been waiting for a good reason to upgrade you computer, this could be it.  But as you can see, even from these prototype images of the Mandelbox, the rich results make all the time and processing power worth it in the end.  Take a look at this internal exploration of a Mandelbox done by bib (Jeremie Brunet) which was based on a series of images posted by Tglad to FF.  I’m sure this took some time to make, but again, well worth the effort, I’d say.

Since that day in early February, 2010 there has been a lot of rendering variations of Tglad’s original formula but Tglad’s own work still ranks among the best that I’ve seen.  Although may not be, as Christian Kleinhuis (Trifox) himself stated in a comment here at Orbit Trap, a fractal art site but simply a fractal site with an associated image gallery, many of the images there have strong artistic qualities and fulfill the role of art as much as they do the role of illustrations embedded in their related discussion threads.  Tglad’s posted work is one of the best examples.  From his earliest examples of the Mandelbox formula to the one below, posted 2 months later, he’s demonstrated that in addition to his technical skills of a formula developer, he also possesses a real eye for art, particularly color and composition.

Helicopter Ride by Tom Lowe (Tglad), March 30, 2010 (click for full-size)

In closing I’d like to say that I think the Mandelbox and the other 3D fractal types have ushered in a new era of fractal imagery.  A lot of the older, 2D stuff looks pretty stale to me right now and I don’t think it’s a temporary feeling.  I noticed this particularly while browsing the gallery.  The old stuff looks even older to me now.  I’ll have to confess that over the last few years I’d become rather bored with fractal art in general.  The only thing that really interested me was my own work and that of Samuel Monnier’s “Pattern Piling” technique.  The Mandelbox and other 3D experiments on the site have changed all that for me.  Fractal art is exciting again and it’s because of these new algorithms and formulas and the great imagery they produce.

It’s more than just being “3D” instead of “2D”.  It’s not like all of a sudden the images are exciting because they’ve been enhanced with some new feature or gimmick.  What the 3D algorithms have added to fractal imagery is much more substantial than just another kind of enhancement.  What’s new and different are these fresh new designs, forms and shapes that the 3D algorithms generate that the old 2D algorithms couldn’t make.  Of course, ultimately, everything becomes a flat, 2D image on a computer screen (unless it’s a 3D stereo image set) and whether the depth and perspective in the image comes from a system based on 3D voxels or just 2D pixel rendering tricks (height-field; bump-map) it all has the same effect of giving fractal artists more tools for use in their creative pursuit of making fractal artwork.  To the fractal scientists however and the formula developers, these differences in the underlying mechanics have more meaning and subsequently attract more of their attention (i.e. not everyone pursues fractals for the same purpose).

It’s a fractal renaissance. And if I had to pin an award on just one of the many people who have played a role in bringing it about I’d choose Tom Lowe.  Or rather, I’d start with Tom Lowe.  I’ve got many more awards to give out, a Nobel prize is just the beginning.  I’ve also got a:  Knighthood; Oscar; Medal of Honor; Purple Heart; Court-Martial; ye olde forty minus one…  There’s more.  A lot more to come.

3-D Fractals: A Voyage to the Mandel-Worlds

I don’t know what happened, but all of a sudden there’s a new crop of 3-D fractals sprouting up and they’re seriously amazing.  I’ve seen 3-D fractals before but these Mandelbulb and Mandel-box things have taken 3-D to a whole new level of sophistication.  The best phrase I can think of to describe them is Majestic Panorama.  It’s like a glimpse of a new world and not merely a new rendering technique or formula.  There’s a depth and style to these types of 3-D images that I’ve only seen in photographs and oil paintings and never before in digital art.  I found them all in the Gallery section of, my latest re-discovery in fractal art.

Is it only eye-candy?  or 3-D video game backgrounds?  Or is it the start of a new genre of fractal landscape and panorama that began with programs like Terragen, Bryce and Xenodream but has only now reached a level of sophistication and creativity that sets it apart from everything else ?  It’s this kind of powerful algorithmic creativity that first got me interested in fractal art and then led me to look elsewhere as most fractal artists headed off down the dead end road of endless layering.   Yes, what a breath of fresh air these bold new 3-D things are –however you may like to label them.

One thing I should note:  Many of these images are snapshots of work in progress and early examples of newly developing rendering techniques.  They weren’t necessarily intended by their authors to be finished artwork for display or exhibition.  I’ve reviewed them here simply because I think they’re extremely interesting and worthy of greater attention and viewership.  Also, I’m not up on the technical side of the Mandelbulb and Mandelbox stuff because it’s very new to me.  I’m not even familiar with the software.  Hey, I just like looking at computer made pictures.  Here’s some cool ones…

mandelbrotbox-experiment-1 by ker2x (click to view in majestic panorama mode!)

— update: 05/12/2010: click here to view a much higher resolution version of ker2x’s mandelbrotbox-experiment-1

Like all of these images, you really have to view them fullsize which you can do by clicking on them.  This one really shows the freaky, sci-fi and particularly three-dimensional awe and wonder aspect to these types of images.  The landscape itself is intriguing but the hovering island (and copper/emerald color palette) makes this image simply monumental.  Also, the hazy, “aerial perspective” accomplished in the rendering makes this image look extremely polished and as carefully created as if it had been painted by hand in oil paints.

Retro Metal Cathedral 3 by MarkJayBee

Click it to check out the larger version at  What makes the detail in images like this so spectacular I think is the depth and incredibly realistic lighting.  Although ray-traced images can be intensely realistic and almost “perfect” looking, they don’t have that “aerial-perspective”, that vast expanding background and distance that this images demonstrates so well.  This reminds me of something painted by the old masters like Raphael in his The School in Athens fresco.  Of course no 3-D fractal will have the expressive human figures and all those sorts of things that human painters depict, but they can like this one match the magnificent perspective and three dimensional design that Raphael’s setting and background has.  Actually, I think MarkJayBee’s image here is better in that respect.  Sorry, Mr. Raphael, but you just didn’t have the Mandelbulber program to help you back then.

before the rain, by Tglad

Doesn’t this have a certain Maxfield Parrish look to it?  I don’t know what all the programming and rendering tools were that went into this one, but the results are unlike anything I’ve ever seen before made digitally.  I don’t just mean the lighting and 3-D look, I mean the creativity in the image itself also.  This has the variety and unpredicability of a real, natural landscape.  It doesn’t have the repetitive look that most fractal formulas have.  There’s recursion here, but it’s not carbon-copy or of a purely repetitive nature like say, sierpinski objects have.  You could wander around in this small sample of landscape for ages and not have explored every detail.

Thing by knighty

Here’s a good closeup of the exquisite and wondrous detail that these 3-D “things” have.  Such things as this, although they look realistic enough, could never be made (gravity’s not a problem in the Mandel-Worlds like it is here) but if they could they would rival the sculpture and design of any human made temple or architectural wonder, at least from a design perspective.  Knighty chose a good title as the image speaks for itself and who could ever give this a fitting name?  I saw a lot of very intriguing architecture and 3-d works in the Star Wars second series of movies, but this kind of imagery exceeds that in quality and creativity.  And these “things” can be animated, too.

Aztec Farms by Timeroot

Here’s an even bigger version than the one you’ll find at the gallery.  You can clearly see by the “Evaluation Copy” watermarks that this image is fresh from the laboratory.  I’ve included it because, like all the others, it’s such a majestic panorama.  I was really stunned when I first stumbled on this one.  It’s got the level of detail that only electron microscope or satellite photos usally have.  The title is quite appropriate too as it does resemble a vast area of farmland in the desert like a kibbutz in Israel.  There’s so much variety and well rendered details in this one that I just had to include it even though it’s got all those watermarks on it.

The Golden Hour 1 by MarkJayBee

You can’t get a better example of perspective than this image.  This is like those Grand Canyon photographs that one sees in every travel magazine: you just want to dive into the picture and fly away.  Artists used to spend a lot of time and get paid good money for making spectacular scenes like this.  We’re really living in a golden age of art, or if you prefer, visual imagery.  We’re seeing things every day that most explorers and world travelers could never imagine or hope to visit.

entrance to the hole, by Tglad

Reminds me a bit of Dave Makin’s video tour of the inside of his golden sierpinski temple which I included in a previous posting on animation.  Again, look at the incredibly lifelike perspective shown in the mouth of the “hole”.  These images are so vividly rendered and yet also so full of rich algorithmic details.  The green, “tarnished bronze” coloring is a nice touch too and adds a subtle outline and resulting perspective to the image.  I keep expecting to see someone walk up to the balcony railing and begin to issue a royal proclamation.  This would make a nice model for rebuilding the Jedi Temple.

Bulbox3 by Jesse

This one really needs to be view full-sized to fully appreciate it.  What I find most impressive about this one is that although everything looks like it’s been roughly chopped out of stone, there is a precision and carefully laid out design that it all fits into.  Very intricate and yet having a primitive style to it at the same time.  Also, although the image has a reflective or mirror-image quality to it, if you look closely you’ll see that very few of the opposing and apparently “mirrored” structures are actually identical.  The plain background is a nice touch and shows off the rest of the image quite well.

Plastic Mandeltoy by MarkJayBee

The smooth plastic texture in this one is unique.  I find it gives the impression that the details have been exposed by chipping the plastic matrix away rather than being carved from it.  I guess it’s probably a simple image in some ways since it’s just a cube, but as with all these Mandelbox things, there is never anything simple about them.

Inside Tglad's Cube by buddhi

I think the best comparison one can make to an image like this is a fossilized plant.  I’ve seen plant fossils in museums and they have the same delicate detail and stone like qualities to them.  I take it that “Tglad’s Cube” is a formula made by Tglad.  Buddhi, the author of this image, also made the program that created it, Mandelbulber (just for Linux).  I tried it out on my ancient computer (P4 2.26 Ghz “single”-core) and it works perfectly although I wasn’t able to make anything approaching the cool stuff these folks I’ve reviewed here have.  You can see the sort of synergy that been developing over at with this 3-D fractal experimentation.

Exploring fractal planet by bib

You see here?  Everything these 3-D fractal programs generate is awesome.  Even this crevice in the side of  this larger (I’m guessing) Mandelbox planet is cool to look at.  It’s like the whole thing is one gigantic carefully carved piece of art.  And I’ll bet every cave and crevice like this one is different in some way or another.  Very nice coloring.  The texture looks genuinely rock-like and the darker tones gives a nice shadowing and relief to the imagery.  Nicely composed too.  And the shadowed area to the right of the center suggests there’s more to be explored if we wander in –unless of course something lives in there.

So there you have it.  For the first time in a long while there’s something I find that’s genuinely new and exciting in the fractal world.  I’ve got more to show you, but I thought I’d just focus on the Majestic Panorama genre for now.  In the meantime I suggest you check out the Gallery section yourself over at  It’s a pretty good collection all on it’s own created by the contributions of the many forum participants that have gathered over there.  It’s not the usual sort of fractal gallery and I think you can see from what I’ve reviewed here that it’s got some really great works in it.