fractalus - Of Fractals and Art

Of Fractals and Art
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robably as long as there has been art, there have been people asking whether this or that qualifies as art. Fractal artists often catch a lot of flak concerning their art. We sometimes have difficulty being included in art shows or in selling our work; we're not always taken seriously, so to speak. We are treated as dabblers, pretenders, rather than as artists expressing ourselves through a new (relatively unexplored) medium. Since I consider myself a fractal artist, I'm not exactly an unbiased party, but I do at least have reasons for why I consider fractal art a valid art form.
Our art is best received by those who know nothing about it. They simply look at what we create, and their reaction is one of surprise, awe, delight... a range of positive emotions. They don't ask whether it's art or not; we present it as art, they accept it as such. No, our problems often seem to come from those who know a little bit about how we do what we do.

Digital art is simply art created with the aid of the computer. Just as there are many traditional media and genres for an artist to choose from (pictures in oils, charcoal, pastels, watercolors... sculptures in stone, clay, metal...) with digital art there are many possible choices. Computers are used to apply effects to photographs traditionally done with darkroom processing techniques; computers can simulate paints and pencils and paper. These don't require the computer, but instead leverage the computer's ability to "undo": an errant brushstroke can be removed, but the artist is also free to experiment with an idea without fear of being unable to recover if the idea turns out to be unworkable.
    Beyond this are forms of art which would not exist without the computer. Artists use computers to create virtual models, which they place in virtual scenes and photograph with virtual cameras. Doing all of this virtually--on the computer--allows things impossible in the real world, things that defy the laws of physics, but are within the realm of imagination. Such things are sometimes achievable in other media, but the power of the computer puts this kind of expression within reach of more artists.
    Fractal art is another matter entirely. The kinds of fractal artwork being developed today would be impossible without the aid of the computer;1 a single image may involve trillions of tedious, repetitive mathematical computations. Computers excel at tedium; they follow simple instructions well and never tire of doing the same thing over and over again. The fractal artist thus instructs the computer to perform the tedium of calculation, while they focus on the important artistic details of shape, color, and lighting.
    In all of these, the computer plays the part of tool. It is the paintbrush; the darkroom; the camera lens; the calculator. It manages the details of the virtual medium selected by the artist--the complex calculations of how that blue watercolor interacts with the paper grain just moistened, or determining how light reflects off the rippled surface of a virtual pond.

To go further is to invite the computer itself to participate in the creative process. This is much harder than it sounds. In a single screen-size image (800x600) there are 480,000 separate pixels; for most computer displays, this yields 103467865 possible images. (That's a 10, followed by over three million zeroes.) Writing a computer program to select images from this vast collection is trivial, but pointless: the overwhelming majority of these combinations are just random noise, with nothing interesting to look at.
    Instead, computer programs have been written to select images in a much narrower range. We set parameters around the computer's image generator, to persuade it to produce a set of images more consistently interesting. Sprott's fractal generators, for example, follow various "recipes", and then apply simple rules to throw out 99% of the recipe's results as uninteresting. But while it is easy to start this program and view an endless series of images, it can only produce less than 1050 images--an infinitesimal shard of a sliver of a tiny portion of the total number of possible images.
    Human brains are very good at recognizing patterns; we get bored easily. Computer programs that produce endless sequences of images without human input aren't very compelling, because we can often quickly spot the limitations of the program, the boundaries set by the program's creator.
    Even more importantly, the images produced by these programs don't really have anything to say to us. The computer isn't aware, it's not trying to communicate anything to humans by self-expression... it's just following instructions and making images blindly. It doesn't know what's good and what's not. It has no ability to get bored with what it is doing and try to do something else, something new; the very thing that makes it a dependable and useful tool for relieving tedium makes it a poor tool for simulating creativity. A computer can do nothing until it is told to do it. Even among programs that allow random, "unpredictable" behavior, it is only unpredictable within the bounds its programming sets for it. We are safe in predicting the computer won't act outside those bounds.
    This does not mean that the computer cannot be an aid to creativity. Other programs like Apophysis generate a batch of images at random, for a human to sift through and find the images that evoke some thought or memory. Hundreds of images may pass by--all equally good to the computer's non-judgmental eye--until a human viewing the image sees something meaningful to them. At that point they take the image, typically working with it further, manipulating it... somewhat like a sculptor can look at a piece of wood and see a shape lurking inside it, waiting to be exposed. Until the artist works with it, it is just a lump of wood... or one of a hundred random fractal images. It is the human element that makes the image worth looking at... that makes it art.

What differentiates fractal art from other forms of digital art is that mathematics plays a much greater role in producing fractal images than it does in other forms. The other forms are not devoid of math--far from it, most things connected with computers use mathematics at some level--but mathematics occupies a special place for fractals, because the shapes that are so prevalent in fractal art are precisely defined by mathematics.
    But the mathematics in fractal art no more produces the art than the computer does. Thousands of fractal formulas are available to the fractal artist, each with dozens or hundreds of possible parameters, and each parameter has an infinite number of possible values. The number of combinations available to the fractal artist is beyond counting. The human element is critically present: only a human can decide what combinations are valuable and communicate something worthwhile.
    The mathematics used in fractal art are not just useful for fractal art. Fractals are used to mimic fluid dynamics and stock market prices. Fractal mathematics have also migrated to other forms of digital art, where they have formed the basis for simulating plant growth, mountain formation, and realistic texturing. Such developments have made their way back into fractal art as well.
    Mathematics are just another tool... a preferred tool for the fractal artist, but by no means the only tool available. Many fractal artists (including Terry Wright) enjoy taking fractal source material and working with it using tools more common to other forms of digital art, sometimes to the point where their work doesn't contain any recognizable fractal shapes. And sometimes fractal artists will use photography or other source material and push it through fractal mathematics (such as this image). In this way, the boundaries between fractal art and other forms of digital art are blurred. Fractal art is characterized by mathematics but it is not enslaved by it.

Digital art is amazingly accessible. Computers are widely available, and the software for creating digital art can be obtained freely or at nominal cost. Once obtained, it can be used again and again to create any number of images. The Internet provides innumerable tutorials and guides to help new artists learn how to use their tools. Compared to times past, when creating art consumed supplies, and knowledge of techniques was obtained by studying with the master in person, today's digital art is fantastically accessible, open to almost anyone.
    But equality of opportunity does not mean equality of results. Pencils and paper are ubiquitous, but some have talent at sketching and some don't. Similarly, those creative skills most valuable in creating digital (and fractal) art are not universally present, even though the tools are. Just as the wide availability of web publishing tools and services has lowered the bar on building web sites to the point where anyone can publish a site2, the ready accessibility of fractal tools has made the production of fractal images so easy that a human can churn out hundreds of fractal images a day. I have actually had several people tell me they would not buy my fractal art because they could obtain the software and produce their own images. Sometimes, they eventually came back, when they discovered the software didn't produce great art without an equal application of great skill.
    That digital art tools will reflect the skill of the artist is not all bad. My father painted with oils when I was young, because he could get the materials and because he liked to. He wasn't very good, but it didn't matter that much to him; he enjoyed doing it. He was expressing himself through painting. And I daresay it helped him appreciate paintings done by those with more skill than him. Likewise, I have both a guitar and an electronic keyboard, neither of which I can play beyond the most basic level, but I persist because it's fun, and it helps me enjoy other music more. Many enthusiasts play with digital art (and fractal art) tools because they enjoy it, even though they don't care whether it is very good or not.
    Although large quantities of enthusiastically-produced low-quality work can easily be found, every means of artistic expression will have those whose work stands out. It may be unusually successful commercially (how many painters envy the commercial success of Thomas Kinkade?) or it may be well-respected by the artist's peers. Few artists' works will be memorable even within their lifetimes, let alone after centuries. Digital and fractal art are so new, no one can tell exactly what will be memorable--but if nothing is created, it is certain that nothing will be memorable.

Digital art has one interesting major difference from traditional media: it can be perfectly copied. There is only one Mona Lisa; one Sistine Chapel ceiling. That is true, physical scarcity. If the Mona Lisa is removed from the Louvre, it is then not in the Louvre. But a digital image can be reproduced perfectly, endlessly.
    Art has run into this before, in a much milder form. When the ability to print quantities of a work became available, the original plates created by the artist would wear out. Limiting the number of prints was a way to ensure quality. Some artists, to guarantee that the last copy of their work had been printed, would intentionally scar the plates. In this way they introduced scarcity when there might have been plenty, but it ensured the value of their work would remain high.
    With digital art this is harder. Digital art is created on a computer; computers work by copying information about and working with it. The act of viewing an image involves making a copy--the computer must copy the data from its hard drive to its memory, process that information to extract the image, and then make another copy into its display system so you can see it. Making a digital print means taking a copy of the image and printing it physically. Many digital artists sign and number their prints (myself included), but ensuring no more can ever be made is very difficult, because copies must be made just to produce the print. And it is possible to take an existing print, scan it back into a computer, and produce another print. With a painting this would be obvious--a painting has texture, which a print lacks. But when even the "original" is a print, telling a fake from the real thing is much harder.
    Such difficulties discourage some from taking any digital art seriously. As a rarity worth collecting just for its cash value, perhaps digital art does not fit. But as the printing press changed the world by making books affordable, making widespread literacy possible, the availability of digital replication will also make information readily available to billions. Art will not escape the change. Collectors will still collect rarities, but everyone else will buy art that they like. Rarity will become quaint, old-fashioned.3

I often wonder what fractal art will look like in another twenty years. The past decade has already seen incredible evolution; our tools have become much more sophisticated, such that things we thought of but could not do just two years ago are now easily possible. I sometimes look back at the images I created years ago and cringe at the obvious "fashion" trends I was in. But I do see images that, even now, seem worthwhile.
Fractal art is evolving as rapidly as computers themselves. Already, distinctive styles are visible; though some artists seem to hop from style to style, others stick to a particular style with vigor. I look forward to the future, because this medium--one of mathematics and art together--is just getting started.

1Some machines can be set up to create fractals by using feedback; many interesting patterns can be created with a video feedback system, for example. But it is difficult to generalize the process. The computer, as a true general purpose computational device, allows far more complexity.

2Making web publishing accessible to everyone made possible the personal web site, a universally-accessible site of interest to virtually no one. I briefly mention the silliness of such things on, well, my personal web site.

3The music industry is currently attempting to address this same issue, as people discover they can digitally duplicate the art (music) they like to listen to. The industry's attempts to restore scarcity in the face of digital ubiquity have repeatedly failed to work, and have also earned them a fair degree of contempt from the public.

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