Are Fractals Art?

My view is that fractal image creation is art, but more on the level of photography than what might be termed imaginative art. As a friend of mine remarked, it takes no imagination to make a fractal.

Making fractals involves manipulating an image that has already been presented by the program, rather than creating the image out of one's own mental space. Because it is very hard to predict what a fractal based on a new equation will look like, you don't set out with a specific shape in mind when starting on a brand new fractal.

What we fractal-makers do is take snaps (or artistic photos, if you prefer) of the natural world. It is the natural world of equations and their representation as images. It is an invisible world made visible through mathematical calculations via the modern computer. When one makes a fractal one usually selects a fragment of the pattern that is the entire fractal and making it one's own production.

Note that a fractal is infinite in the micro sense. It has infinite granularity in that one can zoom in without limit (at least in theory) to show ever finer detail. This is equivalent to making the spatial range smaller and smaller.

Compared to photography there is far more scope for creating images that are not initially visible. In photography you are mostly constrained by the scene you are depicting. Special techniques aside, your photograph is usually little more than a selection of angle and frame of the visible environment around you.

Although both photography and fractal making rely mainly on a process of selection, that selection is much more open-ended, active and manipulative in the case of fractals. Because of this I think there is more scope for creativity in fractal-making than in photography. One could even argue that fractal-making is one of the most interactive of all art forms. The artist is in a feedback loop with the products of their creativity, so that something novel can emerge at any point, spur new activity, and so on.


The essence of creativity is: (1) something new being thought or done by a person and that (2) it be in some sense constructive and appropriate, ie not just destructive or random.

Making fractals satisfies these criteria, but to what degree? The fractal image one produces is often quite novel and it is obviously constructive. However, if the fractal maker is churning out fractals in a mechanical way, eg just trying all the options in the program or fiddling at random, then that is less creative than if they hone in on an aspect of the fractal and seek to develop it further.

There are (at least) two kinds of creativity - the kind where one thinks of a new idea and then puts it into practice, and the other, where the creative process is one of interaction with the materials one is working with, ie there may be no initial image of what the artist is trying to produce. In both kinds, but especially in the second, entirely new ideas may arise as a result of the process of doing the artistic activity. Doodling and fractal making are examples of the second kind of creativity.

Does the concept of creativity in general apply to process or to product? I believe the answer is 'both'. Eg 'creative thinking' is only worthy of that name if it engenders a creative new idea (the product). Conversely, a creative product implies that it has been produced, ie it was the result of a process. Even if it was by accident, it was still an act of generation. In the case of fractals, the process is not very creative compared to some other arts, but the products are undeniably novel.

The anti case

Since most people will readily admit that some fractals are beautiful, the esthetic value of fractals is not at issue. The case against fractals being "art" is based on arguments such as: (1) that the PC is not a valid tool for an artist, (2) that it is too easy and quick to be art, (3) that fractals are only dots on a screen, (4) that the artistry is in the equations, not in the process of image creation, or (5) that the computer does all the work.

1) I can't see any reason why one tool should be deemed valid for creating artwork and another not. What matters are results.

2) That it is "too easy" is often objected against abstract painting ie "that anyone could do it". I don't think this argument is entirely valid, but it does carry some weight. If one produced images simply by clicking a button (or shaking a kaleidoscope), getting a different image each time, it would be hard to justify this activity as an art form. Fractal making is a bit like this, in that the initial image comes up at the click of a mouse. However, there is more to it than that. There is scope for exercising skill and creativity, much as there is in photography, only more so.

Many people regard art as depending in large part on technique. This amounts to confusing art with craft. It seems to me that someone could be a fine visual artist even if they lacked the skill to draw a likeness. On the other hand, a person not in command of the techniques of woodworking could not be said to be competent in that craft. So the argument that fractal-making requires little skill should not be given too much weight.

3) The 'only dots on a screen' argument is specious, if only because the dots can be printed.

4) In some sense one could say that the artistry is in the mathematics. However, the same argument could be used to discount representational art in general, ie that the artistry is in nature and reproducing it (with modifications) is not 'art' but merely craft.

5) As for the computer doing the work, this again has some, though not a great deal, of validity. If a program ran on its own with no user intervention then obviously the person running the program could not claim any credit (unless they had written it). However, human input is usually needed to produce an interesting fractal image.

To sum up, fractal-making is a minor art form involving a minor level of creativity. It involves twiddling the knobs rather than performing acts of imagination.

Notice that I have cleverly avoided defining what 'art' is. For me it is enough to show that fractal-making is as much an art as photography.

Of snails, fractals, artists

Programmed by heredity, the snail picks a pattern to make its characteristic shell, whereas the imaginative artist (eg painter, sculptor) selects a pattern from their imagination. The fractal-maker selects a pattern from those available from a particular program and works with that. I would place fractal-making somewhere in between imaginative creation and the deterministic reproduction of pre-existing forms.

We are as much a part of the natural world as are eagles, snails or rocks. So when the imaginative artist seeks to bring forth something new, they search the part of the natural world called the human mind - whose contents in any case derive from the external world - to select their material. The painting or sculpture produced is as much a fragment of the artist's mind as the fractal image is a part of the totality of a fractal.

As human beings we have no option but to use pre-existing elements for our creations. The imaginative artist takes elements from their memory and manipulates them mentally to produce a new idea or image. The humble fractal-maker works with the images latent in mathematical equations. The process is similar, though in the case of the imaginative artist it is more indirect in the sense of being mediated by memory and imagination.

Note that the visible pattern corresponding to a fractal equation is a pre-existing part of the natural world, although it requires a computer to become manifest. Likewise an artwork is a part of the natural world that requires an artist's mental activity to make it manifest.

The imaginative artist says the painting they produce is "theirs", yet it is no more theirs than the fractal image I produce is "mine", except that, requiring more imagination, the artist's production is more personal and more idiosyncratic. At the other end of the scale, the snail is not an agent of creativity because it always produces the same form.

Is it for everyone?

Briefly, if you are interested in making novel images, yes. Try it and see.

I think that people who have never made a fractal and who believe it requires mathematical ability or computing know-how should be encouraged to try it.

Until you have zoomed into a part of a fractal image and seen the small made large, you haven't really experienced the dynamics of fractals, no matter how many thousands you may have seen.

Warning: you might become a fracto-philiac like me. Making fractals is addictive. It may also be harmful to your hard drive. 24-bit colour fractals are stored as bmp files which weigh in at 4 mb each. One way around the problem is to convert the bmp files to jpg files, using ACDSee or some other program.

Personal notes

Despite what I wrote above, I don't feel comfortable calling myself an 'artist' on account of my fractal-making. Maybe it's because making fractals is too easy and too fast.

However, I should point out that although it only takes a minute or so to paint a complex fractal image (one that would take hours or days to paint by hand), it is often a long process before one produces something one is happy with. Sometimes I spend an hour generating images without producing one that I like. Even when I do produce something good, I may spend a fair bit of time on adjusting the image to achieve what I see as an optimal effect.

For me the attraction of making fractals is to see what shapes are possible. This is not too different from what draws some painters to painting. The fascinating aspect of making fractals is the experience of entering worlds where no-one has been. It is as though a non-human artist is drawing images for you, unconstrained by any human notions such as subject vs background, balance, perspective, flat vs three-dimensional, how colours combine, or any reference to the world of sensory experience.

I want to produce beautiful and intriguing images that no-one has ever seen before. Another attraction of fractals is that they are so obviously inexhaustible. There are always more equations to try, more filters and colours to play with. One can always zoom in more deeply into any given image. Then there are new programs to try out.

People ask me whether making attractive fractals is a matter of luck or skill. In my case it is a matter of spending hours playing around with Tierazon or Sterling, changing filters and colours. Most important is to zoom into the right place. As in photography, one needs to have a good eye. That and patience are two of the main qualities needed.

What appeals to me is complex structure, so when I see a lot of that, I zoom into it and hope to find something satisfying. I always want to know what is further inside, deeper into the pattern. Some of the simpler fractals I have produced were the end points of repeated zooming - the pattern seemed to stop.

Except for making circular images out of the usual rectangular format and putting together images with two axes of symmetry, I don't like to do what is called 'post-production', ie to modify the fractal image using an image editor. Perhaps I am a sterile purist, but I like to think that what I produce is the 'genuine' mathematical object, not something contrived arbitrarily by me.

Chromatic richness

It occurred to me that fractals in 24-bit colour are some of the most colourful images ever created by people. This is because the algorithmic calculation of coloured pixels cycles smoothly through 16 million colours. Note that there are 256 possible choices for each of green, red and blue, giving 16 million combinations.

Randomness and taste

I was puzzled by a friend's comment that my fractals don't seem random enough to be satisfying to him. I don't find images that are very random-looking satisfying at all. I believe that in the visual arts, as in music, the secret is a divine medium of novelty and repetition. Too much novelty and you have a chaotic jumble, too much repetition and you have boring, schematic or mechanical patterns. For me the attraction of fractals is to create intricate and fascinating structures, new worlds of pattern previously unknown.

Ironically, random newness is not really 'new', because psychologically speaking, what we perceive as new is a new order. True chaos doesn't look new to us. Any chaotic jumble looks much the same as any other. If we see ten random arrangements of the same set of elements (such as of six geometric shapes), then these would probably all look 'the same' to us. They look the same not because we don't see the differences between them, but because they all look meaningless, ie we see no pattern.

I guess what my friend was saying is that his optimum of the novelty versus repetition balance is further towards the novelty end than it is for me. So he would favour more chaotic-looking fractals than I do. (I know I am anally retentive.)

Our eyes seem to desire a happy medium between novelty and repetition. These two factors are often harmoniously balanced in nature, eg the branches of a tree. The best fractals achieve interest through novelty, but offset this with pleasing repetition that gives an overall feeling of 'rightness', of the pieces fitting together. As in nature, what we find pleasing in fractals is usually repetition with variation.

Representation vs abstraction

I don't think that I am generating forms that emulate trees, ferns or other natural shapes. To do so you need a program that is designed for this purpose, such as Bryce. I don't think my fractals can compete esthetically with trees. God need not worry.

Often a fractal looks interesting or attractive because it reminds us of a real object, such as a shell, moth or clock. It is as though we want to be reminded of the real world. For most people, abstract painting is often unsatisfying precisely because it has no hooks or links that they can use to relate it to their own experience. It is as though we require a foothold or entry-point to appreciate a piece of art. Of course, fractals are completely abstract (ie they do not depict anything), even if they occasionally resemble things that we see in the physical world.

I believe that in most cases it is inappropriate to look at a fractal and think, 'This looks like...' because most often the resemblance is purely accidental, rather than due to an underlying structural similarity (as with a snow-flake, say). The reason why I have named some of the fractals on this site is that people seem to prefer images to have names. A name provides a link to the real world, even if the link is illusory.

Tad Boniecki
Written in January 2000
Updated in December 2016