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On the debate of fractals as art

Recently, there was a post in the alt.binaries.pictures.fractals newsgroup that attempted to validate the artistic side of fractal images by comparing them to photography. This idea is not new but a recurring theme in the newsgroup as well as on other fractal-related sites and mailing lists. The message stated that fractal pictures are closer to photography than to imaginative art. While I agree with its two general ideas, disagreement arises when examining the implications, regardless of the author’s good intention.

In making that assumption, the message overlooked (or at best diminished) from both photography and fractals a necessary element for considering them as art forms: imagination. I would like to expand this idea to specify that:

  • There are fractal images worth considering as artworks.
  • The creation of a fractal picture is similar to the process of taking a photograph, in the sense that we are capturing an impression of something that exists on its own, and not creating it. (Obviate at this moment the philosophical discussion that could be brought forth from that last assertion).

If fractals are art, then they must be imaginative too, for imagination is a key element in anything considered a work of art. Fractals in themselves are not art, just as a beautiful sunset is not. A sunset (part of the natural world) becomes art when it is transferred, for example, into a painting or a photograph; that is to say, when it is imprinted onto a manmade medium. Thus, art as we understand it is manmade. In our craft, the computer is just the tool that makes it possible for a mathematical expression that lingers in the fantastic realm of complex numbers be transported and transformed into a visual (digital) representation of what would otherwise remain hidden from our view.

When we talk about fractals as an art form, we are not referring to the formula itself or the plain graphical representation of all the numbers belonging to the Mandelbrot set, for example, but to an aesthetically enhanced version of the natural form. This set is defined as the set of all c (c being a complex number) such that iterating z(n+1) = zn2 + c, starting with z = 0, does not go to infinity. By assigning colors to each point that goes to infinity, according to how many calculations are necessary, we transform the graph into an admirable picture. Without these enhancements, a fractal’s picture would be as unattractive and ordinary (but not necessarily uninteresting) as plotting the results of a more simple equation on a chart.

There is another important consideration to make: When we create a picture of a fractal, sometimes we do so with the intention of making it a work of art, not simply to document it. Unlike a picture taken to serve as evidence of an event —to help us preserve a clearer memory of it— any image conceived as art is intentionally crafted through careful control of the input in order to produce a desired output. This holds true for photography, fractal pictures, painting or anything else that could be classified as art.

It doesn’t take imagination to create a fractal (as the message stated), if we think of it as a computer-generated representation of a mathematical entity produced by calculations. But it does take imagination to turn a fractal image into an artistic rendering. It’s one thing to click a button and wait for a figure to appear on our computer screens; it’s another to take that same image, select an area that initially captures our imagination, and apply color (along with other adjustments used in the beautifying process) to give it that special appeal that transforms it into a work of art.

Another simple routine to determine whether a fractal image (or any other visually dependent human creation, for that matter) is a work of art is to examine if, when we look at it, it elicits a response in us. If it leaves us indifferent, then it has failed to provoke any effect on the observer —a sign that may level it from commonness. In that case, it may not qualify as art. But if the opposite occurs, then we’re likely looking at an imaginative piece that combines originality, talent, skills and well-applied technique into a fresh and admirable composition.

We have to admit that there is a high degree of randomness involved in the generation of a fractal image. This is what usually fuels the debate over whether such images should be regarded as art or not. That is true… up to a point. Once when, in our ramblings, we come across something we find interesting and worth developing, careful inspection and conscious control of variables displace arbitrariness. At that moment, a fractal abandons the realm of “simple” equation and begins its metamorphosis into art.

Every art form is imaginative; otherwise, there won’t be art at all.

Juan Luis Martínez-Guzmán
1999.06.07 (Monday)
Last revision: 2025.04.18 (Thursday) for clarity, and to add some references.

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