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Opinion: What I think about fractal art

This site is dedicated to fractal art. But in the first place, what is a fractal?

I’m not a mathematician, so a scholarly explanation of the nature of fractals would have me wandering through space and time forever: like getting into a black hole (I love astronomy, by the way). I prefer to leave that to more knowledgeable fractal enthusiasts with vast experience in the field. A good starting point could be the articles Fractal and Fractal Art, both from Wikipedia, where you will find a comprehensive explanation of fractals and their association with algorithmic art. What I can tell you for sure is that this is a very beautiful field loved by many fractal sympathizers around the world, many of whom are attracted to them as an artistic expression. That’s why people call it fractal art.

There is no single or universal definition of art, but we can derive from them certain “clues” that can help us understand and conclude that what we do is art, for art is an object with aesthetic value as perceived by an observer. Observer, by our human nature, is a human being, possibly the only entity in this world capable of admiring an image for its appeal.

Since our art is created with the aid of a machine, does it have lesser artistic value or none at all?

Anyone who has generated a fractal image knows it involves an entire process, regularly plagued by mathematical equations, variables and numbers to get the right one. That point of “rightness” is reached when the explorer sees a picture come to life: when we see something within the image, when an idea strikes our minds as we observe what we have created.

I have heard people debate whether these graphics should be regarded as an art form. If they limit the creative phase to generating of the figure, then fractals may not necessarily be considered art. But if they take into account the personal input —selecting an interesting region, coloring it, and bringing it to “perfection”— they can begin to understand why these pictures are indeed art. It is not merely the figure that makes them objects of admiration, but the artist’s talent in combining content, form and technique into an original composition.

It is difficult —almost impossible— to explain the creative process in words. I don’t think any other artist, whether a painter, a sculptor, a photographer, an architect, would be able to provide a truly satisfying explanation either. It can only be understood by looking at the work and sharing the creator’s enthusiasm: the pride and satisfaction we all feel when we realize that what we’ve made is what we “wanted” —even if we usually don’t know that beforehand.

Thus, art is defined by aesthetics (although not necessarily beauty), imagination and creativity. And all of that depends on individual tastes, shaped by one’s surroundings, society and culture —influences that, by the way, are impossible to encompass in a simple written explanation.

If I were to give you a definition of what a fractal is, I would begin by saying it is a figure composed of infinite curves contained within a finite surface or area, having consequently a non-integer or fractional dimension. Or I could say that it is a “rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole” (to quote an old document dating back to the late 1990s but still available, known as the sci.fractal FAQ). That means, in simple terms: you start with a basic image derived from one of the functions —let’s say a Mandelbrot or a Julia set—, and zoom in on any portion to come to a new image that has some similar features to the original one. If you continue zooming indefinitely (thus fractioning —breaking— the image into smaller and smaller parts), you’ll still get a new picture that, although different, will still have some recognizable features coming into view. This is generally referred to as self-similarity; it is very obvious in simple fractals, but since Mandelbrot and Julia set fractals are complex ones, sometimes you won’t see the similarities at first sight.

Some fractal structures are as real as a single leaf or a whole tree, a falling snowflake, a mountain range. A close examination of our surroundings, as has been done by chaologists, has revealed a wealth of fractal characteristics everywhere they have looked: from seashores and clouds to the stock market.

Mathematical expressions don’t need to be soulless impenetrable barriers lacking any breath of life, a touch of a warm living beat. They just need to be viewed through a different lens, a colorful filter through which anyone can perceive art. Just think of fractals as the ultimate mathematical images of exquisite and strange beauty coming from a little more complicated world.

After all, there are many who will continue to believe fractal art is not “art”. But, fractals will still be another way of bringing to life what we see in our imagination. Think of it as Hieronymus Bosch in the midst of the Renaissance.

Juan Luis Martínez
2000.11.26 (Friday)
Last revision: 2025.04.18 (Thursday) for clarity.

Other people’s opinions:

And now, 2017…

A lot has changed, and much more has been shared and written about fractals and fractal art since the year 2000 —the year when I penned most of the writings included in the HTML version of Third Apex to Fractovia, a website started in 1998, but which practically died at the end of 2006 as a result of an acute lack of updates. Visit Tatyana Zabanova (2015-2016), Critique of Fractal Art for an outlook of recent developments on the subject.