Theoricrafting

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

I’m not a mathematician, so an expert’s explanation on the nature of fractals will have me wandering through space and time forever: like getting into a black hole (I do love astronomy, by the way). I prefer to leave that to some more knowledgeable fractal enthusiasts with a vast experience in the field. A good start could be Fractal and Fractal Art, both from Wikipedia. In there you will find a comprehensive explanation on fractals and their association with algorithmic art. What I can tell you for sure is that this is a very beautiful field loved by so 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 not a unique or universal definition of art, but we can obtain from them certain “clues” that can help us understand and conclude that what we do is art, for art is an object with an aesthetic value given by an observer. Observer, in our human nature, is a human being, possibly the only entity in this world capable of admiring an image because of its appeal.

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

Anyone that has generated a fractal knows it takes a whole process, regularly plagued by mathematical equations, variables and numbers to get the right one. That point of “righteousness” 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 gotten.

I have heard people debating if these graphics should be regarded as an art form. If they limit the creative phase to the generation of the figure, then fractals may not necessarily be art. But if they consider the personal input, that of selecting an interesting region and coloring and bringing it to “perfection”, they will be able to comprehend why these pictures are indeed art. It is not merely the figure what makes them objects of admiration, but the artist’s talent in putting forward 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, will be able to give a good explanation either. It can only be understood by looking at the job and trying to participate in the enthusiasm of its creator: the pride and satisfaction we all feel when we are sure what we have done is what we wanted, even though we usually don’t know that beforehand.

Thus, art is determined by aesthetics (although not necessarily beauty), imagination and creativity. And all that depend on individuals’ tastes, shaped by their surroundings, societies and cultures –influences that, by the way, would be impossible to encompass in a simple written explanation.

If I were to give you a definition of what is a fractal, I would begin by saying it is a figure composed of infinite curves contained in a finite surface or area, having in consequence 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 any portion to come to a new image that has some similar features to the original one. If you continue zooming indefinitely (thus fractioning 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 big tree, a falling snowflake, a mountain range. A close examination of our surroundings, as has been done by chaologists, has revealed a whole lot of fractal characteristics every way they have looked: from seashores and clouds, even to the stock market.

Mathematical expressions don’t need to be soul-less impenetrable barriers lacking a breath of life, a touch of a warm living beat. They just need to be viewed through a different screen, 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 a lot of people who will keep thinking fractal art is not “art”. But, fractals will still be another way of bringing to reality what we see in our imagination. Think of it as Hieronymus Bosch in the middle of the Renaissance.

Juan Luis Martínez
2000.11.26 (Friday)
Last revision: 2017.01.02 (Monday)

Other people’s opinions:

And now, 2017…

A lot have changed, and a lot 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 that 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 news on the subject.