Okay, assume I'm a total newbie at this. (Not far off the mark!) Why the prevalence of fractals in art? What is a fractal? What does it mean? According to my studies, fractal means irregular, more or less. Irregular geometry was a new way of describing the world around us, not covered by Euclidian, or shape based geometry. Isn't art a way of describing the world around us? Therefore, fractals are another tool, just like perspective, shading, and brushes. What do you think?

Maybe that will get a response.

Not sure I know what you mean by a prevalence of fractals in art. Do you mean classical art, painting, sculpture, or other media? I think it's kinda rare. Even in mainstream modern art I wouldn't say it is prevalent, maybe I'm wrong. Are you referring to it's popularity as a digital media? Fractal can mean irregular, but I think that doesn't really cover it. I think Seirpinski triangles, Koch snowflakes, Peano dragons, Barnsley ferns, Mandlebrot and Julia sets and other geometric constructions are very regular. Of course you are correct that this geometry was born to describe things in nature, mountains, clouds, rivers, trees, circulatory systems. These are two very different kinds of things, trees and Mandelbrot sets. So what do they have in common? I think it would be better to say self-similarity, complexity derived from repeated application of simple rules, is what unites them rather than irregularity. The same mechanisms that make a tree trunk apply to the branches, twigs, and leaves. I'm not trying to pick nits, I hope it didn't sound that way, I reply because you have brought up some interesting topics. I'm not very good at talking about art, I haven't heard many who are, but I'd be interested to hear why others think that nature even the universe has chosen fractal processes for creation. Why are fractals everywhere? For extra credit, what are the alternatives?

"Why does 'nature' use fractal process for creation?"

Simple; once you have a pattern created, reuse it, on varying scales, and in varying positions. Why waste something that works? That is the essence of a fractal's nature: self-similarity and repition of it's parts.

However, I don't believe that "Fractal Mathematics" was "born to describe things in nature..." as Fractographia said. The 'fractal nature' of nature is a hindsight issue. It began as a pure numbers experiment by Mandelbrot, Julia, and others. The art portion arrived when those mathematically derived numbers were plotted in a visual graph of the results, and it was realized then that the results were visually pleasing, and similar to what could be seen in nature. We just didn't have the proper math to describe all of nature's complexity until after fractal math was invented. Thus, the 'art' of fractals is a secondary result of the mathematics.

mytwocentsworthonallthis.....probablymoretosaybutnotjustyet...

Attached Link: http://www.anu.edu.au/ITA/ACAT/contours/docs/fractal-history.html

a brief history of fractals. interesting, non-technical website

I don't really think that fractals are prevalent in nature or art. Instead, it is that both can frequently be described quite succintly in fractal terms. Fractals are derived from mathematics and mathematics is often a very efficent language by which to define things. Fractal methods are also a very effective means by which to store repetitive data and, if nothing else, nature can be quite efficient at times. Just consider the data storage and manipulation potential of genetic coding. Therfore it is not surprising that the complex pattern of a seashell's colours and markings can be so readily emulated by a simple fractal equation. The defining characteristic of fractals is not irregularity but self similarity or repetition- quite the opposite. As you dive into a fractal pattern the view can change enormously. But as you continue to dive deeper you will discover that earlier patterns reappear. Dive again and the pattern disappears only to be resurrected at further depths. As for art, the human psyche appears to have a particular penchance for order and repetition. Quite naturally things that exhibit such characteristics will be attractive to many of us. If one defines art as that which is pleasing to the eye then the effects of fractal domains as exhibited in fractal imagery will naturally be considered artistic. However, if one considers art to be a reflection of the human condition then fractal imagery probably will not be considered artistic. I don't really want to go in that direction as the universe offers no natural laws as to what constitutes art. It is a matter of human perception and need and thus the question of what constitutes art has many answers. While we can find fractals in art, as in many things, I do not believe it is otherwise prevalent in art. While one can point to the many personal fractal art galleries on the web I suspect this is more because it is relatively easy to create pleasing imagery with fractal methods. Before anyone jumps on me let me say that fractal "art" can be very good indeed. It is not simply a mechanical method of letting a program run and those who have mastered this craft tend to consistently produce superior imagery- at least to my eyes. But having said that I personally find the majority of fractal images to be boringly repetitive. Of course, the bulk of this is personal opinion. However, I have experimented with fractals in the past and these are my conclusions. I still have an old and neglected fractal gallery at http://www.fractalus.com/jack/ so you can decide for yourselves whether I am full of crap or not. - Jack

Great thread! Mandlebrot and several others have referred to fractals as a discovery, instead of an invention. It could be that Euclid was just wrong. (It happens.) The appeal of fractal art is in the eye of the beholder. I enjoy it- but I can also look at the patterns in a leaf, or watch currents of water, with the same interest. One of the keys of meditation is illumination through sympathetic attunement with patterns- chant, mandalas, etc. The mind shows a positive response to synchronisation. (Prayer, too. Any formulatic ritual.) I shouldn't conceptualise right after I wake up.

Here's my cut at it:

Fractals represent a new symmetry: dilation symmetry. That's when something looks the same at different scales. (The property of dilation symmetry is what makes MojoWorld possible; planets that you can get as close to or far from as you like, while maintaining essentially perfect detail.)

Symmetry is ubiquitous in art. The human brain is a pattern-recognition machine; fractals represent a new class of patterns we've recognized.

So it's utterly natural that artists would seize upon fractals an run with them, so to speak.

Why? "Because they're there." :-)

-Mo

PS- In case you didn't know, I was Mandelbrot's right-hand man for 6 years, so I know a bit about fractals. He even credited me with being "the first true fractal-based artist." Not trying to brag; just to establish that I'm not just shooting from the hip here. ;-)