Fractal Basics

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f r a c t a l b a s i c s

The art I showcase on my site is made from shapes called fractals. If you’ve been browsing the site for long, you’ve probably begun to wonder just exactly what a fractal is. The question is simple enough… it’s the answer that gets a little complicated. There’s an entire branch of mathematics locked in that answer. But don’t worry—this explanation won’t get mathematical. Read on.


	To put it as simply as possible, a fractal is any object that is self-similar—that is, every one of its parts resembles the whole. The fern drawing at left shows near-perfect self-similarity: look at how every one of the fronds looks like a miniature version of the whole fern. Similarly, a sandscape covered in pebbles, in the absence of a horizon or other such cues, looks very much like a mountainside covered in huge boulders.

In fact, fractals appear often in nature and often describe it. The fern “drawing” above is in fact a computer-generated fractal. Trees are fractal, river forks are fractal, clouds are fractal: even less obvious things like the babble of a stream and the behavior of magnets as they heat up show fractal characteristics. These natural fractals appear everywhere around us and, whether we notice them or not, are very much a part of our lives.

Other fractals arise from mathematical formulas. These are less well-known than the natural fractals and much more complex: most of them are in fact infinitely complex. Oddly enough, though, their complexity arises from very simple rules repeated over and over again. Shapes like the one at right, called the Mandelbrot set, keep repeating themselves right on to infinity.

	The resultant shapes have a wild organic beauty, and as one zooms in on them, show scene after scene of gorgeous vistas. Fractal art concerns itself with the lovely shapes found therein: the art lies in bringing those vistas out and making them speak to the artist and, hopefully, to the viewer.

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