Dragoncave: Fractal Art

Fractals are described by very simple mathematical equations, but they are recursive equations, in which the output is fed back into the input and processed again and again. Fractals have been with us forever, in natural forms, but it was only with computers that it was possible to see the images made by the equations, because it requires millions or billions of calculations to generate the images out of the blank page. That just wasn't possible before computers; although some early mathematical forms we now include in the fractal set were simple enough to be done by hand for at least a few iterations, a century ago. The roots of complexity theory and chaos theory also lie in the need for many calculations. So computers have been the tool used for these mathematical discoveries—but also the tool used to make art from these discoveries.

I've been fascinated by fractals for decades, and once I had fractal generation software in hand, I could being making art. Once again, the equations are very simple recursive equations. What they produce depends on the ways the formulae are tweaked, and what other operations are also used. And what we get is a visual representation of a mathematical set that is trans-finite, actually infinite its possible permutations. So, within the bounds of a finite set we find an infinite world—yet one more paradox among many that one runs into when dealing with fractals and chaos theory.

The visual designer in me loves working with this infinite palette. I've never produced the same image twice, not even by intention. It's always wise to save off each iteration. You can always come back to them later. But you probably won't ever be able to exactly recreate them.