Noise might be the true anti-fractal since it is, by definition, not self similar.

Here's an article on this subject...

http://libnoise.sourceforge.net/glossary/index.html#perlinnoise"Each coherent-noise function that is part of a Perlin-noise function is called an octave. These functions are called octaves because each function has, by default, double the frequency of the previous function; musical tones have this property as well. Perlin noise generated with more octaves produce more detailed coherent noise, at a cost of additional calculation time.

Perlin noise is fractal in nature; a zoomed-in section of Perlin noise tends to look like the original section. Natural objects also have this property; for example, a twig from a tree resembles a branch of the tree, which in turn resembles the original tree. Because of this property, Perlin noise is ideal for generating natural, self-similar textures such as granite, wood, marble, and clouds. It is also ideal for generating realistic terrain.

Ken Perlin invented Perlin noise in ~1983. Because his invention is used everywhere in the special-effects industry, he won an Academy Award?. "