Fractal Art is mathematical art, literally the visual expression of equations,
created on a computer with specially written fractal programs.

In 1975, Benoit Mandelbrot introduced the term "fractal" to describe irregular
objects like the surface of a mountain. If you look at a mountain from a distance,
you see its overall shape. As you approach it, you see it's made up of details
like ravines and outcroppings. As you get even closer, you see the details within
the details, right down to the smallest rocks that make up the surface. If you
examine the small rocks, you see that they too are made up of smaller shapes, right
down to the molecular level and beyond. Each successively smaller detail also shows
self-similarity, which is a key fractal component: the rough uneven surface of a
rock mirrors in miniature the rough uneven surface of the mountain itself. Fractal
geometry describes such a surface, just as plane geometry describes the
surface of a smooth cone that not only has none of this endless detail, but also
doesn't exist in the natural world.

Fractal art consists of mathematical images that reveal more and more detail
the more they are magnified, just like the mountain. A fractal computer program
is used to find the answer to a specific chosen equation at each point in the
picture based on what numbers the user puts into the equation, and assigns a
color to each point. The program can then be used to magnify areas of the
fractal that appear to contain interesting details to explore. Some areas are
symmetrical, and others are more random in appearance. It's not unusual to find
very beautiful spiral shapes. There is no end to a fractal....they can be magnified
infinitely, with more and more detail to be found deep inside them. Once a
pleasing area is located, the colors can be adjusted using the same program.
It's the fractal artist's job to find the most interesting and evocative scenes
a particular equation has to offer, and color them carefully to produce an image
that is not just math, but art.

© Alice Kelley

http://www.AliceKelley.com

It's obvious from my galleries that "regular" fractals and flame fractals (which were named by Scott Draves) are very different. Not only are they made using different programs, but they involve a specific sort of equation (a variant of "iterated function systems"). Unfortunately I don't have a ready explanation for the differences at this time, nor am I mathematical enough to explain iterated function systems, so the best I can do is direct those interested to the Wiki article on flames, and the Apophysis home page.