According to the upstream website:

Fractal Flames are algorithmically generated images and animations. The software was originally written in 1992 and released as open source, aka free software. Since then it has developed a lot. It has been incorporated into many graphics programs and ported to most operating systems. The shape of each image is specified by a long string of numbers - a genetic code of sorts.

You can create your own flames with the Apophysis interactive designer (for windows), Qosmic (for Linux), or Oxidizer (for Mac OS X), or Apophysis-J (cross-platform in Java). Or you can use the Electric Sheep distributed screen saver to join the collective evolution of animated fractal flames.