They are the graphical representations of mathematical formula progressions. When the formula, or progression step is changed, it was found that this dramatically changed the visual representation. When computers came onto the scene, it was found that, not only were they fascinating math problems, but the progressions made amazing visual representations in their own right.
Bottom line. They're way cool to look at. Apophysis is a free fractal generator. It generates what are called flame fractals. That's where the entire figure isn't filled with the color, just the points at each progression.
Enough lesson. Go download a free copy of Apophysis 2.4 Beta ~
noxious-cherub has the link in her journal.