Fractals are defined as geometrical plottings of mathematical formulas that repeat themselves at varying degrees of magnification. Imagine the metaphore of looking at a flea on a larger flea's back. Then imgine a smaller flea on that flea's back. Etc... Makes us think how large we are and also just how small we are. I like to think that fractals are artistic snapshots of chaos.
Awhile ago I recieved a fractal program my friend wrote, and being interested in fractal-like photoshop artwork and filters, I was an instant convert to this artform. There are a plethora of free fractal generating programs out there on the web. Some of my favorites are: