I've been interested in the Mandelbrot set for years, and years ago on the Amiga, I calculated hundreds of frames off line for a zoom along a path of a Julia-ish set and stored on the harddisk and played back in realtime.

Until seeing this website, I'd never even considered what different exponents might do to the image, and was pleased to find a nice logical pattern from changing it, even if the higher exponents don't necessarily have as much interesting stuff going on as you zoom in.