This is the first time math has ever really gotten me excited. It is the graphing of an equation, and it is really fucking cool. Here is a webpage explaining it:
http://www.olympus.net/personal/dewey/mandelbrot.html

Here is a java applet that lets you zoom in to it:
http://math.hws.edu/xJava/MB/index.html

It's really cool.

I have a fractal generator on my linux machine and one of the ones it came with was the Mandlebrot set. Fun to zoom through.

Fractals are one of those awesome things in mathematics that most people don't get to through the typical method of schooling because lowered standards means it should take 6 years of study before you actually start learning basic algebra.