The Mandelbrot set is a set of complex number for which the iterator z(n+1) = z(n)^2 + c is bounded. In the image above, black values fail to converge, and are part of the set. Other colors diverge, and brighter colors diverge faster. The set forms a fractal, is self-similar, and has a lot of other cool properties
The canvas above is drawn the fly using HTML5 things.
http://en.wikipedia.org/wiki/Mandelbrot_set
http://en.wikipedia.org/wiki/Fractal
http://library.thinkquest.org/3288/usesfrac.html