Alexander Boswell has posted some code that generates a beautiful picture of the Mandelbrot set. It differs from the usual images which record the number of iterations a point takes goes through to escape from infinity - it instead traces the chaotic orbit of each point and colors each pixel the orbit passes through. I'll let you read about it at his site. He's chosen wonderful colors that make the set look like a nebula.
His sample code out of the box generates this image (click to enlarge):