After my brief stint in the world of fractal geometry and Clojure, I decided to make a real Mandelbrot set viewer. The resulting source code is here. Here's a simple output (click for bigger version):
It's a pretty naive implementation, barely 100 lines of code, but even with my brute-force approach, given a liberal sprinkling of type hints it runs fast enough. Programming Swing from Clojure couldn't be easier (though I doubt programming Swing from any language is ever really enjoyable, it's a painful bunch of libraries).
There's a discussion of different coloring algorithms on Wikipedia, but even after reading that, getting this thing to look good was difficult. I don't know enough math for it. I ended up cheating and I colored a couple of them in the GIMP, so I could use them as desktop wallpapers.
There are some more PNGS over here including one that's 16000x16000 (producing it almost melted my CPU last night).