I have written many Mandelbrot set generators in Java. One of my first Java applets (possibly the first) was a Mandelbrot set viewer. It was the most usable one I've written, since it allowed you to zoom in by just clicking or selecting an area to magnify.
One of the more intersting ones is this version that traverses around the boundary of sets that approach the true set. It works by taking a triangle with at least one vertex inside the set and one vertex outside the set. Since the Mandelbrot set (and every iteration approaching it) is connected, you know that you can make a triangle that shares an edge with the current triangle that shares the in/out property. So you just keep flipping along the sides, and eventually you'll go all the way around the set.
What can I say? I wish I had thought of it! You can read all about the Buddhabrot technique on the originator's site. The images she has created make mine look like a joke. Also, she has some absurdly beautiful videos. Just amazing. Anyway, I never really faithfully reproduced the technique, but I did take some reasonably successful stabs at it. I have some source available, and I have a fair number of screenshots.