See also: Mandelbrot Animation
This program explores the Mandelbrot set. Blue pixels are possible members of the Mandelbrot set; the other colors are determined by how quickly the pixel was proven to not be in the set. Unfortunately, it can take an infinite amount of time to prove that a particular point is in the set, so this program can be very CPU-intensive.
Once the initial picture has been drawn, the program refines the picture by going back to the blue points and attempts to re-color them. If your other programs slow down or your laptop gets too hot, it's because it is working hard to solve this fundamentally unsolvable math problem. It will give up once it has the best approximation it can get, but this may take a while. Close this window to make it stop immediately.
The most interesting areas to explore are the places where you see the most colors-- these are most likely to continue to have a variety of colors and shapes as you zoom in.
If you search for Mandelbrot programs on the internet, you'll discover dozens of them. Most of them (including this one) are pure hobbyist productions, and many are quite amateur. This one started out in 1996 or '97 as an attempt to disprove the prevailing wisdom that programs written in the Java language were necessarily slow. This is by no means the fastest Mandelbrot program out there, but it's no slouch. More important to me is the quality of the images. I know of no other program which automatically balances between quality and speed, nor any other which goes back and improves a finished image.