This is a fun little experiment that proves that strange attractors really exist. The result can be easily reproduced in the real world with a ruler, a pencil and a piece of paper. It's not just some philosophical idea or some far out complicated mathematics.
The experiment is known as the Chaos Game. It's possible to perform the experiment by hand but realistically, it would take quite awhile and a lot of effort as the steps would need to be repeated at least 100 times to begin to see a result. So, to make things easier, I created the experiment in code:
The code uses the Wes Mantooth game engine.