Langton's Ant

Langton's Ant is a two-dimensional cellular automaton with a beautifully simple rule: the ant turns right on a white square and left on a black one, flipping the color behind it as it goes. From these two rules alone, something remarkable emerges — early chaos that eventually collapses into an infinitely repeating diagonal "highway," no matter what starting configuration you give it. Nobody has proved why this happens. It just does. I have a lot more to say about this one — the multi-ant dynamics, the topology experiments, and some surprising connections to other areas of math — so a longer writeup is coming soon.