Langton’s Ant (designed by artificial life researcher Christopher Langton) is a cellular automaton with a single agent (the ‘ant’) moving across a two-dimensional grid. When the ant moves one step forward, it changes the color of the cell it occupies (from black to white and vice-versa). It also rotates clockwise or counter-clockwise depending on if it is on a black or white cell.
Although at the beginning of the simulation the ant appears to traverse a chaotic path, leaving behind random black and white cells in its wake, at about 10,000 steps in, it discovers a pattern, and begins tracing a wide path toward the southeast. On an infinite grid, it would continue in this direction forever, but on a toroidal grid (as shown here), it eventually collides with cells it previously traced, and returns to chaos.