Conway's cellular automaton Game of Life. From wikipedia.org:
The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton.
The game shows how complexity can emerge from simple rules, which are as follows:
0, 1, or 2 neighbours - cell dies
3 neighbours - cell survives
3+ neighbours - cell dies