Conway's Game of Life (1970)

Invented by mathematician John Horton Conway, this is the most famous cellular automaton.
1. Underpopulation: A live cell with < 2 live neighbors dies.
2. Survival: A live cell with 2 or 3 live neighbors lives on.
3. Overpopulation: A live cell with > 3 live neighbors dies.
4. Reproduction: A dead cell with exactly 3 live neighbors becomes a live cell.
These impossibly simple rules lead to Turing-complete emergent complexity, demonstrating how life-like behavior arises from simple physics.