Cellular automaton with simple rules that produces gliders, oscillators, spaceships, even Turing-complete computation. The most-studied toy of complexity science.
From Wikipedia
The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves in discrete time steps called generations. There is no limit to the number of generations or win condition.