Conway's Game of Life

Conway's Game of Life is a cellular automaton created by John Horton Conway.

Cellular automata
Cellular automata (the plural of cellular automaton) are simulations that take place on a (supposedly) infinite grid of cells. Each cell is a very simple machine that can take on a number of states--usually just a small number, like 2 or 4, though it can be anything greater than 1--even an infinite number! Every generation, or cycle, every cell looks at its neighbors' states and its own, then "decides" what state it's going to become. After that, every cell becomes the state it's "chosen".

Conway's Game of Life
In Conway's Game of Life, the grid is a 2-dimensional grid of squares, and each cell can be in either of two states: "alive" or "dead". A cell's "neighborhood" consists of the eight cells touching it. Each cell looks only at the number of neighbors it has which are alive. If a dead cell sees that exactly three of its neighbors are alive, it decides to come to life; otherwise, it decides to stay dead. If a living cell sees that exactly two or three of its neighbors are alive, it decides to stay alive; otherwise, it decides to die.