Conway's Game of Life

The Game of Life, usually just called Conway's Game of Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970: a grid of cells, each either alive or dead, that evolves from one generation to the next purely by four fixed rules with no further input from any player. A living cell with fewer than two or more than three living neighbors dies, a living cell with two or three living neighbors survives, and a dead cell with exactly three living neighbors becomes alive. Despite these simple rules, the patterns that emerge range from still shapes that never change, to oscillators that repeat, to gliders and other spaceships that travel steadily across the grid, and the system has been shown capable of simulating a full Turing machine. First published in Scientific American in 1970, it has remained a subject of active study ever since.