Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.

Rules

  • The universe of the Game of Life is an infinite, two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead (or populated and unpopulated, respectively).
  • 1. Any live cell with two or three live neighbours survives.
  • 2. Any dead cell with three live neighbours becomes a live cell.
  • 3. All other live cells die in the next generation. Similarly, all other dead cells stay dead.
  • 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. It is Turing complete and can simulate a universal constructor or any other Turing machine.