Conway's Game of Life

About the Game of Life:

The Game of Life is a very well-known program devised by English mathematician John Horton Conway in 1970. The Game of Life simulates a cellular automaton, which is a program that consists of a grid of cells and a simple set of rules that describes how the state of each cell will change over time, usually as a result of its neighborhood (the set of cells surrounding it). Typically the set of rules do not change, and the rules are the same for every cell. Cellular automata have many applications, including but not limited to computer processors, cryptography and biological and chemical simulations.


A program is said to be Turing complete (and a universal Turing machine) if anything that can be computed algorithmically can be computed by or within the system. The Game of Life is theoretically considered to be Turing complete, given a large enough grid and enough time.


The Game of Life is a zero-player game. To “play” the game, simply create an initial configuration (or select one of the preset patterns) and click Start to watch how it evolves. Over the years, several common pattern types have emerged, including: still lifes (do not change from one generation to the next), spaceships (traverse the grid), oscillators (return to initial state after a finite number of generations) and Methuselahs (evolve for long periods of time before stabilizing). The preset patterns include an example of each of the above.

The Rules:

  1. Any live cell with fewer than 2 live neighbors dies, as if by underpopulation
  2. Any live cell with 2 or 3 live neighbors lives on to the next generation
  3. Any live cell with more than 3 live neighbors dies, as if by overpopulation
  4. Any dead cell with exactly 3 live neighbors becomes a live cell, as if by reproduction
View Simulation