Any live cell with two or three live neighbours lives on to the next generation.Any live cell with fewer than two live neighbours dies, as if by underpopulation.At each step in time, the following transitions occur: Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. 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). It is Turing complete and can simulate a universal constructor or any other Turing machine. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input.

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. A screenshot of a puffer-type breeder (red) that leaves glider guns (green) in its wake, which in turn create gliders (blue) ( animation)

For cycle mathematica