John Conway’s Game of Life

Description taken from Wikipedia, the free encyclopedia.

The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton. The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. A variant exists where two players compete. 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. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

Any live cell with fewer than two live neighbors dies, as if by loneliness.
Any live cell with more than three live neighbors dies, as if by overcrowding.
Any live cell with two or three live neighbors lives, unchanged, to the next generation.
Any dead cell with exactly three live neighbors comes to life.

The initial pattern constitutes the 'seed' of the system. The next generation is created by applying the above rules simultaneously to every cell in the seed - births and deaths happen simultaneously, and the discrete moment at which this happens is sometimes called a tick. (In other words, each generation is a pure function of the one before.) The rules continue to be applied repeatedly to create further generations.