It made its first public appearance in the October 1970 issue of Scientific American, in Martin Gardner's " Mathematical Games" column. By coupling his previous success with Leech's problem in group theory with his interest in von Neumann's ideas concerning self-replicating machines, Conway devised the Game of Life. Conway tried to simplify von Neumann's ideas and eventually succeeded. (In other words, each generation is a pure function of the one before.) The rules continue to be applied repeatedly to create further generations.Ĭonway was interested in a problem presented in the 1940s by renowned mathematician John von Neumann, who tried to find a hypothetical machine that could build copies of itself and succeeded when he found a mathematical model for such a machine with very complicated rules on a rectangular grid.
The first 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. The initial pattern constitutes the 'seed' of the system. Any dead cell with exactly three live neighbours comes to life.Any live cell with two or three live neighbours lives, unchanged, to the next generation.Any live cell with more than three live neighbours dies, as if by overcrowding.Any live cell with fewer than two live neighbours dies, as if by loneliness.At each step in time, the following transitions occur: Every cell interacts with its eight neighbours, which are the cells that are directly 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. A variant exists where two players compete. One interacts with the Game of Life by creating an initial configuration and observing how it evolves.
The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players. It is the best-known example of a cellular automaton. The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970.
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