(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 live cell with two or three live neighbours lives, unchanged, to the next generation.Any live cell with more than three live neighbours dies (referred to as overpopulation or overcrowding).
Any live cell with fewer than two live neighbours dies (referred to as underpopulation or exposure ).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 (at any given time) is in one of two possible states, "live" (alternatively "on") or "dead" (alternatively "off").
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