Since its publication, the Game of Life has attracted much interest because of the surprising ways in which the patterns can evolve. Gardner wrote, "Because of Life's analogies with the rise, fall and alterations of a society of living organisms, it belongs to a growing class of what are called 'simulation games' (games that resemble real-life processes)." Theoretically, the Game of Life has the power of a universal Turing machine: anything that can be computed algorithmically can be computed within the Game of Life. The game made its first public appearance in the October 1970 issue of Scientific American, in Martin Gardner's " Mathematical Games" column. The rules should be as simple as possible, whilst adhering to the above constraints.There should be potential for von Neumann universal constructors.There should exist small initial patterns with chaotic, unpredictable outcomes.While the definitions before the Game of Life were proof-oriented, Conway's construction aimed at simplicity without a priori providing proof the automaton was alive.Ĭonway chose his rules carefully, after considerable experimentation, to meet these criteria: It was a significant challenge and an open problem for years before experts on cellular automata managed to prove that, indeed, the Game of Life admitted of a configuration which was alive in the sense of satisfying von Neumann's two general requirements. For example, he wanted some configurations to last for a long time before dying and other configurations to go on forever without allowing cycles. Conway's initial goal was to define an interesting and unpredictable cell automaton. Motivated by questions in mathematical logic and in part by work on simulation games by Ulam, among others, John Conway began doing experiments in 1968 with a variety of different two-dimensional cellular automaton rules. Over time, simpler life constructions were provided by other researchers, and published in papers and books. His construction was complicated because it tried to simulate his own engineering design. Although successful, he was busy with other projects and left some details unfinished. In parallel, von Neumann attempted to construct Ulam's cellular automaton. Ulam discussed using computers to simulate his cellular automata in a two-dimensional lattice in several papers. Stanislaw Ulam invented cellular automata, which were intended to simulate von Neumann's theoretical electromagnetic constructions. This turned out not to be realistic with the technology available at the time. Von Neumann was thinking about an engineering solution which would use electromagnetic components floating randomly in liquid or gas.
In late 1940, John von Neumann defined life as a creation (as a being or organism) which can reproduce itself and simulate a Turing machine. The rules continue to be applied repeatedly to create further generations. Each generation is a pure function of the preceding one. The first generation is created by applying the above rules simultaneously to every cell in the seed, live or dead births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick. The initial pattern constitutes the seed of the system. Similarly, all other dead cells stay dead. All other live cells die in the next generation.