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.Any dead cell with three live neighbours becomes a live cell.Any live cell with two or three live neighbours survives.These rules, which compare the behavior of the automaton to real life, can be condensed into the following: Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.Any live cell with more than three live neighbours dies, as if by overpopulation.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).

Circle of life gif