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, which was based on personal conversations with Conway. Conway later wrote that the basic motivation for Life was to create a "universal" cellular automaton. Moreover, some "simple initial patterns" should "grow and change for a considerable period of time" before settling into a static configuration or a repeating loop. According to Martin Gardner, Conway experimented with different rules, aiming for rules that would allow for patterns to "apparently" grow without limit, while keeping it difficult to prove that any given pattern would do so. Conway's initial goal was to define an interesting and unpredictable cellular 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. This design is known as the tessellation model, and is called a von Neumann universal constructor. Von Neumann gave an existence proof that a particular pattern would make endless copies of itself within the given cellular universe by designing a 200,000 cell configuration that could do so. The result was a universal copier and constructor working within a cellular automaton with a small neighborhood (only those cells that touch are neighbors for von Neumann's cellular automata, only orthogonal cells), and with 29 states per cell.
Like Ulam's lattice network, von Neumann's cellular automata are two-dimensional, with his self-replicator implemented algorithmically. : 8 Thus was born the first system of cellular automata. The driving concept of the method was to consider a liquid as a group of discrete units and calculate the motion of each based on its neighbors' behaviors. : 3 : xxix Ulam and von Neumann created a method for calculating liquid motion in the late 1950s. : 1 Ulam was the one who suggested using a discrete system for creating a reductionist model of self-replication. Neumann wrote a paper entitled "The general and logical theory of automata" for the Hixon Symposium in 1948. As he developed this design, von Neumann came to realize the great difficulty of building a self-replicating robot, and of the great cost in providing the robot with a "sea of parts" from which to build its replicant. This design is known as the kinematic model. : 1 Von Neumann's initial design was founded upon the notion of one robot building another robot. At the same time, John von Neumann, Ulam's colleague at Los Alamos, was working on the problem of self-replicating systems. Stanislaw Ulam, while working at the Los Alamos National Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. 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:
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