For example, philosopher and cognitive scientist Daniel Dennett has used the analogue of Conway's Life "universe" extensively to illustrate the possible evolution of complex philosophical constructs, such as consciousness and free will, from the relatively simple set of deterministic physical laws governing our own universe. The game can also serve as a didactic analogy, used to convey the somewhat counter-intuitive notion that "design" and "organization" can spontaneously emerge in the absence of a designer. Scholars in various fields, such as computer science, physics, biology, biochemistry, economics, mathematics, philosophy, and generative sciences have made use of the way that complex patterns can emerge from the implementation of the game's simple rules.
Life provides an example of emergence and self-organization. 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).Įver since its publication, Conway's Game of Life has attracted much interest, because of the surprising ways in which the patterns can evolve. The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata . From a theoretical point of view, it is interesting because it has the power of a universal Turing machine: that is, anything that can be computed algorithmically can be computed within Conway's 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 Game of Life emerged as Conway's successful attempt to drastically simplify von Neumann's ideas. OriginsĬonway was interested in a problem presented in the 1940s by mathematician John von Neumann, who attempted 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 rules continue to be applied repeatedly to create further generations. The first generation is created by applying the above rules simultaneously to every cell in the seed - births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick (in other words, each generation is a pure function of the preceding one). The initial pattern constitutes the seed of the system. 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 over-population.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 caused by under-population.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, alive or dead. One interacts with the Game of Life by creating an initial configuration and observing how it evolves or, for advanced players, by creating patterns with particular properties. The "game" is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. A screenshot of a puffer-type breeder (red) that leaves glider guns (green) in its wake, which in turn create gliders (blue).
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