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A cellular automaton (CA) is a specifically shaped group of colored grid cells known for evolving through multiple and discrete time steps according to a rule set depending on neighboring cell states. These steps are repeated multiple times in an iterative manner.
During the 1940s, the CA concept was initiated by John von Neumann and Stanislaw Ulam while working at the Los Alamos National Laboratory in North Central New Mexico. It is the simplest model of spatially distributed systems. A well-known CA is The Game of Life, which was invented in the 1960s by mathematician John Conway.
A CA consists of a regular cell grid, each in a finite number of states that are generally ON and OFF. The grid has any number of dimensions. All neighboring cells are defined relative to a specified cell, and all cells look into neighboring cells. With this information, each cell applies simple rules to determine which state must be changed.
A CA's fundamental property is based on the grid on which it is computed. The simplest grid is a one-dimensional line. Square, triangular and hexagonal grids are common in two dimensions that are arbitrarily constructed in a number of dimensions via a Cartesian grid.
The basic type of CA is a binary nearest neighbor, which is a one-dimensional automaton known as the elementary CA. There are 256 such cellular automata, all indexed by a unique binary number with a decimal representation known as the rule for a particular automaton. These 256 CAs are known as Wolfram code.
Another CA form is one-dimensional and totalistic, where evolution is determined by adjacent cell averages. The simplest examples contain colors.
In a reversible CA, for every current CA configuration, there exists exactly one pre-image. A continuous automaton uses continuous functions, and its states are also continuous, where the state of location are finite real numbers.