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A '''cellular automaton''' is a 4-tuple <math> \{ Z, S, N, f\} </math>, where:
[[Image:2dCCA-n16.png|right|thumb|A two-dimensional cyclic cellular automaton with 16 states, on a 300×300 torus, after 400 steps starting from a random initial configuration. At this stage in the automaton's evolution, three different types of pattern can be seen: random fields similar to the starting configuration, large blocks of color, and spirals. Eventually the spirals will take over the entire field.]]
A '''cellular automaton''' is a 4-tuple <math> \left ( Z, S, N, f\right ) </math>, where:
* <math>Z</math> is a [[lattice]].
* <math>Z</math> is a [[lattice]].
* <math>S</math> is a finite set of cell ''states'' or ''values''.
* <math>S</math> is a finite set of cell ''states'' or ''values''.
* <math>I</math> is the finite ''neighborhood''.
* <math>I</math> is the finite ''neighborhood''.
* <math>f</math> is the ''local transition function''.
* <math>f</math> is the ''transition function''.
The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the local transition function with respect to the discrete time variable.
The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the transition function with respect to the discrete time variable.
[[Image:Rule 184.png|left|thumb|The Rule 184 cellular automaton, run for 128 steps each from three random initial confgurations with density 25%, 50%, and 75%.]]
Lattice-Gas Cellular Automatons can be used to model physical systems such as fluid and biological systems. ''Mathematica'' uses a cellular automatons as a random number generator.
[[category:mathematics]]
==Further reading==
[[category:computer science]]
:[http://www.stephenwolfram.com/publications/articles/ca/86-fluids/index.html Cellular Automaton Fluids: Basic Theory], Stephen Wolfram, 1986.
:[http://www.stephenwolfram.com/publications/articles/ca/86-random/index.html Random Sequence Generation by Cellular Automata], Stephen Wolfram, 1986.
:[http://www.stephenwolfram.com/publications/articles/ca/85-thermodynamics/index.html Thermodynamics and Hydrodynamics of Cellular Automata], Stephen Wolfram, 1985.
:[http://www.stephenwolfram.com/publications/articles/ca/85-cryptography/index.html Cryptography with Cellular Automata], Stephen Wolfram, 1986.
[[Category:Mathematics]]
[[Category:Computer Science]]