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A '''cellular automaton''' (pl. cellular automata, abbrev. CA) is a [[Discrete mathematics|discrete]] model studied in [[computability theory]], [[mathematics]], [[physics]], complexity science, theoretical biology and microstructure modeling. 

== Description ==

Cellular automata are also called:

* Cellular spaces
* Tessellation automata
* Homogeneous structures
* Cellular structures
* Tessellation structures
* Iterative arrays

A cellular automaton consists of a regular grid of cells, each in one of a finite number of [[State (computer science)|states]], such as on and off (in contrast to a coupled map lattice). 

The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. 

An initial state (time t = 0) is selected by assigning a state for each cell. 

A new generation is created (advancing t by 1), according to some fixed rule (generally, a [[Function (mathematics)|mathematical function]]) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. 

Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the [[stochastic cellular automaton]] and [[asynchronous cellular automaton]].

== See also ==

* [[Automata theory]]
* [[Bidirectional traffic]]
* [[Cantor space]]
* [[Cellular automata in popular culture]]
* [[Computability theory]]
* [[Conway's Game of Life]]
* [[Cyclic cellular automaton]]
* [[Discrete mathematics]]
* [[Elementary cellular automaton]]
* [[Excitable medium]]
* [[Mirek's Cellebration]]
* [[Movable cellular automaton]]
* [[Procedural generation]]
* [[Quantum cellular automata]]
* [[Reversible cellular automaton]]
* [[Second-order cellular automaton]]
* [[Spatial decision support system]]
* [[Turmites]]

=== Specific rules ===

* [[Brian's Brain]]
* [[Langton's ant]]
* [[Wireworld]]
* [[Rule 30]]
* [[Rule 90]]
* [[Rule 184]]
* [[von Neumann cellular automata]]
* [[Nobili cellular automata]]
* [[Codd's cellular automaton]]
* [[Langton's loops]]
* [[CoDi]]

=== Problems solved ===

Problems that can be solved with cellular automata include:

* [[Firing squad synchronization problem]]
* [[Majority problem]]

== External links ==

* [http://en.wikipedia.org/wiki/Cellular_automaton Cellular automaton] @ Wikipedia
* [http://mathworld.wolfram.com/ElementaryCellularAutomaton.html Elementary cellular automata] @ mathworld.wolfram.com

=== Software ===

* [https://github.com/gollygang/ready Ready] - "Ready is a program for exploring continuous and discrete cellular automata, including reaction-diffusion systems, on grids and arbitrary meshes."

[[Category:Cellular automata]]
[[Category:Computation]]
[[Category:Computer science]]
[[Category:Digital art]]
[[Category:Mathematics]]
[[Category:Visual arts]]