## Description

This article is from the Nonlinear Science FAQ, by James D. Meiss jdm@boulder.colorado.edu with numerous contributions by
others.

# 3.16] What are cellular automata? (nonlinear science)

(Thanks to Pavel Pokorny for Contributions to this answer)

A Cellular automaton (CA) is a dynamical system with discrete time (like

a map, see [2.6]), discrete state space and discrete geometrical space (like

an ODE), see [2.7]). Thus they can be represented by a state s(i,j) for

spatial state i, at time j, where s is taken from some finite set. The update

rule is that the new state is some function of the old states, s(i,j+1) =

f(s). The following table shows the distinctions between PDE's, ODE's, coupled

map lattices (CML) and CA in taking time, state space or geometrical space

either continuous (C) of discrete (D):

time state space geometrical space
PDE C C C
ODE C C D
CML D C D
CA D D D

Perhaps the most famous CA is Conway's game "life." This CA evolves

according to a deterministic rule which gives the state of a site in the next

generation as a function of the states of neighboring sites in the present

generation. This rule is applied to all sites.

For further reading see

S. Wolfram (1986) Theory and Application of Cellular Automata, World

Scientific Singapore.

Physica 10D (1984)--the entire volume

Some programs that do CA, as well as more generally "artificial life" are

available at

http://www.alife.org/links.html

http://www.kasprzyk.demon.co.uk/www/ALHome.html

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