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3.16] What are cellular automata? (nonlinear science)




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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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