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C. Rößler, A. Körner:
"A Different Kind of Modelling: Cellular Automata";
Talk: MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien; 2012-02-14 - 2012-02-17; in: "Preprints Mathmod 2012 Vienna - Full Paper Volume", F. Breitenecker, I. Troch (ed.); Argesim / Asim, 38 (2012), 402 - 403.

Introduction. In a simple case, a cellular automaton consists of a line of cells, each with value 0 or 1. These
values are updated in discrete time steps, according to a definite, fixed rule. Denoting the value of a cell at position
i by ai, a simple rule gives its new value as ^~ ai = f(ai􀀀1;ai;ai+1).
In general, the cells in a cellular automaton may have any finite number k of possible values. The rules for
updating these cells may depend on values up to any finite distance r away. In addition, the representation of
cellular automaton cells may be arranged not on a line, but on a regular lattice. Cellular automata have a number
of basic defining characteristics, see the table below.
Characteristic Signification
Discrete in space They consist of a discrete grid of spatial cells.
Discrete in time The value of each cell is updated in discrete time steps.
Discrete states Each cell has a finite number of possible values.
Homogeneous All cells are identical.
Synchronous updating All cell values are updated in synchrony, each depending on the previous values
of neighbouring cells.
Deterministic rule Each cell value is updated according to a fixed, deterministic rule.
Spatially local rule The rule at each cell depends only on the values of a local neighbourhood of
cells around it.
Temporally local rule The rule for the new value of a cell depends only on values for a fixed number
of preceding steps.
Table: Basic defining characteristics of cellular automata