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Simulating Experiences: Excursions in Programming. Modelling Nature with Cellular Automata, Part 1: One-Dimensional CAs

Richard J. Gaylord
Organization: University of Illinois at Urbana-Champaign
Department: Department of Material Science and Engineering
Journal / Anthology

Mathematica in Education
Year: 1993
Volume: 2
Issue: 3
Page range: 21-26

A cellular automaton (CA) is a discrete dynamic system of lattice sites that evolve in discrete time steps as each site assumes a value from a finite set of values. The value is determined by applying local and uniform rules to the values of a neighborhood of sites around the site. Stephen Wolfram has expressed the view that “any physical process can be described by an algorithm and therefore can be represented by a computational process” and that "cellular automata can be regarded as computers and as models of physical systems” [Wolfram, 1984]. One cellular automaton which was discussed earlier [Gaylord, 1992], is the sandpile model which has been used to describe self-organized criticality (SOC) and catastrophes in complex systems. Now I want to take a look at the two most famous cellular automata. In Part I, I'll discuss one-dimensional cellular automata. In Part II, I'll turn to the two-dimensional cellular automaton known as the “Game of Life”

*Mathematics > Discrete Mathematics > Cellular Automata
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OneDimensionalCA.nb (470.8 KB) - Mathematica Notebook

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