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Excursions in Programming: A Simple Rule-Based Programming Approach to Modeling Complex Random Walk Systems with Cellular Automata

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

Mathematica in Education and Research
Year: 1995
Volume: 4
Issue: 2
Page range: 37-45

Many, apparently disparate, processes in nature can be modeled as random walks in which one or more objects move about in space, taking successive steps in randomly chosen directions. While a great deal of analytical (equational) work has been done on the properties of a lone random walker, the multiple random walker system is less well analyzed and exact analytical treatments soon become intractable when interactions between the walkers are introduced. Computer simulation provides an invaluable tool for studying these complex systems. We show here, in detail, how cellular automata and a rule-based programming approach can be used to model a system of interacting random walkers. In a sequel to this article, we will demonstrate the application of the approach using examples taken from the physical, materials and biological sciences.

*Applied Mathematics > Complex Systems
*Mathematics > Discrete Mathematics > Cellular Automata
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RandomWalkCA.nb (128.5 KB) - Mathematica Notebook

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