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Excursions in Programming: A Simple Rule-Based Programming Approach to Modeling Complex Random Walk Systems with Cellular Automata
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| Organization: | University of Illinois at Urbana-Champaign |
| Department: | Department of Material Science and Engineering |
| Organization: | Iwate University |
| Department: | Department of Electrical and Electronic Engineering |
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| Mathematica in Education and Research |
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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.
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| RandomWalkCA.nb (128.5 KB) - Mathematica Notebook |
Files specific to Mathematica 2.2 version:
| | RandomWalkCA.ma (89.6 KB) - Mathematica Notebook 2.2 or older |
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