Analytical formulation of cellular automata rules using data models

Holger M. Jaenisch; James W. Handley

doi:10.1117/12.834141

29 April 2009 Analytical formulation of cellular automata rules using data models

Holger M. Jaenisch, James W. Handley

Proceedings Volume 7347, Evolutionary and Bio-Inspired Computation: Theory and Applications III; 734715 (2009) https://doi.org/10.1117/12.834141
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

We present a unique method for converting traditional cellular automata (CA) rules into analytical function form. CA rules have been successfully used for morphological image processing and volumetric shape recognition and classification. Further, the use of CA rules as analog models to the physical and biological sciences can be significantly extended if analytical (as opposed to discrete) models could be formulated. We show that such transformations are possible. We use as our example John Horton Conway's famous "Game of Life" rule set. We show that using Data Modeling, we are able to derive both polynomial and bi-spectrum models of the IF-THEN rules that yield equivalent results. Further, we demonstrate that the "Game of Life" rule set can be modeled using the multi-fluxion, yielding a closed form n^th order derivative and integral. All of the demonstrated analytical forms of the CA rule are general and applicable to real-time use.

Citation Download Citation

Holger M. Jaenisch and James W. Handley "Analytical formulation of cellular automata rules using data models", Proc. SPIE 7347, Evolutionary and Bio-Inspired Computation: Theory and Applications III, 734715 (29 April 2009); https://doi.org/10.1117/12.834141

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