Analytical formulation of cellular automata rules using data models
Holger M. Jaenisch, James W. Handley · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
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 nth order derivative and integral. All of the demonstrated analytical forms of the CA rule are general and applicable to real-time use.