Qualitative and quantitative cellular automata from differential equations

Authors:
Philippe Narbel
Affiliations:
LaBRI, University of Bordeaux 1, France
Venue:
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
Year:
2006

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Abstract

We give a synthetic and formalized account of relationships between cellular automata (CA) and differential equations (DE): Numerical schemes and phase portraits analysis (via cell-to-cell mappings) can be translated into CA, and compositions of differential operators and phase portraits induce CA compositions Based on DE, CA can be tuned according to discretization parameters so that faithful CA sequences can be built describing qualitative as well as quantitative solutions.