Evaluating the Quality of Local Structure Approximation Using Elementary Rule 14

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10875)

Abstract

Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensional approximations have been proposed. The most commonly used one is known as the local structure theory, developed by H. Gutowitz et al. in 1987. In spite of the popularity of this approximation in CA research, examples of rigorous evaluations of its accuracy are lacking. In an attempt to fill this gap, we construct a local structure approximation for rule 14, and study its dynamics in a rigorous fashion, without relying on numerical experiments. We then compare the outcome with known exact results.

Keywords

Rule 14 Local structure approximation Invariant manifolds 

Notes

Acknowledgement

H.F. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of Discovery Grant.

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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBrock UniversitySt. CatharinesCanada

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