Towards generalized measures grasping CA dynamics

Authors:
Jan M. Baetens;Bernard De Baets
Affiliations:
KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium;KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium
Venue:
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Year:
2010

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Abstract

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA.