Abstract
Inspired by the theory of continuous dynamical systems, Lyapunov exponents have been previously defined in the framework of cellular automata (CAs) in order to quantify a CA’s sensitive dependence on initial conditions, i.e. a CA’s sensitivity to a perturbation of an initial configuration. However, the application of these Lyapunov exponents is currently limited to two-state CAs, which limits their usefulness in the framework of CA-based models since these typically involve more than two states. This paper proposes an extension of the existing methodological framework to three-state CAs. Our method is illustrated for some interesting totalistic three-state rules, although it is generally applicable. Our proposed extension to the existing framework reveals some interesting features regarding CAs classified as class IV according to Wolfram’s classification.
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Vispoel, M., Daly, A.J., Baetens, J.M. (2022). Lyapunov Profiles of Three-State Totalistic Cellular Automata. In: Chopard, B., Bandini, S., Dennunzio, A., Arabi Haddad, M. (eds) Cellular Automata. ACRI 2022. Lecture Notes in Computer Science, vol 13402. Springer, Cham. https://doi.org/10.1007/978-3-031-14926-9_10
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