Abstract
In the preceding section we introduced a classification of cellular automata based on attractors, their number and structure. In the present section we focus on the complexity of the dynamics. The two aspects are not independent, but differ slightly. We start with Devaney’s definition of chaos, and relate this definition to the Hurley classification. Thereafter we investigate a class of cellular automata that induce chaotic dynamics: permutive cellular automata. In the last part of this section we focus on one special property of chaotic dynamics: sensitive dependency on initial conditions. It is possible to recognize complex dynamics by inspecting the fate of two neighboring points.
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Hadeler, KP., Müller, J. (2017). Chaos and Lyapunov Stability. In: Cellular Automata: Analysis and Applications. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-53043-7_6
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DOI: https://doi.org/10.1007/978-3-319-53043-7_6
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