Classification of Elementary Cellular Automata Based on Their Limit Cycle Lengths in Z/k
Hans-Peter Stricker
Berlin, Germany
Abstract
In this paper we introduce a classification of elementary cellular automata based solely on numerical properties of the lengths of their limit cycles on finite lattices Z/k. The classification has a formal definition, and it could in principle be proved whether a given cellular automaton belongs to a given class. It will remain open if this is generally possible, that is, if the question is decidable.
Keywords: cellular automata; limit sets; limit cycles; cycle length spectra; decidability problems; classification
Cite this publication as:
H.-P. Stricker, “Classification of Elementary Cellular Automata Based on Their Limit Cycle Lengths in Z/k,” Complex Systems, 32(3), 2023 pp. 229–251.
https://doi.org/10.25088/ComplexSystems.32.3.229
