A Comprehensive Taxonomy of Cellular Automata
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and abundant computational power, the current lack of a com...
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Zusammenfassung: | Cellular automata (CAs) are fully-discrete dynamical models that have
received much attention due to the fact that their relatively simple setup can
nonetheless express highly complex phenomena. Despite the model's theoretical
maturity and abundant computational power, the current lack of a complete
survey on the 'taxonomy' of various families of CAs impedes efficient and
interdisciplinary progress. This review paper mitigates that deficiency; it
provides a methodical overview of five important CA 'families': asynchronous,
stochastic, multi-state, extended-neighbourhood, and non-uniform CAs. These
five CA families are subsequently presented from four angles. First, a rigorous
mathematical definition is given. Second, we map prominent variations within
each CA family, as such highlighting mathematical equivalences with types from
other families. Third, we discuss the genotype and phenotype of these CA types
by means of mathematical tools, indicating when established tools break down.
Fourth, we conclude each section with a brief overview of applications related
to information theory and mathematical modelling. |
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DOI: | 10.48550/arxiv.2401.08408 |