Basic Concepts of Cellular Automata

This chapter reviews some basic concepts and results of the theory of cellular automata (CA). Topics discussed include classical results from the 1960s, relations between various concepts of injectivity and surjectivity, and dynamical system concepts related to chaos in CA. Most results are reported without full proofs but sometimes examples are provided that illustrate the idea of a proof. The classical results discussed include the Garden-of-Eden theorem and the Curtis– Hedlund–Lyndon theorem, as well as the balance property of surjective CA. Different variants of sensitivity to initial conditions and mixing properties are introduced and related to each other. Also, algorithmic aspects and undecidability results are mentioned.

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