Abstract
This chapter reviews some fundamental concepts and outcomes of the idea of cellular automata (CA). Topics discussed include classical is a result of the 1960s, relations between various concepts of injectivity and surjectivity, and dynamical system concepts associated with chaos in CA. Most answers are reported without full proofs but may examples are supplied that illustrate the thought of an evidence. The classical results discussed range from the Garden-of-Eden theorem and also the Curtis–Hedlund–Lyndon theorem, along with the balance property of surjective CA. Different variants of sensitivity to initial conditions and mixing qualities are introduced and associated with one another. Also, algorithmic aspects and undecidability answers are pointed out.
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