Classsification of Cellular Automata

Glossary Cellular Automaton For our purposes, a (one-dimensional) cellular automaton (CA) is given by a local map ρ : Σ → Σ where Σ is the underlying alphabet of the automaton and w is its width. As a data structure, suitable as input to a decision algorithm, a CA can thus be specified by a simple lookup table. We abuse notation and write ρ(x) for the result of applying the global map of the CA to configuration x ∈ ΣZ. Wolfram Classes Wolfram proposed a heuristic classification of cellular automata based on observations of typical behaviors. The classification comprises four classes: evolution leads to trivial configurations, to periodic configurations, evolution is chaotic, evolution leads to complicated, persistent structures. Undecidability