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Cellular automata are both computational and dynamical systems. We give acomplete classification of the dynamic behaviour of elementary cellularautomata (ECA) in terms of fundamental dynamic system notions such assensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but notchaotic and not eventually weakly periodic. Based on this classification, weconjecture that elementary cellular automata capable of carrying out complexcomputations, such as needed for Turing-universality, are at the "edge ofchaos".

A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata