title: A full computation-relevant topological dynamics classification of elementary cellular automata.
abstract: Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos."
authors.affiliation: Institute of Neuroinformatics, ETH and University of Zurich, 8057 Zurich, Switzerland. schuelem@ini.phys.ethz.ch
authors.forename: Martin
authors.initials: M
authors.lastname: Schüle
authors.forename: Ruedi
authors.initials: R
authors.lastname: Stoop
mesh_terms: D002477:Cells; D008962:Models, Theoretical; D017711:Nonlinear Dynamics