GENERALIZED SUB-SHIFTS IN ELEMENTARY CELLULAR-AUTOMATA - THE STRANGE CASE OF CHAOTIC RULE-180

We study the dynamical behavior of elementary cellular automaton 180. This rule gives rise to a global dynamics on the phase space of all on e-dimensional bi-infinite configurations which is Devaney topologicall y chaotic. The dense sub-dynamical system of configurations in backgro und of 0s is a generalized sub-shift, i.e., multiple sub-shift whose m ultiplicity constant depends on the initial configuration. This sub-dy namical system is deeply ''stable'' in the sense that the null configu ration is a global attractor, but with some components of the chaotic behaviour (transitivity and unpredictability). The dense sub-dynamical system of configurations in background of Is is a fractal-like system , with strongly chaotic components (expansivity). (C) 1998 - Elsevier Science B.V. All rights reserved.