title: Attractor vicinity decay for a cellular automaton.
abstract: The temporal decay of an attractor's vicinity for a domain-wall dominated cellular automaton (CA) is studied. Using selected initial pattern ensembles, state space structures in this high-dimensional nonlinear spatial system can be identified via the resulting decay to its attractors. Considered over a range of lattice sizes, the decay behavior falls into three main classes, each of which shows a characteristic profile. The first consists of even-size lattices showing a decelerating decay to small nonattracted ensemble fractions. The second class, also for even lattices, is a catastrophic decay to very small or vanishing nonattracted fractions. The third class also shows catastrophic decay and contains all odd-size lattices. Stochastic models are constructed that mimic the behavior of typical lattices throughout their evolution until finite-size effects appear. Weak additive noise causes all states on all lattices to fall into the attractor. In the end we find it overwhelmingly likely that the recently proposed attractor-basin portrait captures the CA's qualitative dynamics.
authors.affiliation: Center for Complex Systems Research, Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801(a)).
authors.forename: James P.
authors.initials: JP
authors.lastname: Crutchfield
authors.forename: James E.
authors.initials: JE
authors.lastname: Hanson