Attractor vicinity decay for a cellular automaton.
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.
Crutchfield
James P.
JP
Center for Complex Systems Research, Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801(a)).
Hanson
James E.
JE