You should also note Andy Wuensche's work, ddlab, and his beautiful book "The Global Dynamics of Cellular Automata: An Atlas of Basin of Attraction Fields of One-Dimensional Cellular Automata" (forward by Christpher Langton). Free PDF download:
http://www.ddlab.org/gdca.html
Back Cover Text: The Global Dynamics of Cellular Automata introduces a powerful new perspective for the study of discrete dynamical systems. After first looking at the unique trajectory of a system's future, an algoritm is presented that directly computes the multiple merging trajectories of the systems past. A given cellular automaton will "crystallize" state space into a set of basins of attraction that typically have a topology of trees rooted on attractor cycles. Portraits of these objects are made accessible through computer generated graphics. The "Atlas" presents a complete class of such objects, and is inteded , with the accompanying software, as an aid to navigation into the vast reaches of rule behaviour space. The book will appeal to students and researchers interested in cellular automata, complex systems, computational theory, artificial life, neural networks, and aspects of genetics.
