About the Book
The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices.Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole.Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.
Table of Contents:
Part 1 Mathematical analysis of cellular automata: aperiodicity in one-dimensional cellular automata, E. Jen; cyclic cellular automata and related processes, R. Fisch; nearest neighbour cellular automata over Z2 with periodic boundary conditions, B. Voorhees; cellular automaton ruled by an eccentric conservation law, A.M. Barbe; Boolean derivatives on cellular automata, G. Vichniac. Part 2 Structure of the space of cellular automata: transition phenomena in cellular automata: transition phenomena in cellular automata rule space, W. Li, et al; is there a sharp phase transition for deterministic cellular automata?, W.W. Wootters and C.G. Langton; Wolfram's class IV automata and a good life, H.V. McIntosh; criticality in cellular automata, H. Chate and P. Manneville; a hierarchical classification of cellular automata, H.A. Gutowitz. Part 3 Learning rules with specified properties: adaptive stochastic cellular automata - theory, Y.C. Lee, et al; adaptive stochastic cellular automata - experiment, S. Qian, et al; extracting cellular automaton rules directly from experimental data, F.C. Richards, et al. Part 4 Cellular automata and the natural sciences - biology: what can automaton theory tell us about the brain?, J.D. Victor; simulation of HIV-infection in artificial immune systems, H. Sieburg, et al; physics and chemistry - invertible cellular automata - a review, T. Toffoli and N. Margolus; digital mechanics - an informational process based on reversible universal cellular automata, E. Fredkin; representations of geometrical and topological quantities in cellular automata, M.A. Smith; relaxation properties of elementary reversible cellular automata, S. Takesue; a comparison of spin exchange and cellular automaton models for diffusion-controlled reactions, A. Canning and M. Droz; reversible cellular automata and chemical turbulence, H. Hartman and P. Tamayo; soliton turbulence in one-dimensional cellular automata, Y. Aizawa, et al; knot invariants and cellular automata, B. Hasslacher and D.A. Meyer; critical dynamics of one-dimensional irreversible systems, O. Martin. Part 5 comutation theory of cellular automata, computation theoretic aspects of cellular automata, K. Culik II; reversibility of 2D cellular automata is undecidable, J. Kari; classifying circular cellular automata, K. Sutner; formal languages and global cellular automaton behaviour, K. Culik II; a characterization of constant-time cellular automata computation, S. Kim and R. McCloskey; constructive chaos by cellular automata and possible sources of an arrow to time, K. Svozil. Part 6 Generalizations of cellular automata: cellular automata and discrete neural networks, M. Garzon; attractor dominance patterns in sparsely connected Boolean nets, C.C. Walker; periodic orbits and log transients in coupled map lattices, R. Livi. Appendices: a brief review of cellular automata packages, D. Hiebeler; maps of recent cellular automata and lattice gas automata literature, H.A. Gutowitz.
About the Author :
Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.
