Cellular Automata: Theory and Experiment

This work analyzes the structure of the space of cellular automata and the natural sciences - biology: what can automaton theory tell us about the brain?

Abstract

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.