Cellular Automata: Theory and Experiment

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MIT Press, 1991 - Science - 483 pages
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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 Resonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.
  

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Contents

Aperiodicity in onedimensional cellular automata
3
Cyclic cellular automata and related processes
19
Dimension spectra of linear cellular automata
36
A cellular automaton ruled by an eccentric conservation
49
Boolean derivatives on cellular automata
63
Transition phenomena in cellular automata rule space
77
Is there a sharp phase transition for deterministic cellular automata?
94
Theory
159
A comparison of spin exchange and cellular automaton models for diffusioncontrolled reactions
285
Reversible cellular automata and chemical turbulence
293
Soliton turbulence in onedimensional cellular automata
307
Knot invariants and cellular automata
328
Critical dynamics of onedimensional irreversible systems
345
Computation theoretic aspects of cellular automata
357
Reversibility of 2D cellular automata is undecidable
379
Classifying circular cellular automata
386

Experiment
188
Extracting cellular automaton rules directly from experimental data
189
Biology
205
Physics and chemistry
229
An informational process based on reversible universal cellular automata
254
Representations of geometrical and topological quantities in cellular automata
271
Relaxation properties of elementary reversible cellular automata
278
Formal languages and global cellular automaton behavior
396
A characterization of constanttime cellular automata computation
404
Constructive chaos by cellular automata and possible sources of an arrow of time
420
Attractor dominance patterns in sparsely connected Boolean nets
441
A brief review of cellular automata packages
463
Maps of recent cellular automata and lattice gas automata literature
477
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Teia Da Vida, a
Fritjof Capra
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