## Cellular Automata: Theory and ExperimentCellular 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 |

### Common terms and phrases

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