Revisão Bibliográfica: Autômatos Celulares

Referências em Papel:

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  Chopard B. (1993), Droz M., Study of the A+B to C reaction-diffusion process, International Journal of Modern Physics C, 4, 209-215
  

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  Dirac P.M. (1963), The Evolution of the Physicists, Scientific American, May 1963, p.45
  
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  Doolen G. (Ed.) (1991), Lattice Gas Methods for PDE's, Physica D 47
  
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  Heidelberg Kauffman S.A. (1984), Emergent Properties in Random Complex Automata, Physica 10D, 145-156
  
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  Langton C.G. (1984), Self-Reproduction in Cellular Automata, Physica 10D, 135-144
  
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  Vichiniac G.Y. (1984), Simulating Physics with Cellular Automata, Physica 10D, 96-116
  

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  http://www.wolfram.com/s.wolfram/articles/indices/ca.html: Collection of Papers from Stephen Wolfram
  
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  http://www.wolfram.com/s.wolfram: Stephen Wolframs Homepage
  

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  Cellular Automata and Complexity: Collected Papers
  

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  Cellular Automata: Proceedings of an Interdisciplinary Workshop (1984)
  

Published by Elsevier Science (1984)

ISBN 0-444-86850-X

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  Theory and Applications of Cellular Automata (1986)
  

Published by World Scientific (1986)

ISBN 9971-50-123-6 (hardcover/560 pages) (out of print)

ISBN 9971-50-124-4 (paperback/560 pages) (out of print)

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  Cellular Automata as Simple Self-Organizing Systems (1982)
  

Abstract: Cellular automata provide simple discrete deterministic mathematical models for physical, biological and computational systems. Despite their simple construction, cellular automata are shown to be capable of complicated behaviour, and to generate complex patterns with universal features. An outline of their statistical mechanics is given.

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  Statistical Mechanics of Cellular Automata (1983)
  

Abstract: Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ``elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states or generate self-similar patterns with fractal dimensions or . With ``random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.

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  Cellular Automata (1983)
  

Introduction: It appears that the basic laws of physics relevant to everyday phenomena are now known. Yet there are many everyday natural systems whose complex structure and behavior have so far defied even qualitative analysis. For example, the laws that govern the freezing of water and the conduction of heat have long been known, but analyzing their consequences for the intricate patterns of snowflake growth has not yet been possible. While many complex systems may be broken down into identical components, each obeying simple laws, the huge number of components that make up the whole system act together to yield very complex behavior.

In some cases this complex behavior may be simulated numerically with just a few components. But in most cases the simulation requires too many components, and this direct approach fails. One must instead attempt to distill the mathematical essence of the process by which complex behavior is generated. The hope in such an approach is to identify fundamental mathematical mechanisms that are common to many different natural systems. Such commonality would correspond to universal features in the behavior of very different complex natural systems.

To discover and analyze the mathematical basis for the generation of complexity, one must identify simple mathematical systems that capture the essence of the process. Cellular automata are a candidate class of such systems. This article surveys their nature and properties, concentrating on fundamental mathematical features. Cellular automata promise to provide mathematical models for a wide variety of complex phenomena, from turbulence in fluids to patterns in biological growth. The general features of their behavior discussed here should form a basis for future detailed studies of such specific systems.

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  Geometry of Binomial Coefficients (1984)
  

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  Algebraic Properties of Cellular Automata (1984)
  

Abstract: Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.

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  Universality and Complexity in Cellular Automata (1984)
  

Abstract: Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.

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  Preface to Cellular Automata (1984)
  

1. Introduction:

Differential equations form the mathematical basis for most current models of natural systems. Cellular automata may be considered as an alternative and in some respects complementary basis for mathematical models of nature. Whereas ordinary differential equations are suitable for systems with a small number of continuous degrees of freedom, evolving in a continuous manner, cellular automata describe the behaviour of systems with large numbers of discrete degrees of freedom.

In the simplest case, a cellular automaton consists of a line of sites, with each site having a value 0 or 1. The sequence of site values is the "configuration" of the cellular automaton. The cellular automaton evolves in discrete time steps. At each time step, the value of each site is updated according to a definite rule. The rule specifies the new value of a particular site in terms of its own old value, and the old values of sites in some neighbourhood around it. The neighbourhood is typically taken to include sites up to some small finite range from a particular site.

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  Computation Theory of Cellular Automata (1984)