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Journal ArticleDOI

Statistical mechanics of cellular automata

Stephen Wolfram
- 01 Jul 1983 - 
- Vol. 55, Iss: 3, pp 601-644
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TLDR
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 p definite rules involving the values of its nearest neighbors.
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 \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 1.69. 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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Citations
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Proceedings ArticleDOI

Cellular Automata Synthesis Based On Precomputed Test Vectors For Built-in Self-test

TL;DR: A new deterministic BIST approach to generate a set of test vectors is proposed, based on a cellular automata structures, which is very efJicient in terms of hardware size and speed performance while being very regular and easy to test.
Posted Content

Control instabilities and incite slow-slip in generalized Burridge-Knopoff models

TL;DR: A theory for preventing GBK avalanches, control its dynamics and incite slow-slip is proposed and the mathematical Theory of Control is used, for the first time, in stabilizing and restricting chaos in GBK models and guaranteeing slow frictional dissipation.
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Generative complexity of Gray–Scott model

TL;DR: It is shown that the Gray–Scott systems expressing highest levels of the complexity are composed of the wave-fragments and travelling localisations and quasi-dissipative solitons and gliders in Conway’s Game of Life.
Book ChapterDOI

Complexity and forecasting in dynamical systems

TL;DR: In this article, the authors discuss ways of defining complexity in physics and in particular for symbol sequences typically arising in autonomous dynamical systems, and consider the difficulty of making optimal forecasts as one (but not the only) suitable measure.
Journal ArticleDOI

Utility, Revealed Preferences Theory, and Strategic Ambiguity in Iterated Games

Michael Harre
- 29 Apr 2017 - 
TL;DR: By explicitly expanding out the mutual information between past states and the next action the authors show under what circumstances the explicit values of the utility are irrelevant for iterated games and this is then related to revealed preferences theory of classical economics.
References
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Book

Introduction to Automata Theory, Languages, and Computation

TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Journal ArticleDOI

The Chemical Basis of Morphogenesis

TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Journal ArticleDOI

On Computable Numbers, with an Application to the Entscheidungsproblem

TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
Journal ArticleDOI

Metabolic stability and epigenesis in randomly constructed genetic nets

TL;DR: The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”.
Journal ArticleDOI

Diffusion-limited aggregation, a kinetic critical phenomenon

Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth