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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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Journal ArticleDOI

Local causal states and discrete coherent structures.

TL;DR: In this article, the authors present a formal theory of coherent structures in fully discrete dynamical field theories, based on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting.
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Hierarchical Nonlinear Spatio-temporal Agent-Based Models for Collective Animal Movement

TL;DR: A general hierarchical framework for modeling collective movement behavior with multiple stages that allows for the discrete time prediction of animal locations in the presence of missing observations and develops an approximate Bayesian computation algorithm for estimation.
Book ChapterDOI

Overview: PCA Models and Issues

TL;DR: This book is an attempt to present a wide panorama of the current status of PCA theory and applications, which cover important issues and applications in probability, statistical mechanics, computer science, natural sciences, and dynamical systems.
DissertationDOI

Toward a Theory of Emergence: The Role of Social Influence in Emergent Self-Organisation

Omer Yezdani
TL;DR: This paper explored how complex organisations adapt through emergent self-organisation, with a focus on the role of social influence between agents, and argued that social influence is a principal mechanism for energetic transfer in complex human social systems.
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