Journal ArticleDOI
Statistical mechanics of cellular automata
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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.read more
Citations
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Upper bound on the products of particle interactions in cellular automata
TL;DR: A rigorous upper bound is established on the number of distinct products that these interactions can generate in one-dimensional cellular automata, controlled by the structural complexity of the interacting particles.
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Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow
TL;DR: In this paper, the authors analyzed the Newell-Whitham-type car-following model described by a differential-difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the heading of the immediately preceding one.
Journal ArticleDOI
Weak models of distributed computing, with connections to modal logic
Lauri Hella,Matti Järvisalo,Antti Kuusisto,Juhana Laurinharju,Tuomo Lempiäinen,Kerkko Luosto,Jukka Suomela,Jonni Virtema +7 more
TL;DR: The linear order identified in this work has direct implications in the study of the expressibility of modal logic, and is shown that the constant-time variants of these classes can be characterised by a corresponding modal Logic.
Journal ArticleDOI
Wolfram's class IV automata and good life
TL;DR: A comprehensive discussion of Wolfram's four classes of cellular automata is given, with the intention of relating them to Conway's criteria for a good game of Life.
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.
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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.
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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.
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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”.
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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