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
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The quantum coin toss-testing microphysical undecidability
TL;DR: It is suggested to test microphysical undecidability by physical processes with low extrinsic complexity, such as polarized laser light, to ensure that this sequence can be safely applied for all purposes requiring stochasticity and high complexity.
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Predicting nonlinear cellular automata quickly by decomposing them into linear ones
TL;DR: It is shown that a wide variety of nonlinear cellular automata (CAs) can be decomposed into a quasidirect product of linear ones, and that CAs based on nilpotent groups can be predicted in depth O(log t) or O(1) by circuits with binary or “sum mod p” gates, respectively.
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Complexity Science, Complex Systems, and Land-Use Research
TL;DR: This issue had its genesis in multiple sessions on `Geographical Perspectives on Complexity Theory and Complex Systems'' held at annual meetings of the Association of American Geographers in Los Angeles and New Orleans and arose as a theme issue of spatially oriented, complexity-based research.
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Atmospheric dispersion modeling using Artificial Neural Network based cellular automata
TL;DR: Cellular Automata coupled with an Artificial Neural Network (CA-ANN) are developed here to calculate the atmospheric dispersion of methane (CH4) in 2D to reduce computation time while keeping accuracy.
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