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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Scale-invariant cellular automata and self-similar Petri nets
Martin Schaller,Karl Svozil +1 more
TL;DR: In this paper, two computing models based on an infinite tessellation of space-time are introduced, one is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets.
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2D Cellular Automata with an Image Processing Application
TL;DR: Theoretical aspects of two-dimensional linear cellular automata with image applications with respect to uniform periodic and adiabatic boundary cellular Automata conditions are investigated.
Journal ArticleDOI
Classifying elementary cellular automata using compressibility, diversity and sensitivity measures
TL;DR: This work attempts to uncover correlations between the following measures of ECA behavior: compressibility, sensitivity, sensitivity and diversity, and uncovers and characterize novel groupings of rules.
Journal ArticleDOI
Cellular automaton for bacterial towers
TL;DR: A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis.
Journal ArticleDOI
Reversible boolean networks II. Phase transitions, oscillations, and local structures
TL;DR: In this paper, the authors investigated the behavior of the Hamming distance and the distribution of orbit lengths as N and K are varied, and showed that the observed oscillation phenomena can be largely understood in terms of these local structures.
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