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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Journal ArticleDOI
Novel SCAN-CA-based image security system using SCAN and 2-D von Neumann cellular automata
Rong-Jian Chen,Shi-Jinn Horng +1 more
TL;DR: Simulation results obtained using some color and gray-level images clearly demonstrate the strong performance of the proposed SCAN-CA-based image security system.
Journal ArticleDOI
Long-range effects in an elementary cellular automaton
TL;DR: Evidence is presented that one of the “elementary” one-dimensional cellular automata in the sense of Wolfram involves very complex long-range effects, similar to a critical phenomenon, in contrast to superficial evidence that would suggest that this rule leads to fairly simple behavior.
Journal ArticleDOI
Simulating chaotic behavior with finite-state machines
TL;DR: Although this result questions the validity of digital computer simulations of chaos, it is found that the statistical properties of the continuous equation, such as the invariant probability distribution and the Lyapunov exponent, are preserved in these cycles.
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Invariant Measures and Convergence Properties for Cellular Automaton 184 and Related Processes
TL;DR: In this article, the authors studied the long time limit properties of a deterministic dynamics that is common for a wide class of processes that have been studied so far during at least last two decades.
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From equilibrium spin models to probabilistic cellular automata
TL;DR: The general equivalence between D-dimensional probabilistic cellular automata and (D+1)-dimensional equilibrium spin models satisfying a "disorder condition" is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata as discussed by the authors.
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