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
Integration of multicriteria evaluation and cellular automata methods for landslide simulation modelling
TL;DR: In this article, the authors developed a novel approach that couples geographic information systems (GIS), multicriteria evaluation (MCE) and cellular automata (CA) to simulate shallow landslide flows occurring in urban areas.
Book ChapterDOI
Unpredictability and Computational Irreducibility
Hervé Zwirn,Jean-Paul Delahaye +1 more
TL;DR: It is proved that, through a robust definition of what means “to be unable to compute the n th step without having to follow the same path than simulating the automaton”, this implies genuinely that if the behavior of an object is computationally irreducible, no computation of its n th state can be faster than the simulation itself.
Journal ArticleDOI
Discretionary lane-changing behavior: empirical validation for one realistic rule-based model
TL;DR: It is found that the classical lane-changing rules of rule-based model cannot explain many cases in the empirical dataset, so one new decision rule is proposed, comparing the position after a time horizon of several seconds without a lane-change.
Small universal Turing machines
TL;DR: It is shown that the problem of predicting t steps of the 1D cellular automaton Rule 110 is P-complete and the small weakly universal Turing machines of Rogozhin, Minsky and others run in polynomial time, an exponential improvement on their previously known simulation time overhead.
Journal ArticleDOI
Random packing of digitized particles
TL;DR: In this paper, the random packing of digitized particles is studied using the packing routines available in the cellular automata hydration model by D.P. Lubachevsky and F.H. Stillinger.
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