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
A discrete stochastic model for oil migration in chocolate-coated confectionery
Pieter Van der Weeën,Nathalie De Clercq,Jan M. Baetens,Claudia Delbaere,Koen Dewettinck,Bernard De Baets +5 more
TL;DR: A model based on a cellular automaton is proposed and parameterized using experimental data obtained from confectionery model systems and shown to be able to describe the oil migration in an adequate manner and can therefore be used to calculate an effective diffusion coefficient.
Journal ArticleDOI
Parallel path planning on the distributed array processor
Chang Shu,Hilary Buxton +1 more
TL;DR: An approach to the path planning problem is presented in which a distributed representation of the workspace is used, and related to it, parallel processing techniques are presented to search the world model based on a cellular automaton.
Journal ArticleDOI
Information transport in classical statistical systems
TL;DR: In this paper, the authors describe the propagation of information from the boundary to the bulk by classical wave functions, and show that the dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrodinger equation.
Posted Content
On Local Symmetries And Universality In Cellular Autmata
TL;DR: In this article, it was shown that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries and that the universality problem remains undecidable in some of those families.
Journal ArticleDOI
Block transformations of one-dimensional deterministic cellular automaton rules
Nino Boccara,Michel Roger +1 more
TL;DR: In this article, the evolution of a one-dimensional cellular automaton rule towards its limit set is discussed in terms of the annihilation of defects, which are often simply related to the defects characterizing the evolution according to rule f.
References
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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
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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