Journal ArticleDOI
Statistical mechanics of cellular automata
TLDR
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
Control of cellular automata
TL;DR: This work studies the problem of master-slave synchronization and control of totalistic cellular automata and presents three control strategies that exploit local information in order to choose the sites to be synchronized.
Journal ArticleDOI
Transient behavior of cellular automaton rule 110
Wentian Li,Mats G. Nordahl +1 more
TL;DR: The simulations show that the average transient time Tave increases algebraically with system size N, Tave∼Nα, with α≈1.08, and that the density of propagating objects (gliders) decays with time as ngl∼-γ with γ≈0.64.
Journal ArticleDOI
Systematics of transitions of square-lattice cellular automata
S.S. Manna,D. Stauffer +1 more
TL;DR: In this paper, the initial concentration in the computer simulation of all 65536 square-lattice cellular automata was varied and the phase transition was investigated systematically, including the phase transitions.
Journal ArticleDOI
Two extensions of exact nonequilibrium steady states of a boundary-driven cellular automaton
Atsuo Inoue,Shinji Takesue +1 more
Journal ArticleDOI
Simulation of flow through a two-dimensional random porous medium
U. Brosa,D. Stauffer +1 more
TL;DR: In this paper, the cellular automata approximation of two-dimensional hydrodynamics is used to model flow between randomly placed, partially overlapping circles, and the flow resistance is first roughly proportional to the number of circles and then increases more strongly for higher numbers of such obstacles.
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