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
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Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
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Universality and complexity in cellular automata
TL;DR: In this article, it was shown that all one-dimensional cellular automata fall into four distinct universality classes: limit points, limit cycles, chaotic attractors, and limit cycles.
Journal ArticleDOI
Universality and complexity in cellular automata
TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
BookDOI
Lattice-Gas Cellular Automata and Lattice Boltzmann Models
TL;DR: In this paper, the authors provide an introduction to lattice gas cellular automata (LGCA) and lattice Boltzmann models (LBM) for numerical solution of nonlinear partial differential equations.
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Non-equilibrium critical phenomena and phase transitions into absorbing states
TL;DR: In this article, a review of recent developments in non-equilibrium statistical physics is presented, focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail.
References
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Book
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TL;DR: The Mathematics 160 course at the California Institute of Technology as discussed by the authors was the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the University of California during the last 25 years.
Journal ArticleDOI
Prediction and entropy of printed English
TL;DR: A new method of estimating the entropy and redundancy of a language is described, which exploits the knowledge of the language statistics possessed by those who speak the language, and depends on experimental results in prediction of the next letter when the preceding text is known.
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Instabilities and pattern formation in crystal growth
TL;DR: In this article, the authors examined several common modes of crystal growth and identified a few new theoretical ideas and a larger number of outstanding problems, including sidebranching and tip-splitting instabilities.
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Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs.
TL;DR: A theory is proposed for the development of filamentous organisms, based on the assumptions that the filaments are composed of cells which undergo changes of state under inputs they receive from their neighbors, and the cells produce outputs as determined by their state and the input they receive.
Journal ArticleDOI
Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems
TL;DR: In this article, a tutorial approach to cooperative phenomena in systems far from thermal equilibrium and in non-physical systems is presented, with particular emphasis on the question of how order and self-organization may arise.