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Journal ArticleDOI

Statistical mechanics of cellular automata

Stephen Wolfram
- 01 Jul 1983 - 
- Vol. 55, Iss: 3, pp 601-644
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.

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Citations
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Journal ArticleDOI

Cellular automata based deterministic self-test strategies for programmable data paths

TL;DR: Novel and optimized test strategies are presented for the generation of a set of predetermined test vectors on chip to be used as part of a BIST strategy for complex programmable data paths, guaranteed with 100% stuck-at and stuck-open/close fault coverage for all detectable faults.
Journal ArticleDOI

Spatiotemporal order, disorder, and propagating defects in homogeneous system of relaxation oscillators.

Rajeev Singh, +1 more
- 14 Jan 2013 - 
TL;DR: It is shown that diffusive coupling through the inactivating component in a system of relaxation oscillators extends such complexity to the temporal domain, generating remarkable spatiotemporal phenomena.
Journal ArticleDOI

Measurement of the muon neutrino inclusive charged-current cross section in the energy range of 1–3 GeV with the T2K INGRID detector

K. Abe, +322 more
- 05 Apr 2016 - 
TL;DR: In this article, the neutrino energy spectrum as a function of the off-axis angle, combined with event topology information, is used to calculate the current cross section of neutrinos, at energies of 1.1, 2.0 and 3.3 GeV.
Book ChapterDOI

Shocks in the Burgers Equation and the Asymmetric Simple Exclusion Process

TL;DR: In this article, the Burgers equation is used as a model of transport in highways and the number of cars entering an infinitesimal time interval (r, r + dr + dr) is given as θu(r, dr, t), where r is the velocity of a single car in the absence of other cars.
Journal ArticleDOI

Cellular Automata Modelling of Fluvial Evolution: Real and Parametric Numerical Results Comparison Along River Pellice (NW Italy)

TL;DR: In this article, a cellular automaton model (CAESAR) is applied to a wandering stretch of River Pellice in the Italian north-western Alps to compare simulated and measured data through statistical approaches.
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