Journal ArticleDOI
Statistical mechanics of cellular automata
Reads0
Chats0
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
More filters
Book
An Introduction to Logic Circuit Testing
TL;DR: An Introduction to Logic Circuit Testing provides a detailed coverage of techniques for test generation and testable design of digital electronic circuits/systems and introduces the key concepts of testability.
Journal Article
Power Spectra of Regular Languages and Cellular Automata
TL;DR: Simulation and analytical results are given for the power spectra of attractors produced by many cellular automata and their characteristic length is related to non trivial eigenvalues of th e arc-to-arc transition matrix in the regular langua ge graph.
Book ChapterDOI
Stochastic Growth Models
TL;DR: This paper is based on a talk given by the first author at the I.M.A. in February, 1986 but incorporates improvements discovered during six later repiti-tions, and tries to preserve the informal style of the talk and concentrate on the “main ideas” rather than giving complete details of the proofs.
Journal Article
Using shape grammar to derive cellular automata rule patterns
TL;DR: This paper shows how shape grammar can be used to derive cellular automata (CA) rules using shape grammar to visually depict the desired conditional rules of a behavior or system architecture under investigation, followed by a transcription of these rules as patterns into CA.
Journal ArticleDOI
The evolution of parallel cellular machines : toward evolware
TL;DR: The methodology described herein represents one possible approach to attaining truly evolving ware, evolware, with current implementations centering on hardware, while raising the possibility of using other forms in the future, such as bioware.
References
More filters
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