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
Journal ArticleDOI
Multiplicities and instabilities in chemically reacting systems — a review
Luis F. Razon,Roger A. Schmitz +1 more
TL;DR: In this paper, a review brings attention to much of the recent literature describing these developments and their applications, particularly regarding complex and chaotic oscillations, as well as reported experimental observations which, in many cases, have provided support for prior theory and in many others, have led to new theoretical developments.
Book
Diffuse X-Ray Scattering and Models of Disorder
TL;DR: In this paper, the authors review the earlier 1D models in order to develop the framework necessary for a discussion of the later higher-dimensional results, illustrated with optical analogue diffraction examples.
Journal Article
The Structure of the Elementary Cellular Automata Rule Space
Wentian Li,Norman H. Packard +1 more
TL;DR: The structure of the elementary cellular automata rule space is investigated and the probabilities for a rule to be connected to other rules in the same class (intra-class), as well as rules in inter-class classes (inter-class).
Journal ArticleDOI
Self-Organized Phase Transitions in Cellular Automaton Models for Pedestrians
Minoru Fukui,Yoshihiro Ishibashi +1 more
TL;DR: Two models have been studied for the behavior avoiding from collision when the pedestrians meet with each other in a system where one pedestrian and many pedestrians walk in the opposite direction and encounter each other on a passageway.
Book
Introduction to the Modeling and Analysis of Complex Systems
TL;DR: Add the following footnote right after this: “You may not see those interactive icons if your plot is displayed in-line within your console unless you change the setting of your Python environment so that plots are displayed in separate windows.
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