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Cellular automataanalysis and applic...

Hadeler, Karl-Peter.

Cellular automataanalysis and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cellular automataby Karl-Peter Hadeler, Johannes Muller.
Reminder of title:	analysis and applications /
Author:	Hadeler, Karl-Peter.
other author:	Muller, Johannes.
Published:	Cham :Springer International Publishing :2017.
Description:	xi, 467 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Cellular automata.
Online resource:	http://dx.doi.org/10.1007/978-3-319-53043-7
ISBN:	9783319530437$q(electronic bk.)

Cellular automataanalysis and applications /
Hadeler, Karl-Peter.

Cellular automataanalysis and applications /[electronic resource] :by Karl-Peter Hadeler, Johannes Muller. - Cham :Springer International Publishing :2017. - xi, 467 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

1.Introduction -- 2.Cellular automata - basic definitions -- 3.Cantor topology of cellular automata -- 4.Besicovitch and Weyl topologies -- 5 Attractors -- 6 Chaos and Lyapunov stability -- 7 Language classification of Kurka -- 8.Turing machines, tiles, and computability -- 9 Surjectivity and injectivity of global maps -- 10.Linear Cellular Automata -- 11 Particle motion -- 12 -- Pattern formation -- 13.Applications in various areas -- A.Basic mathematical tools.

This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology) The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kurka classification) These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit) Pattern formation is related to linear cellular automata, to the Bar-Yam model for Turing pattern, and Greenberg-Hastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predator-prey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit.

ISBN: 9783319530437$q(electronic bk.)

Standard No.: 10.1007/978-3-319-53043-7doiSubjects--Topical Terms:

211503
Cellular automata.

LC Class. No.: QA267.5.C45

Dewey Class. No.: 006.3822

Cellular automataanalysis and applications /
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490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a 1.Introduction -- 2.Cellular automata - basic definitions -- 3.Cantor topology of cellular automata -- 4.Besicovitch and Weyl topologies -- 5 Attractors -- 6 Chaos and Lyapunov stability -- 7 Language classification of Kurka -- 8.Turing machines, tiles, and computability -- 9 Surjectivity and injectivity of global maps -- 10.Linear Cellular Automata -- 11 Particle motion -- 12 -- Pattern formation -- 13.Applications in various areas -- A.Basic mathematical tools.
520 $a This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology) The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kurka classification) These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit) Pattern formation is related to linear cellular automata, to the Bar-Yam model for Turing pattern, and Greenberg-Hastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predator-prey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit.
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