Cellular Automata: Analysis and Applications. 1st ed. 2017

種類:

電子ブック

責任表示:

by Karl-Peter Hadeler, Johannes Müller

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Hadeler, Karl-Peter.
• Müller, Johannes.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783319530437 [3319530437]    

注記:

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 Kůrka -- 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 (Kůrka classification). These classifications suggest to cluster cell

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