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Titlebook: Cellular Automata: Analysis and Applications; Karl-Peter Hadeler,Johannes Müller Book 2017 Springer International Publishing AG 2017 cellu

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发表于 2025-3-21 18:56:29 | 显示全部楼层 |阅读模式
书目名称Cellular Automata: Analysis and Applications
编辑Karl-Peter Hadeler,Johannes Müller
视频videohttp://file.papertrans.cn/223/222999/222999.mp4
概述Contains a coherent representation of the main approaches to analyze the dynamics of cellular automata.Emphasizes classification strategies and methods that allow a rigorous analysis and precise under
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Cellular Automata: Analysis and Applications; Karl-Peter Hadeler,Johannes Müller Book 2017 Springer International Publishing AG 2017 cellu
描述.This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult 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 to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various 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 that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the q
出版日期Book 2017
关键词cellular automata; classification of cellular automata; dynamics of cellular automata; applications of
版次1
doihttps://doi.org/10.1007/978-3-319-53043-7
isbn_softcover978-3-319-85047-4
isbn_ebook978-3-319-53043-7Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer International Publishing AG 2017
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Attractors,ellular automata is asymptotic behavior. Although transient states are interesting, often enough the dynamics settles quite fast on typical structures. The set consisting of these asymptotic states is the attractor. The first part of this section is devoted to the definition of an attractor and the
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Particle Motion, this is a most powerful formalism. Cellular automata provide an alternative mathematical structure. However, a justification is required why cellular automata could be preferred over partial differential equations.
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Pattern Formation, [137], but also invertebrates and plants show various patterns. In the present context the patterns on the shells of molluscs (especially snails and mussels) are of special interest. These patterns are not produced all at once. Since the shell gradually grows by adding material to the outer edge an
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