Cellular Automata: Analysis and Applications
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 equ
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Karl-Peter Hadeler Johannes Müller
Cellular Automata: Analysis and Applications
Springer Monographs in Mathematics
Editors-in-Chief Isabelle Gallagher Minhyong Kim
More information about this series at http://www.springer.com/series/3733
Karl-Peter Hadeler • Johannes MRuller
Cellular Automata: Analysis and Applications
123
Karl-Peter Hadeler FB Biologie UniversitRat TRubingen TRubingen, Germany
Johannes MRuller Centre for Mathematical Sciences Technical University Munich Garching, Germany
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-53042-0 ISBN 978-3-319-53043-7 (eBook) DOI 10.1007/978-3-319-53043-7 Library of Congress Control Number: 2017937054 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
1
Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.1 Discreteness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.2 The Game of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.3 Contact Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.4 Some Wolfram Automata .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.5 Greenberg-Hastings Automata . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.6 Langton’s Ant and Life Without Death . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.7 A Nic
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