Game of Life Cellular Automata
In the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. Each cell takes two states, live and dead. The cells’ states are updated simultaneously and in discrete ti
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Andrew Adamatzky Editor
Game of Life Cellular Automata
Editor Prof. Andrew Adamatzky University of the West of England Bristol BS16 1QY United Kingdom [email protected]
ISBN 978-1-84996-216-2 e-ISBN 978-1-84996-217-9 DOI 10.1007/978-1-84996-217-9 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010928553 © Springer-Verlag London Limited 2010 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
In 1970 Martin Gardner spelled out the rules of a new solitaire game forged by John Horton Conway.1 An unparalleled combination of functional simplicity with behavioural complexity made Conway’s Game of Life the most popular cellular automaton of all time. We commemorate the Game of Life’s 40th birthday with a unique collection of works authored by renowned mathematicians, computer scientists, physicists and engineers. The superstars of science, academy and industry present their visions of the Game of Life cellular automaton, its extensions and modifications, and spatially-extended systems inspired by the Game. The book covers hot topics in theory of computation, pattern formation, optimization, evolution, non-linear sciences and mathematics. Academics, researchers, hobbyists and students interested in the Game of Life theory and applications will find this monograph a valuable guide to the field of cellular automata and excellent supplementary reading. Bristol, UK
Andrew Adamatzky
1 “. . . each
cell of the checkerboard (assumed to be an infinite plane) has eight neighboring cells, four adjacent orthogonally, four adjacent diagonally. The rules are: 1. Survivals. Every counter with two or three neighboring counters survives for the next generation. 2. Deaths. Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one neighbor or none dies from isolation. 3. Births. Each empty cell adjacent t
