Fractals and Chaos Simplified for the Life Sciences PDF
Preview Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences Larry S. Liebovitch JAMES C. GRAHAM FUND Fractals and Chaos Simplified for the Life Sciences Fractals and Chaos I' Simplified for the Life Sciences LARRY S. LIEBOVITCH Center for Compl~x Systems Florida Atlantic University http://www. ccs.fau. edul-liebovitch/larry. html New York Oxford OXFORD UNIVERSITY PRESS 1998 NOV 9 1998 Oxford University Press Oxford New York Athens Auckland Bangkok Bogota Bombay Buenos Aires Calcutta Cape Town Dares Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin lbadan Copyright© 1998 by Oxford University Press, Inc. Published by Oxford University Press, Inc., 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced. stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Liebovitch, Larry S. Fractals and chaos simplified for the life sciences I Larry S. Liebovitch. p. em. Includes bibliographical references and index. · ISBN 0-19-512024-8 (pbk.) I. Medicine-Mathematics. 2. Biology-Mathematics. 3. Fractals. 4. Chaotic behavior in systems. I. Title. R853.M3L54 1997 97-20864 570'.1 '51474-dc21 CIP 987654321 Printed in the United States of America on acid-free paper "Chance favors the prepared mind." -Louis Pasteur Digitized by the Internet Archive in 2019 with funding from Kahle/A ustin Foundation https://archive.org/details/fractalschaossimOOOOiieb Preface "Fractals" and "chaos" have attracted wide attention and excitement in mathematics and the physical sciences. This book explains the properties of fractals and chaos and shows how they are now being used in biology and medicine. These ideas are presented in a way that is understandable to people who may not be familiar with advanced mathematical concepts. This is done by presenting one concept at a time on each set of facing pages. The left-hand page is text and the right-hand page is graphics. The text and graphics each explain the same concept in different ways. Sometimes the text and graphics provide similar information. Sometimes they provide complementary information. Nonspecialists can use this book to gain a basic understanding of fractals and chaos and their importance in biomedical research. Teachers in high school or college can use this book as the basis for a unit on fractals and chaos. The right-hand graphics pages can be copied onto transparencies to illustrate the concepts described on the facing left-hand pages. Biomedical scientists can use this book to understand how concepts from fractals and chaos are being used to study the shape and function of proteins, cell membranes, nerve cells, muscle cells, the lung, the heart, and the brain. They can see how to use these methods to analyze their own data and interpret the results. Acknowledgments I thank David Axelrod, Gregory Dewey, Zbigniew Grzywna, Leo Levine, Cynthia Park, Monika Sasksena. Daniela Scheurle, Virginia Standish, Angelo Todorov, and Michal Zochowski for their helpful comments and suggestions. vii
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