Fractals and Chaos Simplified for the Life Sciences

292 Pages·1998·11.48 MB·English

by  Larry S. Liebovitch

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
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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.
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