The Colours of Infinity: The Beauty and Power of Fractals

220 Pages·2010·24.75 MB·English

by  Ian Stewart (auth.)

The Colours of Infinity
The Beauty and Power of Fractals

The Colours
of Infinity
The Beauty and
Power of Fractals
With contributions by
Ian Stewart, Sir Arthur C. Clarke,
Benoît Mandelbrot, Michael and Louisa Barnsley,
Will Rood, Gary Flake and David Pennock
and Nigel Lesmoir-Gordon
The authors have asserted their rights under the Copyright, Designs and
Patents Act, 1988, to be identifi ed as authors of their individual contributions
Editor
Nigel Lesmoir-Gordon
Gordon Films UK
MK45 4AD Bedfordshire
United Kingdom
[email protected]
Additional material to this book can be downloaded from http://extras.springer.com
ISBN 978-1-84996-485-2 e-ISBN 978-1-84996-486-9
DOI 10.1007/978-1-84996-486-9
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: 2010937321
Mathematics Classification Number (2010) 28A80
© 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
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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
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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)
This book is dedicated
to Benoît Mandelbrot

‘The most beautiful thing
we can experience is the mysterious.
It is the source of all true
art and science.’
Albert Einstein

Contents
Colours Book Amendments
Contributors
1 The Nature of Fractal Geometry
2
Ian Stewart
2 Exploring the Fractal Universe
24
Arthur C. Clarke
3 A Geometry Able to Include Mountains and Clouds
38
Benoît Mandelbrot
4 Fractal Transformations
58
Michael Barnsley and Louisa Barnsley
5 Fractal Limits: The Mandelbrot Set and the self-similar
tilings of M.C. Escher
74
Will Rood
6 Self-organization, Self-regulation, and Self-similarity
on the Fractal Web
88
Gary William Flake and David M. Pennock Yahoo! Research Labs
7 Fractal Financial Fluctuations
120
Benoît Mandelbrot
8 Filming The Colours of Infinity 136
Nigel Lesmoir-Gordon
9 The Colours of Infinity-the Film Script
144
Arthur C. Clarke
Index
173