Becker, Doerfler. Dynamical systems and fractals in Pascal (CUP, 1990)(410s).pdf

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Dynamical systems
and fractals
Computer graphics experiments
in Pascal
Published by the Press Syndicate of the University of Cambridge
The Pitt Building, Trumpington Street, Cambridge CB2 1RP
40 West 20th Street, New York, NY lOOllL4211, USA
10 Stamford Road, Oakleigh, Melbourne 3166, Australia
Originally published in German as Computergrafische Experimente mit Pascal: Chaos und
Ordnung in Dynamischen Systemen by Friedr. Vieweg & Sohn, Braunschweig 1986,
second edition 1988, and 0 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH,
Braunschweig 1986, 1988
First published in English 1989
Reprinted 1990 (three times)
English translation 0 Cambridge University Press 1989
Printed in Great Britain at the University Press, Cambridge
Library
of
Congress cataloguing in publication data available
British Library cataloguing in publication data
Becker, Karl-Heinze
Dynamical systems and fractals
1. Mathematics. Applications of computer graphics
I. Title II. Doffler, Michael III.
Computergrafische Experimente mit Pascal.
English
5 lo’.28566
ISBN 0 521 36025 0 hardback
ISBN 0 521 36910 X paperback
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Dynamical systems
and fractals
Computer graphics experiments in Pascal
Karl-Heinz Becker
Michael Diirfler
Translated by Ian Stewart
CAMBRIDGE UNIVERSITY PRESS
Cambridge
New York Port Chester Melbourne Sydney
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Contents
Foreword
New Directions in Computer Graphics : Experimental Mathematics
Preface to the German Edition
vii
xi
Researchers Discover Chaos
1.1
1
Chaos and Dynamical Systems - What Are They?
3
1.2
Computer
Graphics
Experiments
and
Art
6
2
Between
Order and Chaos: Feigenbaum Diagrams
17
First
Experiments
18
2.1
2.1.1
It’s Prettier with Graphics
27
2.1.2
GraphicalIteration
34
2.2
Fig-trees Forever
37
2.2.1
Bifurcation Scenario
- the Magic Number ‘Delta
46
2.2.2
Attractors
and
Frontiers
48
2.2.3
FeigenbaumLandscapes
51
Chaos - Two Sides to the Same Coin
53
2.3
3
Strange
Attractors
55
3.1
The Strange Attractor
56
3.2
The Henon Attractor
62
3.3
The Lorenz
Attractor
64
4
Greetings
from Sir Isaac
71
4.1
Newton’s Method
72
4.2
Complex Is Not Complicated
81
4.3
Carl Friedrich Gauss meets Isaac Newton
86
Complex Frontiers
91
5
92
5.1
Julia and His Boundaries
Simple Formulas give Interesting Boundaries
108
5.2
6
Encounter with the Gingerbread Man
127
A Superstar with Frills
128
6.1
Tomogram of the Gingerbread Man
145
6.2
159
Fig-tree
and
Gingerbread
Man
6.3
Metamorphoses
167
6.4
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Dynamical Systems and Fractals
vi
7
New Sights - new Insights
7.1
179
186
186
192
199
Up Hill and Down Dale
7.2
Invert It - It’s Worth It!
The World is Round
7.3
Inside
Story
7.4
Fractal Computer Graphics
203
8
8.1
All Kinds of Fractal Curves
204
8.2
Landscapes: Trees, Grass, Clouds, Mountains, and Lakes
211
8.3
Graftals
216
RepetitiveDesigns
224
8.4
Step by Step into Chaos
9
231
10 Journey to the Land of Infinite Structures
247
11 Building Blocks for Graphics Experiments
257
The
Fundamental
Algorithms
11.1
258
FractalsRevisited
267
11.2
11.3
Ready, Steady, Go!
281
The Loneliness of the Long-distance Reckoner
11.4
288
What You See Is What You Get
11.5
303
A Picture Takes a Trip
319
11.6
12 Pascal and the Fig-trees
12.1
327
Some Are More Equal Than Others - Graphics on
Other
Systems
328
328
337
347
361
366
374
12.2
MS-DOS and PS/2 Systems
UNIX Systems
12.3
Macintosh
Systems
12.4
Atari
Systems
12.5
12.6
Apple II Systems
12.7
‘Kermit
Here’
- Communications
379
13 Appendices
13.1
Data for Selected Computer Graphics
380
383
13.2
Figure
Index
13.3
Program Index
388
Bibliography
391
13.4
13.5
Acknowledgements
393
Index
395
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