Dynamical Systems and Fractals: Computer Graphics Experiments with Pascal

✍ Scribed by Karl-Heinz Becker, Michael Dörfler

• Publisher: Cambridge University Press
• Year: 1989
• Tongue: English
• Leaves: 410
• Category: Library

✦ Synopsis

This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST.

✦ Table of Contents

Contents......Page 5
Foreword......Page 7
Preface to the German Edition......Page 11
1 Researchers Discover Chaos I......Page 13
1.1 Chaos and Dynamical Systems - What Are They?......Page 15
1.2 Computer Graphics Experiments and Art.......Page 18
2 Between Order and Chaos: Feigenbaum Diagrams......Page 29
2.1 First Experiments......Page 30
2.1.1 It's Prettier with Graphics......Page 39
2.1.2 Graphicallteration......Page 46
2.2 Fig-trees Forever......Page 49
2.2.1 Bifurcation Scenario - the Magic Number'Delta......Page 58
2.2.2 Attractors and Frontiers......Page 60
2.2.3 FeigenbaumLandscapes......Page 63
2.3 Chaos - Two Sides to the Same Coin......Page 65
3 Strange Attractors......Page 67
3.1 The Strange Attractor......Page 68
3.2 The H6non Attractor......Page 74
3.3 The Lorenz Attractor......Page 76
4 Greetings from Sir Isaac......Page 83
4.1 Newton's Method......Page 84
4.2 Complex Is Not Complicated......Page 93
4.3 Carl Friedrich Gauss meets Isaac Newton......Page 98
5 Complex Frontiers......Page 103
5.1 Julia and His Boundaries......Page 104
5.2 Simple Formulas give Interesting Boundaries......Page 120
6 Encounter with the Gingerbread Man......Page 139
6.1 A Superstar with Frills......Page 140
6.2 Tomogram of the Gingerbread Man......Page 157
6.3 Fig-tree and Gingerbread Man......Page 171
6.4 Metamorphoses......Page 179
7 New Sights - new Insights......Page 191
7.2 Invert It - It's Worth It!......Page 198
7.3 The World is Round......Page 204
7.4 Inside Story......Page 211
8 Fractal Computer Graphics......Page 215
8.1 All Kinds of Fractal Curves......Page 216
8.2 Landscapes: Trees, Grass, Clouds, Mountains, and Lakes......Page 223
8.3 Graftals......Page 228
8.4 Repetitive Designs......Page 236
9 Step by Step into Chaos......Page 243
10 Journey to the Land of Infinite Structures......Page 259
11 Building Blocks for Graphics Experiments......Page 269
11.1 The Fundamental Algorithms......Page 270
11.2 Fractals Revisited......Page 279
11.3 Ready, Steady, Go!......Page 293
11.4 The Loneliness of the Long-distance Reckoner......Page 300
11.5 What You See Is What You Get......Page 315
11.6 A Picture Takes a Trip......Page 331
12 Pascal and the Fig-trees......Page 339
12.2 MS-DOS and PS/2 Systems......Page 340
12.3 UNIX Systems......Page 349
12.4 Macintosh Systems......Page 359
12.5 Atari Systems......Page 373
12.6 Apple II Systems......Page 378
12.7 'Kermit Here' - Communications......Page 386
13 Appendices......Page 391
13.1 Data for Selected Computer Graphics......Page 392
13.2 Figure Index......Page 395
13.3 Program Index......Page 400
13.4 Bibliography......Page 403
13.5 Acknowledgements......Page 405
Index......Page 407

✦ Subjects

Математика;Нелинейная динамика;Теория хаоса;