Strange attractors: creating patterns in chaos

Julien Clinton Sprott9781558512986, 1558512985

Chaos and fractals are new mathematical ideas that have revolutionized our view of the world. They have application in virtually every academic discipline. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns. Disk includes a full working version of the program.

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Table of contents :
Title Page……Page 1
Table of Contents……Page 2
Why This Book Is for You……Page 4
Strange Attractors……Page 5
1.1: Predictability and Uncertainty……Page 6
1.2: Bucks and Bugs……Page 8
1.3: The Butterfly Effect……Page 14
1.4: The Computer Artist……Page 17
2.1: More Knobs to Twiddle……Page 25
2.2: Randomness and Pseudorandomness……Page 26
2.3: What’s in a Name?……Page 28
2.4: The Computer Search……Page 30
2.5: Wiggles on Wiggles……Page 40
2.6: Making Music……Page 48
3.1: Quadratic Maps in Two Dimensions……Page 50
3.2: The Butterfly Effect Revisited……Page 54
3.3: Searching the Plane……Page 56
3.4 The Fractal Dimension……Page 74
3.5: Higher-Order Disorder……Page 80
3.6: Strange Attractor Planets……Page 107
3.7: Designer Plaids……Page 125
3.8: Strange Attractors that Don’t……Page 132
3.9: A New Dimension in Sound……Page 142
4.1: Projections……Page 147
4.2: Shadows……Page 171
4.3: Bands……Page 191
4.4: Colors……Page 208
4.5: Characters……Page 211
4.6: Anaglyphs……Page 216
4.7: Stereo Pairs | Stereo Pairs……Page 222
4.8: Slices……Page 241
5.1: Hyperspace……Page 259
5.2: Projections……Page 263
5.3: Other Display Techniques……Page 288
5.4: Writing on the Wall……Page 315
5.5: Murals and Movies……Page 317
5.6: Search and Destroy……Page 318
6.1: Beam Me Up Scotty!……Page 322
6.2: Professor Lorenz and Dr. Rössler……Page 326
6.3: Finite Differences……Page 329
6.4: Flows in Four Dimensions……Page 352
6.5: Strange Attractors that Aren’t……Page 368
6.6: Donuts and Coffee……Page 384
7.1: Steps and Tents……Page 397
7.2: ANDs and ORs……Page 408
7.3: Roots and Powers……Page 418
7.4: Sines and Cosines……Page 428
7.5: Webs and Wreaths……Page 438
7.6: Swings and Springs……Page 448
7.7: Roll Your Own……Page 459
8.1: How Common is Chaos?……Page 460
8.2: But Is It Art?……Page 467
8.3: Can Computers Critique Art?……Page 468
8.4: What’s Left to Do?……Page 470
8.5: What Good Is It?……Page 476
Appendix A: Annotated Bibliography……Page 480
Appendix B: BASIC Program Listing……Page 491
Appendix C: Other Computers and BASIC Versions……Page 514
Appendix D: C Program Listing……Page 528
Appendix E: Summary of Equations……Page 566
Appendix F: Dictionaries of Strange Attractors……Page 576