Computers, Pattern, Chaos and Beauty

by Pickover, Clifford A.

• ISBN13: 9780486417097
• ISBN10: 0486417093
• Format: Paperback
• Copyright: 2001-07-24
• Publisher: Dover Publications

Summary

Combining fractal theory with startling computer art, this book reveals an entirely new way of seeing. Part I introduces computer graphics and the creative use of computers. Part II describes various graphical methods for representing and detecting patterns in complicated data. Part III illustrates simple techniques for visualizing chaotic behavior. "No human being should pass up the experience of stepping through the portals of this beautiful book . . ."-Martin Gardner, Scientific American. Over 275 illus., 29 in color.

Table of Contents

Introduction
Computers and Creativity	p. 3
Objectives	p. 4
Lateral Use of Computer Software Tools	p. 4
Reading List for Chapter 1	p. 5
Hidden Worlds	p. 7
Digits, Symbols, Pictures	p. 7
Computers and Art	p. 8
Computer Graphics: Past and Present	p. 10
Computers: Past and Present	p. 11
The Human Brain vs. the Computer Brain	p. 12
The Human Brain	p. 12
Human Computers	p. 13
New Applications of Calculating: A Sampling and Digression	p. 14
One Final Word	p. 15
Reading List for Chapter 2	p. 15
Representing Nature
Fourier Transforms (The Prisms of Science)	p. 21
Fourier Analysis: A Digression and Review	p. 21
Singing Computers	p. 23
Bach, Beethoven, The Beatles	p. 28
Breathing Proteins	p. 30
Cancer Genes (DNA Waveforms)	p. 33
Reading List for Chapter 3	p. 35
Unusual Graphic Representations	p. 37
Acoustics	p. 38
New Ways of Displaying Data	p. 38
Snowflakes from Sound: Art and Science	p. 39
Medicine: Cardiology and SDPs	p. 41
Another Dot-Display Used in Molecular Biophysics	p. 45
Autocorrelation Cartoon-Faces for Speech	p. 47
Cartoon Faces in Education	p. 50
Cognitive Association of Coordinates with Facial Features	p. 50
Target-Pictures for Children	p. 51
Learning by Means of Analogy	p. 53
Educational Aid for the Presentation of Statistical Concepts	p. 53
Commercial and Military Air Traffic Control	p. 55
Faces and Cancer Genes	p. 55
Back to Acoustics: Phase Vectorgrams	p. 55
Fractal Characterization of Speech Waveform Graphs	p. 57
Scale Invariance	p. 57
Fractal Characterization of Speech	p. 57
Classification of Shapes	p. 58
Speech Fractal Dimension	p. 59
Catalog of Other Acoustic Sounds	p. 63
A Monte Carlo Approach to Fractal Dimension	p. 64
Other Speech Graphics, Wigner Distributions, FM Synthesis	p. 64
Wigner Distribution	p. 64
FM Synthesis of Speech	p. 65
Molecular Genetics: DNA Vectorgram	p. 66
Background	p. 66
DNA Vectorgram	p. 66
Reading List for Chapter 4	p. 68
Image Processing of the Shroud of Turin	p. 73
Image Processing	p. 73
The Shroud	p. 73
A Sampling of Results of Past Scientific Examination	p. 74
Past Image Processing Studies	p. 74
Present Study	p. 75
Pseudo-Gray Transformation via Look-up Table (LUT)	p. 76
Processing via Pseudocolor LUT	p. 78
Reading List for Chapter 5	p. 80
Physics: Charged Curves	p. 83
Recipe for Accelerating the Iterative Process	p. 86
Reading List for Chapter 6	p. 87
Summary of Part II	p. 89
Pattern, Symmetry, Beauty
Genesis Equations (or Biological Feedback Forms)	p. 95
Feedback	p. 96
A Computer Program "Bug"	p. 102
Genesis Equations	p. 104
The Leeuwenhoek Program	p. 104
Brief Sampling of Past Work in Natural Object Creation	p. 105
Biological Forms Generated from Mathematical Feedback Loops	p. 106
The Habitation of Abstract Geometric Space	p. 107
Creation and Search in the Manifold Dimensions of Space	p. 108
Reading List for Chapter 8	p. 109
More Beauty from Complex Variables	p. 113
Turbulent Complex Curls	p. 113
Transcendental Functions in the [mu] Plane	p. 117
What is "cosh"?	p. 118
Review of Some Definitions of Terms Used in This Chapter	p. 120
Graphics Gallery and Observations	p. 121
Recipes for Cosh Pictures	p. 123
Maps	p. 128
How to Design Textures Using Recursive Composite Functions	p. 129
Secrets and Tricks	p. 130
Chaos and Pattern	p. 132
Where Do We Go From Here?	p. 133
Recipe	p. 134
Networks, Repeller-Towers	p. 135
Reading List for Chapter 9	p. 136
Mathematical Chaos	p. 141
What is Chaos?	p. 141
Pattern Formation and Chaos in Networks	p. 142
Networks	p. 144
Drawing the Network	p. 145
Some Examples	p. 149
Summary	p. 150
Recipes for Generating Networks	p. 150
Automatic Computer Generation of Networks	p. 150
Graphics, Bifurcation, Order and Chaos	p. 151
Recipe for Bifurcation Plot Generation	p. 157
Image Processing Techniques and Deterministic Chaos	p. 158
A Note on Rendering 3-D Strange Attractors	p. 160
Recipe	p. 162
Quaternion Images	p. 163
Quaternion Julia Sets	p. 164
A Note on Rendering Chaotic Repeller Distance-Towers	p. 168
Reading List for Chapter 10	p. 171
Number Theory	p. 173
Introduction	p. 173
Exotic Symmetries from Large Pascal's Triangles	p. 174
Computation	p. 174
Nomenclature	p. 177
Gaskets	p. 178
Size Changes of Internal Triangles	p. 179
Symmetries	p. 181
Plotting a Complete PT	p. 183
Perfect Numbers	p. 183
Practical Importance	p. 184
Future Work	p. 185
Patterns in Hailstone (3n+1) Numbers	p. 185
Is There a Double Smoothly Undulating Integer?	p. 188
Reading List for Chapter 11	p. 191
Synthesizing Nature	p. 195
Wild Monopodial Tendril Plant Growth	p. 195
Spirals in Nature	p. 197
Graphics Gallery of Plant Forms	p. 198
Natural Growth	p. 199
Recipe for Picture Computation	p. 202
How to Design with Directed Random Walks	p. 202
Directed Random Walk	p. 203
The Algorithm	p. 204
Recipe for Transition Probability Plants	p. 208
A Sampling of Spirals in Science, Nature, and Art	p. 209
Traditional Mathematical Spirals (Clothoid, Littus, et al.)	p. 209
Spirals Made by Humans	p. 216
Strange Spirals	p. 217
Galaxies	p. 217
Seashells	p. 218
Fuzzy Spirals	p. 219
Spiral-Like Forms from Differential Equations	p. 220
Trigonometric Iteration (Bushy Spirals)	p. 221
Concluding Remarks on Spirals	p. 222
A Vacation on Mars	p. 223
Reading List for Chapter 12	p. 225
Synthesizing Ornamental Textures	p. 227
Self-decorating Eggs	p. 227
The Algorithm	p. 229
Graphics Gallery	p. 230
Summary of Egg Tiling Patterns	p. 232
Self-Decorating Surfaces (Beauty from Noise)	p. 234
Recipe	p. 235
Biometric Art from Retinal Vascular Patterns	p. 237
Reading List for Chapter 13	p. 238
Dynamical Systems	p. 249
Time-discrete Phase Planes Associated with a Cyclic System	p. 250
Recipe	p. 258
Cycles and Centers in Time-Discrete Dynamical Systems	p. 258
A Review of Some Definitions of Terms	p. 260
Reading List for Chapter 14	p. 266
Numerical Approximation Methods	p. 275
Halley Maps for a Trigonometric and Rational Function	p. 275
Overrelaxation and Chaos	p. 284
Buridan's Ass	p. 285
Beauty, Symmetry and Chaos in Chebyshev's Paradise	p. 285
Chebyshev Rings	p. 287
Recipe for Chebyshev's Paradise	p. 287
Reading List for Chapter 15	p. 289
Tesselation Automata Derived from a Single Defect	p. 295
Method and Observations	p. 296
TA Type 1	p. 297
TA Type 2. Time Dependence of Rules	p. 298
TA Type 3. Contests Between Defects	p. 300
TA Type 4. Defects in a Centered Rectangular Lattice	p. 301
TA Type 5. Larger Local Neighborhood	p. 304
Recipe for Tesselation Automata	p. 310
Reading List for Chapter 16	p. 310
Summary of Part III and Conclusion of Book	p. 313
Color Plates	p. 319
Additional Recipes	p. 323
Chaos from bits	p. 323
Dynamical Systems	p. 323
Cartoon Faces for Multidimensional Data Portrayal	p. 323
Symmetrized Random-Dot Patterns	p. 324
Recipe	p. 324
Sqrt(r) Dot-Patterns	p. 325
Random Walk Dot-Patterns	p. 326
Burnt Paper	p. 328
Picturing Randomness with Truchet Tiles	p. 329
Circles Which Kiss: A Note on Osculatory Packing	p. 332
Markov Aggregation on a Sticky Circle	p. 337
Suggestions for Future Experiments	p. 339
Descriptions for Chapter Frontpiece Figures	p. 343
References (General)	p. 349
Recommended Reading	p. 349
Interesting and Unusual Newsletters, Distributors, Columns, Misc.	p. 351
Recommended Journals	p. 352
References by Topic and Section	p. 353
Introduction	p. 353
Representing Nature	p. 353
Pattern, Symmetry, and Beauty	p. 358
Additional Reading	p. 366
Works of the Author	p. 368
Glossary	p. 377
Index	p. 385
Credits	p. 393
A Final Illustration of Chaos	p. 394
Acknowledgements	p. 395
About the Author	p. 397
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