Computers, Pattern, Chaos and Beauty
by Pickover, Clifford A.Format: Paperback
Pub. Date: 2001-07-24
Publisher(s): Dover Publications
Other versions by this Author
List Price: $18.13
Rent Book
Select for Price
Digital
$16.79*
New Book
We're Sorry
Sold Out
Used Book
We're Sorry
Sold Out
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
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 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.