Combining fractal theory with computer art, this book introduces a creative use of computers. It describes graphic methods for detecting patterns in complicated data and illustrates simple techniques for visualizing chaotic behavior. "Beautiful." — Martin Gardner, Scientific American. Over 275 illustrations, 29 in color.

Table of Contents for Computers, Pattern, Chaos and Beauty

PART I INTRODUCTION
Chapter 1. Computers and Creativity
1.1 Objectives
1.2 Lateral Use of Computer Software Tools
1.3 Reading List for Chapter 1
Chapter 2. Hidden Words
2.1 "Digits, Symbols, Pictures"
2.2 Computers and Art
2.3 Computer Graphics: Past and Present
2.4 Computers: Past and Present
2.5 The Human Brain vs. the Computer Brain
2.5.1 The Human Brain
2.5.2 Human Computers
2.6 New Applications of Calculating: A Sampling and Digression
2.7 One Final Word
2.8 Reading List for Chapter 2
PART II REPRESENTING NATURE
Chapter 3. Fourier Transforms (The Prisms of Science)
3.1 Fourier Analysis: A Digression and Review
3.2 Singing Computers
3.3 "Bach, Beethoven, The Beatles"
3.4 Breathing Proteins
3.5 Cancer Genes (DNA Waveforms)
3.6 Reading List for Chapter 3
Chapter 4. Unusual Graphic Representations
4.1 Acoustics
4.2 New Ways of Displaying Data
4.3 Snowflakes from Sound: Art and Science
4.4 Medicine: Cardiology and SDPs
4.5 Another Dot-Display Used in Molecular Biophysics
4.6 Autocorrelation Cartoon-Faces for Speech
4.7 Cartoon Faces in Education
4.7.1 Cognitive Association of Coordinates with Facial Features
4.7.2 Target-Pictures for Children
4.7.3 Learning by Means of Analogy
4.8 Educational Aid for the Presentation of Statistical Concepts
4.9 Commercial and Military Air Traffic Control
4.10 Faces and Cancer Genes
4.11 Back to Acoustics: Phase Vectorgrams
4.12 Fractal Characterization of Speech Waveform Graphs
4.12.1 Scale Invariance
4.12.2 Fractal Characterization of Speech
4.12.3 Classification of Shapes
4.12.4 Speech Fractal Dimension
4.12.5 Catalog of Other Acoustic Sounds
4.13 A Monte Carlo Approach to Fractal Dimension
4.14 "Other Speech Graphics, Wigner Distributions, FM Synthesis"
4.14.1 Wigner Distribution
4.14.2 FM Synthesis of Speech
4.15 Molecular Genetics: DNA Vectorgram
4.15.1 Background
4.15.2 DNA Vectorgram
4.16 Reading List for Chapter 4
Chapter 5. Image Processing of the Shroud of Turin
5.1 Image Processing
5.2 The Shroud
5.3 A Sampling of Results of Past Scientific Examination
5.4 Past Image Processing Studies
5.5 Present Study
5.6 Pseudo-Gray Transformation via Look-up Table (LUT)
5.7 Processing via Pseudocolor LUT
5.8 Reading List for Chapter 5
Chapter 6. Physics: Charged Curves
6.1 Recipe for Accelerating the Iterative Pr
6.2 Reading List for Chapter 6
Chapter 7. Summary of Part II
"PART III PATTERN, SYMMETRY, BEAUTY"
Chapter 8. Genesis Equations (or Biological Feedback Forms)
8.1 Feedback
8.2 "A Computer Program "Bug"
8.3 Genesis Equations
8.3.1 The Leeuwenhoek Program
8.3.2 Brief Sampling of Past Work in Natural Object Creation
8.3.3 Biological Forms Generated from Mathematical Feedback Loops
8.3.4 The Habitation of Abstract Geometric Space
8.3.5 Creation and Search in the Manifold Dimensions of Space
8.4 Reading List for Chapter 8
Chapter 9. More Beauty from Complex Variables
9.1 Turbulent Complex Curls
9.2 Transcendental Functions in the µ Plane
9.2.1 "What is "cosh"?"
9.2.2 Review of Some Definitions of Terms Used in This Chapter
9.2.3 Graphics Gallery and Observations
9.2.4 Recipes for Cosh Pictures
9.2.5 Maps
9.3 How to Design Textures Using Recursive Composite Functions
9.3.1 Secrets and Tricks
9.3.2 Chaos and Pattern
9.3.3 Where Do We Go From Here?
9.3.4 Recipe
9.3.5 "Networks, Repeller-Towers"
9.4 Reading List for Chapter 9
Chapter 10. Mathematical Chaos
10.1 What is Chaos?
10.2 Pattern Formation and Chaos in Networks
10.2.1 Networks
10.2.2 Drawing the Network
10.2.3 Some Examples
10.2.4 Summary
10.2.5 Recipes for Generating Networks
10.2.6 Automatic Computer Generation of Networks
10.3 "Graphics, Bifurcation, Order and Chaos"
10.3.1 Recipe for Bifurcation Plot Generation
10.4 Image Processing Techniques and Deterministic Chaos
10.5 A Note on Rendering 3-D Strange Attractors
10.5.1 Recipe
10.6 Quaternion Images
10.6.1 Quaternion Julia Sets
10.7 A Note on Rendering Chaotic Repeller Distance-Towers
10.8 Reading List for Chapter 10
Chapter 11. Number Theory
11.1 Introduction
11.2 Exotic Symmetries from Large Pascal's Triangles
11.2.1 Computation
11.2.2 Nomenclature
11.2.3 Gaskets
11.2.4 Size Changes of Internal Triangles
11.2.5 Symmetries
11.2.6 Plotting a Complete PT
11.2.7 Perfect Numbers
11.2.8 Practical Importance
11.2.9 Future Work
11.3 Patterns in Hailstone (3n+1) Numbers
11.4 Is There a Double Smoothly Undulating Integer?
11.5 Reading List For Chapter 11
Chapter 12. Synthesizing Nature
12.1 Wild Monopodial Tendril Plant Growth
12.1.1 Spirals in Nature
12.1.2 Graphics Gallery of Plant
12.1.3 Natural Growth
12.1.4 Recipe for Picture Computation
12.2 How to Design with Directed Random Walks
12.2.1 Directed Random Walk
12.2.2 The Algorithm
12.2.3 Recipe for Transition Probability Plants
12.3 "A Sampling of Spirals in Science, Nature, and Art"
12.3.1 "Traditional Mathematical Spirals (Clothoid, Littus, et al.)"
12.3.2 Spirals Made by Humans
12.3.3 Strange Spirals
12.3.4 Galaxies
12.3.5 Seashells
12.3.6 Fuzzy Spirals
12.3.7 Spiral-Like Forms from Differential Equations
12.3.8 Trigonometric Iteration (Bushy Spirals)
12.3.9 Concluding Remarks on Spirals
12.4 A Vacation on Mars
12.5 Reading List for Chapter 12
Chapter 13. Synthesizing Ornamental Textures
13.1 Self-decorating Eggs
13.1.1 The Algorithm
13.1.2 Graphics Gallery
13.1.3 Summary of Egg Tiling Patterns
13.2 Self-Decorating Surfaces (Beauty from Noise)
13.2.1 Recipe
13.3 Biometric Art from Retinal Vascular Patterns
13.4 Reading List for Chapter 13
Chapter 14. Dynamical Systems
14.1 Time-discrete Phase Plans Associated with a Cyclic System
14.1.1 Recipe
14.2 Cyles and Centers in Time-Discrete Dynamical Systems
14.2.1 A Review of Some Definitions of Terms
14.3 Reading List for Chapter 14
Chapter 15. Numerical Approximation Methods
15.1 Halley Maps for a Trigonometric and Rational Function
15.1.1 Overrelaxation and Chaos
15.1.2 Buridan's Ass
15.2 "Beauty, Symmetry and Chaos in Chebyshev's Paradise"
15.2.1 Chebyshev Rings
15.3 Recipe for Chebyshev's Paradise
15.4 Reading List for Chapter 15
Chapter 16. Tesselation Automata Derived from a Single Defect
16.1 Method and Observations
16.1.1 TA Type 1
16.1.2 TA Type 2. Time Dependence of Rules
16.1.3 TA Type 3. Contest Between Defects
16.1.4 TA Type 4. Defects in a Centered Rectangular Lattice
16.1.5 TA Type 5. Large Local Neighborhood
16.2 Recipe for Tesselation Automata
16.3 Reading List for Chapter 16
Chapter 17. Summary of Part III and Conclusion of Book
Appendix A. Color Plates
Appendix B. Additional Recipes
B.1 Chaos from bits
B.2 Dynamical Systems
B.3 Cartoon Faces for Multidimensional Data Portrayal
B.4 Symmetrized Random-Dot Patterns
B.4.1 Recipe
B.4.2 Sqrt(r) Dot-Patterns
B.4.3 Cartoon Faces for Multidimensional Data Portrayal
B.5 Burnt Paper
B.6 Picturing Randomness with Truchet Tiles
B.7 Circles Which Kiss: A Note on Osculatory Pa
B.8 Markov Aggregation on a Sticky Circle
Appendix C. Suggestions for Future Experiments
Appendix D. Descriptions for Chapter Frontpiece Figures
References (General)
Recommended Reading
"Interesting and Unusual Newsletters, Distributors, Columns, Misc."
Recommended Journals
References by Topic and Section
Part I - Introduction
Part II - Representing Nature
"Part III - Pattern, Symmetry, and Beauty"
Additional Reading
Works of the Author
Glossary
Index
Credits
A Final Illustration of Chaos
Acknowledgements
About the Author

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