Chaos and fractals [electronic resource] : a computer graphical journey : ten year compilation of advanced research / edited by Clifford A. Pickover.
- Amsterdam ; New York : Elsevier, 1998.
1 online resource (469 p.)
- Computer graphics.
- Electronic books.
- These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteratio
- Front Cover; CHAOS AND FRACTALS; Copyright Page; Preface; Introduction; Contents; Part I: Geometry and Nature; Chapter 1. Chaos game visualization of sequences; Chapter 2. Tumor growth simulation; Chapter 3. Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems; Chapter 4. Generating fractals from Voronoi diagrams; Chapter 5. Circles which kiss: a note on osculatory packing; Chapter 6. Graphical identification of spatio-temporal chaos; Chapter 7. Manifolds and control of chaotic systems
Chapter 8. A vacation on Mars - an artist's journey in a computer graphics worldPart II: Attractors; Chapter 9. Automatic generation of strange attractors; Chapter 10. Attractors with dueling symmetry; Chapter 11. A new feature in Henon's map; Chapter 12. Lyapunov exponents of the logistic map with periodic forcing; Chapter 13. Toward a better understanding of fractality in nature; Chapter 14. On the dynamics of real polynomials on the plane; Chapter 15. Phase portraits for parametrically excited pendula: an exercise in multidimensional data visualisation
Chapter 16. Self-reference and paradox in two and three dimensionsChapter 17. Visualizing the effects of filtering chaotic signals; Chapter 18. Oscillating iteration paths in neural networks learning; Chapter 19. The crying of fractal batrachion 1,489; Chapter 20. Evaluating pseudo-random number generators; Part III: Cellular Automata, Gaskets, and Koch Curves; Chapter 21. Sensitivity in cellular automata: some examples; Chapter 22. One tub, eight blocks, twelve blinkers and other views of life; Chapter 23. Scouts in hyperspace; Chapter 24. Sierpinski fractals and GCDs
Chapter 25. Complex patterns generated by next nearest neighbors cellular automataChapter 26. On the congruence of binary patterns generated by modular arithmetic on a parent array; Chapter 27. A simple gasket derived from prime numbers; Chapter 28. Discrete approximation of the Koch curve; Chapter 29. Visualizing Cantor cheese construction; Chapter 30. Notes on Pascal's pyramid for personal computer users; Chapter 31. Patterns generated by logical operators; Part IV: Mandelbrot, Julia and Other Complex Maps
Chapter 32. A tutorial on efficient computer graphic representations of the Mandelbrot setChapter 33. Julia sets in the quaternions; Chapter 34. Self-similar sequences and chaos from Gauss sums; Chapter 35. Color maps generated by ""trigonometric iteration loops""; Chapter 36. A note on Halley's method; Chapter 37. A note on some internal structures of the Mandelbrot set; Chapter 38. The method of secants; Chapter 39. A generalized Mandelbrot set and the role of critical points; Chapter 40. A new scaling along the spike of the Mandelbrot set; Chapter 41. Further insights into Halley's method
Chapter 42. Visualizing the dynamics of the Rayleigh quotient iteration
- Description based upon print version of record.
Includes bibliographical references and indexes.
- Pickover, Clifford A.
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