| Description |
1 online resource (xv, 144 pages) : illustrations (some color). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
K & E series on knots and everything ; v. 17
|
|
K & E series on knots and everything ; v. 17.
|
| Bibliography |
Includes bibliographical references (pages 139-141) and index. |
| Note |
Accompanied by CD-ROM containing an interactive tour of the space of hypercomplex Julia sets and an educational mini-documentary introducing fractals and hypercomplex geometry. |
| Contents |
pt. 1. Introduction. ch. 1. Hypercomplex iterations in a nutshell -- ch. 2. Deterministic fractals and distance estimation -- pt. 2. Classical analysis: complex and quaternionic. ch. 3. Distance estimation in complex space -- ch. 4. Quaternion analysis -- ch. 5. Quaternions and the Dirac string trick -- pt. 3. Hypercomplex iterations. ch. 6. Quaternion Mandelbrot sets -- ch. 7. Distance estimation in higher dimensional spaces -- pt. 4. inverse iteration, ray tracing and virtual reality. ch. 8. Inverse iteration: an interactive visualization -- ch. 9. Ray tracing methods by distance estimation -- ch. 10. Quaternion deterministic fractals in virtual reality. |
| Summary |
This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex plane. It was justified, through the work of Douady and Hubbard, by deep results in complex analysis. In this book, the authors generalise the distance estimation to quaternionic and other higher dimensional fractals, including fractals derived from iteration in the Cayley numbers (octonionic fractals). The generalization is justified by new geometric arguments that circumvent the need for complex analysis. This puts on a firm footing the authors' present work and the second author's earlier work with John Hart and Dan Sandin. The results of this book will be of great interest to mathematicians and computer scientists interested in fractals and computer graphics. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Iterative methods (Mathematics)
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Iterative methods (Mathematics) |
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Quaternions.
|
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Quaternions. |
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Mandelbrot sets.
|
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Mandelbrot sets. |
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Fractals.
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Fractals. |
| Genre/Form |
Electronic books.
|
| Added Author |
Kauffman, Louis H., 1945-
|
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Sandin, Daniel J.
|
| Added Title |
Distance estimation and higher dimensional fractals |
| Other Form: |
Print version: Dang, Yumei. Hypercomplex iterations. River Edge, NJ : World Scientific, ©2002 9810232969 9789810232962 (DLC) 2003545471 (OCoLC)52887332 |
| ISBN |
9789812778604 (electronic book) |
|
9812778608 (electronic book) |
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