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Hypercomplex Interations, Distance Estimation and Higher Dimensional Fractals

By: Yumei Dang, Louis H Kauffman, Daniel Sandin

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Hardcover | 1 August 2002

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Hardcover
164 Pages

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23.5 x 15.88 x 1.91

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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 quatemionic 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.

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?The subject is very interesting and very modern. The book is very well written and contains various coloured fractal images.?

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Non-Fiction Mathematics Calculus & Mathematical Analysis Geometry Fractal Geometry Mathematical Foundation Applied Mathematics Booktopia Publisher Services World Scientific Publishing

Acknowledgements
Preface
Introduction	p. 1
Hypercomplex Iterations in a Nutshell	p. 3
Deterministic Fractals and Distance Estimation	p. 11
Classical Analysis: Complex and Quaternionic	p. 15
Distance Estimation in Complex Space	p. 17
Quaternion Analysis	p. 39
Quaternions and the Dirac String Trick	p. 57
Hypercomplex Iterations	p. 63
Quaternion Mandelbrot Sets	p. 65
Distance Estimation in Higher Dimensional Spaces	p. 71
Inverse Iteration, Ray Tracing and Virtual Reality	p. 89
Inverse Iteration: An Interactive Visualization	p. 91
Ray Tracing Methods by Distance Estimation	p. 107
Quaternion Deterministic Fractals in Virtual Reality	p. 129
App. A	p. 135
App. B	p. 137
Bibliography	p. 139
Index	p. 143
Table of Contents provided by Blackwell. All Rights Reserved.

Hypercomplex Interations, Distance Estimation and Higher Dimensional Fractals

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Hardcover

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