Hypercomplex Interations, Distance Estimation and Higher Dimensional Fractals
by Yumei Dang;Louis H DangKauffman (9789810232962)

Hypercomplex Interations, Distance Estimation and Higher Dimensional Fractals
 

Yumei Dang;Louis H DangKauffman


Release Date: 01 August 2002
Format: Mixed media product
Pages: 150
Category: Discrete Mathematics
Publisher: World Scientific Publishing Company
ISBN: 9789810232962
ISBN-10: 9810232969



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.

AUD $103.95

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