ENGLISH

Hypercomplex Iterations, Distance Estimation and Higher Dimensional Fractals

By Louis H. Kauffman , Yumei Dang , Daniel J. Sandin

Book information

Publisher
World Scientific Publishing Company
Year
2002
ISBN
9789810232962, 981-02-3296-9
Open Library ID
OL3778593M
Language
english
Format
PDF
Filesize
7 MB (7175555 bytes)
Series
Series on Knots and Everything , Vol 17
Pages
162\162
Topic
Computers
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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 generalize 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.

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