Wow! eBook
HYPERCOMPLEX ITERATIONS: DISTANCE ESTIMATION AND HIGHER DIMENSIONAL FRACTALS (WITH CD ROM) (Knots and Everything)
Author(s):Yumei Dang (Author), Louis H Kauffman (Author), Daniel Sandin (Author)
- Publisher: World Scientific Publishing Company
- Publication Date: November 1, 2002
- Language: English
- Print length: 164 pages
- ISBN-10: 9810232969
- ISBN-13: 9789810232962
Book 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 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.
Editorial Reviews
Review
?The subject is very interesting and very modern. The book is very well written and contains various coloured fractal images.?
