TY - BOOK ID - 77942662 TI - Hypercomplex iterations : distance estimation and higher dimensional fractals AU - Dang, Yumei. AU - Kauffman, Louis H. AU - Sandin, Daniel J. PY - 2002 SN - 9812778608 9789812778604 9810232969 9789810232962 PB - Singapore ; River Edge, NJ : World Scientific, DB - UniCat KW - Iterative methods (Mathematics) KW - Quaternions. KW - Mandelbrot sets. KW - Fractals. KW - Fractal geometry KW - Fractal sets KW - Geometry, Fractal KW - Sets, Fractal KW - Sets of fractional dimension KW - Dimension theory (Topology) KW - Molecules, Mu KW - Mu molecules KW - Sets, Mandelbrot KW - Fractals KW - Algebra, Universal KW - Algebraic fields KW - Curves KW - Surfaces KW - Numbers, Complex KW - Vector analysis KW - Iteration (Mathematics) KW - Numerical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:77942662 AB - 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 it ER -