Hypercomplex Iterations. Distance Estimation and Higher Dimensional Fractals, CD-ROM Included Livre électronique


Hypercomplex Iterations. Distance Estimation and Higher Dimensional Fractals, CD-ROM Included - Daniel Sandin pdf epub

PRIX: GRATUIT

INFORMATION

LANGUE: FRANÇAIS
L'HISTOIRE: 26/09/2002
ÉCRIVAINE/ÉCRIVAIN: Daniel Sandin
ISBN: 981-02-3296-9
FORMAT: PDF EPUB MOBI TXT
TAILLE DU FICHIER: 4,45

EXPLICATION:

In 1843, after a 15-year search, Sir William Rowan Hamilton discovered the quaternions, the highly significant algebra of four-dimensional space. A century later, in his round-breaking work The Fractal Geometry of Nature (1977), Benoit Mandelbrot brought mathematical iterations and their images into the world of applications and simulations. Intricate infinite mathematical tapestries entered the domains of statistical physics and computer-generated natural scenes. In this book, we study the mathematics and graphical geometry of quaternionic iterations, combining the insights of Hamilton and Mandelbrot with our own work on the mathematics of quaternionic and hypercomplex distance estimation. Our distance estimation algorithms are generalizations of algorithms known to work over the complex numbers. Proofs that justify the original distance estimation algorithm rely on delicate and subtle complex analysis. In order to justify the generalized algorithms, we needed to find new proofs that would apply to hypercomplex numbers. Our proofs turn out to be surprisingly simple and geometrical. The book details many different points of view about distance estimation, gives algorithms for computing these images and is accompanied by an interactive CD-ROM with much additional information.

... was originally applied to Julia sets and the Mandelbrot set in the complex plane ... PDF BC7ED FG>@7HD-I 'K*O1436, '09P; .0= >@QSRT/TU. 7E ... - evl ... . 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 ... Buy Hypercomplex Iterations: Distance Estimation And Higher Dimensional Fractals (With Cd Rom) (Series on Knots & Everything) Har/Cdr by Yumei Dang, Louis H. Kauffman, Daniel Sandin (ISBN: 9789810232962) from Amazon's Book Store. Everyda ... Comptines des crèches à mimer PDF Gratuit - Le livre ... . Kauffman, Daniel Sandin (ISBN: 9789810232962) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. A proof of this was later given by Dang, Kaufmann, and Sandin in the book Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals (2002). I used the same distance estimator formula, when drawing the 3D hypercomplex images in the last post - it seems to be quite generic and applicable to most polynomial escape time fractal ... Hypercomplex Iterations, Distance Estimation and Higher Dimensional Fractals Yumei Dang , Louis H. Kauffman , Daniel J. Sandin This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. Hypercomplex Iterations -- Distance Estimation and Higher Dimensional Fractals « on: March 09, 2007, 09:25:28 PM » The Electronic Visualization Laboratory (EVL) is an interdisciplinary graduate research laboratory that com...