Yumei Dang is a computer scientist working for Lucent Technologies. This book is based on her doctoral thesis at the University of Illinois at Chicago.
Lou Kauffman is a mathematics professor at the University of Illinois at Chicago. He works in knot theory, differential topology, and diagrammatic mathematics.
Dan Sandin is the director of the Electronic Visualization Laboratory at the University of Illinois at Chicago. He is a pioneer in the fields of virtual reality and video.
Hypercomplex Iterations. Distance Estimation And Higher Dimensional Fractals, Cd-Rom Included
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- Retrait Click and Collect en magasin gratuit
- Nombre de pages144
- PrésentationRelié
- Poids0.505 kg
- Dimensions16,0 cm × 23,8 cm × 1,7 cm
- ISBN981-02-3296-9
- EAN9789810232962
- Date de parution26/09/2002
- CollectionKnots and everything
- ÉditeurWorld Scientific Publishing
Résumé
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.