Hypercomplex Iterations: Distance Estimation And Higher Dimensional Fractals (With Cd Rom) PDF Download
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Author: Yumei Dang
Publisher: World Scientific
ISBN: 9814496804
Category : Computers
Languages : en
Pages : 163
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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.
Author: Yumei Dang
Publisher: World Scientific
ISBN: 9814496804
Category : Computers
Languages : en
Pages : 163
Get Book Here
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.
Author: Yumei Dang
Publisher:
ISBN: 9789810232962
Category : Fractals
Languages : en
Pages : 144
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Book Description
Author: Hector Sabelli
Publisher: World Scientific
ISBN: 9814481335
Category : Science
Languages : en
Pages : 670
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Book Description
This book focuses on a prototype of creative causal processes termed BIOS and how the concept can be applied to the physical world, in medicine and in social science. This book presents methods for identifying creative features in empirical data; studies showing biotic patterns in physical, biological, and economic processes; mathematical models of bipolar (positive and negative) feedback that generate biotic patterns. These studies support the hypothesis that natural processes are creative (not determined) and causal (not random) and that bipolar feedback plays a major role in their evolution. Simple processes precede, coexist, constitute and surround the complex systems they generate (priority of the simple). In turn, complex processes feedback and transform simpler ones (supremacy of the complex).
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 930
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Book Description
Author: Andrzej Katunin
Publisher: CRC Press
ISBN: 1351801201
Category : Computers
Languages : en
Pages : 104
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Book Description
This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry – a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.
Author: Yumei Dang
Publisher:
ISBN:
Category :
Languages : en
Pages : 294
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Book Description
Author: Rafal Ablamowicz
Publisher: Springer Science & Business Media
ISBN: 1461581575
Category : Mathematics
Languages : en
Pages : 328
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Book Description
This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.
Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1475747403
Category : Mathematics
Languages : en
Pages : 1013
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Book Description
For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
Author: Sergeĭ Petrovich Novikov
Publisher: World Scientific
ISBN: 981283687X
Category : Mathematics
Languages : en
Pages : 278
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Book Description
1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby
Author: José Braz
Publisher: Springer
ISBN: 3540752749
Category : Computers
Languages : en
Pages : 408
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Book Description
This book includes selected papers of the VISAPP and GRAPP International Conferences 2006, held in Funchal, Madeira, Portugal, February 25-28, 2006. The 27 revised full papers presented were carefully reviewed and selected from 314 submissions. The topics include geometry and modeling, rendering, animation and simulation, interactive environments, image formation and processing, image analysis, image understanding, motion, tracking and stereo vision.
