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
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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: 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: 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: José Braz
Publisher: Springer Science & Business Media
ISBN: 3540752722
Category : Computers
Languages : en
Pages : 407
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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.
Author: Rachel Armstrong
Publisher:
ISBN: 9781950192182
Category :
Languages : en
Pages : 600
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Book Description
If we lived in a liquid world, the concept of a "machine" would make no sense. Liquid life is metaphor and apparatus that discusses the consequences of thinking, working, and living through liquids. It is an irreducible, paradoxical, parallel, planetary-scale material condition, unevenly distributed spatially, but temporally continuous. It is what remains when logical explanations can no longer account for the experiences that we recognize as part of "being alive."Liquid Life references a third-millennial understanding of matter that seeks to restore the agency of the liquid soul for an ecological era, which has been banished by reductionist, "brute" materialist discourses and mechanical models of life. Offering an alternative worldview of the living realm through a "new materialist" and "liquid" study of matter, Armstrong conjures forth examples of creatures that do not obey mechanistic concepts like predictability, efficiency, and rationality. With the advent of molecular science, an increasingly persuasive ontology of liquid technologies can be identified. Through the lens of lifelike dynamic droplets, the agency for these systems exists at the interfaces between different fields of matter/energy that respond to highly local effects, with no need for a central organizing system.Liquid Life seeks an alternative partnership between humanity and the natural world. It provokes a re-invention of the languages of the living realm to open up alternative spaces for exploration, including contributor Rolf Hughes' "angelology" of language, which explores the transformative invocations of prose poetry, and Simone Ferracina's graphical notations that help shape our concepts of metabolism, upcycling, and designing with fluids. A conceptual and practical toolset for thinking and designing, liquid life reunites us with the irreducible "soul substance" of living things, which will neither be simply "solved," nor go away.
Author: Xin-She Yang
Publisher: Springer
ISBN: 3319676695
Category : Technology & Engineering
Languages : en
Pages : 332
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Book Description
This book reviews the state-of-the-art developments in nature-inspired algorithms and their applications in various disciplines, ranging from feature selection and engineering design optimization to scheduling and vehicle routing. It introduces each algorithm and its implementation with case studies as well as extensive literature reviews, and also includes self-contained chapters featuring theoretical analyses, such as convergence analysis and no-free-lunch theorems so as to provide insights into the current nature-inspired optimization algorithms. Topics include ant colony optimization, the bat algorithm, B-spline curve fitting, cuckoo search, feature selection, economic load dispatch, the firefly algorithm, the flower pollination algorithm, knapsack problem, octonian and quaternion representations, particle swarm optimization, scheduling, wireless networks, vehicle routing with time windows, and maximally different alternatives. This timely book serves as a practical guide and reference resource for students, researchers and professionals.
Author: Matti Pitkanen
Publisher: Bentham Science Publishers
ISBN: 1681081792
Category : Science
Languages : en
Pages : 1235
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Book Description
Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.
Author: Cristian Calude
Publisher: World Scientific
ISBN: 9812770828
Category : Science
Languages : en
Pages : 466
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Book Description
The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.
Author: Stephen Lynch
Publisher: Springer Science & Business Media
ISBN: 0817645861
Category : Mathematics
Languages : en
Pages : 481
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Book Description
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
