Application Of Chaos And Fractals To Computer Vision
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Application Of Chaos And Fractals To Computer Vision
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Author : Michael E. Farmer
language : en
Publisher: Bentham Science Publishers
Release Date : 2015-07-23
Application Of Chaos And Fractals To Computer Vision written by Michael E. Farmer and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-23 with Computers categories.
This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithms are very helpful for a broad range of computer vision problems like motion segmentation, texture analysis and change detection. The contents of this book include chapters in biological vision systems, foundations of chaos and fractals, behavior of images and image sequences in phase space, mathematical measures for analyzing phase space, applications to pre-attentive vision and applications to post-attentive vision. This book is intended for graduate students, upper division undergraduates, researchers and practitioners in image processing and computer vision. The readers will develop a solid understanding of the concepts of chaos theory and their application to computer vision. Readers will be introduced to a new way of thinking about computer vision problems from the perspective of complex dynamical systems. This new approach will provide them a deeper understanding of the various phenomena present in complex image scenes.
Chaos And Fractals
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Author : C.A. Pickover
language : en
Publisher: Elsevier
Release Date : 1998-08-03
Chaos And Fractals written by C.A. Pickover and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-03 with Computers categories.
These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.
Chaos And Fractals The Mathematics Behind The Computer Graphics
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Author : Robert L. Devaney
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Chaos And Fractals The Mathematics Behind The Computer Graphics written by Robert L. Devaney and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
"Robert Devaney communicates his deep understanding as well as his enthusiasm for chaos, fractals, and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Equations and graphs are clearly shown with computer-generated characters, and Devaney's explanations are lucid and instructive. Illustrating the mathematics are forays into the colorful, unpredictable world of fractals and Julia sets. Devaney explains how the computer is used to generate the pictures and shows how the various colors are chosen for graphical representations ... Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate ... the clarity of exposition and the sheer beauty of the graphics."--Container.
Fractals And Chaos
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Author : A.J. Crilly
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fractals And Chaos written by A.J. Crilly and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. A fractal object is self-similar in that subsections of the object are similar in some sense to the whole object.
Applications Of Fractals And Chaos
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Author : A.J. Crilly
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Applications Of Fractals And Chaos written by A.J. Crilly and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Computers categories.
Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.
Introduction To Chaos Fractals And Dynamical Systems
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Author : Phillip A Laplante
language : en
Publisher: World Scientific
Release Date : 2023-07-26
Introduction To Chaos Fractals And Dynamical Systems written by Phillip A Laplante and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-26 with Mathematics categories.
This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems particularly focuses on natural and human phenomenon that can be modeled as fractals, using simple examples to explain the theory of chaos and how it affects all of us. Then, using straightforward mathematic and intuitive descriptions, computer generated graphics and photographs of natural scenes are used to illustrate the beauty of fractals and their importance in our world. Finally, the concept of Dynamical Systems, that is, time-dependent systems, the foundation of Chaos and Fractal, is introduced. Everyday examples are again used to illustrate concepts, and the importance of understanding how these vital systems affect our lives. Throughout the fascinating history of the evolution of chaos theory, fractals and dynamical systems is presented, along with brief introductions to the scientists, mathematicians and engineers who created this knowledge.Introduction to Chaos, Fractals and Dynamical Systems contains ample mathematical definitions, representations, discussions and exercises, so that this book can be used as primary or secondary source in home schooling environments.The book is suitable for homeschooling as a focused course on the subject matter or as a classroom supplement for a variety of courses at the late junior high or early high-school level. For example, in addition to a standalone course on Chaos, Fractals and Dynamical Systems (or similar title), this book could be used with the following courses:The text can also be used in conjunction with mathematics courses for undergraduates for non-science majors. The book can also be used for informal and lively family study and discussion.For each chapter, exercises and things to do are included. These activities range from simple computational tasks to more elaborate computer projects, related activities, biographical research and writing assignments.
Multi Chaos Fractal And Multi Fractional Artificial Intelligence Of Different Complex Systems
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Author : Yeliz Karaca
language : en
Publisher: Academic Press
Release Date : 2022-06-22
Multi Chaos Fractal And Multi Fractional Artificial Intelligence Of Different Complex Systems written by Yeliz Karaca and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-22 with Science categories.
Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.
Chaos And Fractals
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Author : Heinz-Otto Peitgen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Chaos And Fractals written by Heinz-Otto Peitgen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Chaos Fractals And Dynamics
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Author : Robert L. Devaney
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1990
Chaos Fractals And Dynamics written by Robert L. Devaney and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.
Fractals Chaos Power Laws
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Author : Manfred Schroeder
language : en
Publisher: Courier Corporation
Release Date : 2009-08-21
Fractals Chaos Power Laws written by Manfred Schroeder and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-21 with Science categories.
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.