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Fractals and Chaos

Fractals and Chaos Author Benoit Mandelbrot
ISBN-10 9781475740172
Release 2013-06-29
Pages 308
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Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

Fractals and Scaling in Finance

Fractals and Scaling in Finance Author Benoit B. Mandelbrot
ISBN-10 9781475727630
Release 2013-03-09
Pages 551
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Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.

Thinking in Patterns

Thinking in Patterns Author Benoit B. Mandelbrot
ISBN-10 9812702741
Release 2004
Pages 323
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Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors. This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics OCo from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."

Chaos and Order in the Capital Markets

Chaos and Order in the Capital Markets Author Edgar E. Peters
ISBN-10 0471139386
Release 1996-08-30
Pages 274
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The latest developments in chaos theory – from an industry expert Chaos and Order in the Capital Markets was the first book to introduce and popularize chaos as it applies to finance. It has since become the classic source on the topic. This new edition is completely updated to include the latest ripples in chaos theory with new chapters that tie in today′s hot innovations, such as fuzzy logic, neural nets, and artificial intelligence. Critical praise for Peters and the first edition of Chaos and Order in the Capital Markets "The bible of market chaologists." – BusinessWeek "Ed Peters has written a first–class summary suitable for any investment professional or skilled investor." – Technical Analysis of Stocks & Commodities "It ranks among the most provocative financial books of the past few years. Reading this book will provide a generous payback for the time and mental energy expended." – Financial Analysts Journal This second edition of Chaos and Order in the Capital Markets brings the topic completely up to date with timely examples from today′s markets and descriptions of the latest wave of technology, including genetic algorithms, wavelets, and complexity theory. Chaos and Order in the Capital Markets was the very first book to explore and popularize chaos theory as it applies to finance. It has since become the industry standard, and is regarded as the definitive source to which analysts, investors, and traders turn for a comprehensive overview of chaos theory. Now, this invaluable reference – touted by BusinessWeek as "the bible of market chaologists" – has been updated and revised to bring you the latest developments in the field. Mainstream capital market theory is based on efficient market assumptions, even though the markets themselves exhibit characteristics that are symptomatic of nonlinear dynamic systems. As it explores – and validates – this nonlinear nature, Chaos and Order repudiates the "random walk" theory and econometrics. It shifts the focus away from the concept of efficient markets toward a more general view of the forces underlying the capital market system. Presenting new analytical techniques, as well as reexamining methods that have been in use for the past forty years, Chaos and Order offers a thorough examination of chaos theory and fractals as applied to investments and economics. This new edition includes timely examples from today′s markets and descriptions of cutting–edge technologies–genetic algorithms, wavelets, complexity theory–and hot innovations, such as fuzzy logic and artificial intelligence. Beyond the history of current capital market theory, Chaos and Order covers the crucial characteristics of fractals, the analysis of fractal time series through rescaled range analysis (R/S), the specifics of fractal statistics, and the definition and analysis of chaotic systems. It offers an in–depth exploration of: ∗ Random walks and efficient markets – the development of the efficient market hypothesis (EMH) and modern portfolio theory ∗ The linear paradigm – why it has failed ∗ Nonlinear dynamic systems – phase space, the Henon Map, Lyapunov exponents ∗ Applying chaos and nonlinear methods – neural networks, genetic algorithms ∗ Dynamical analysis of time series – reconstructing a phase space, the fractal dimension Tonis Vaga′s Coherent Market Hypothesis – the theory of social imitation, control parameters, Vaga′s implementations Plus, Chaos and Order now contains a Windows–compatible disk including data sets for running analyses described in the appendices. Written by a leading expert in the field, Chaos and Order in the Capital Markets has all the information you need for a complete, up–to–date look at chaos theory. This latest edition will undoubtedly prove to be as invaluable as the first.

The Fractal Geometry of Nature

The Fractal Geometry of Nature Author Benoit B. Mandelbrot
ISBN-10 0716711869
Release 1982-08-15
Pages 468
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Three classic fractals, tamed. Galaxies and eddies. Scaling fractals. Nonscaling fractals. Self-mapping fractals. Randomness. Stratified random fractals. Fractional brown fractals. A book-within-the-book, in color. Random tremas; texture. Miscellany. Of men and ideas.

Multifractals and 1 Noise

Multifractals and 1    Noise Author Benoit B. Mandelbrot
ISBN-10 9781461221500
Release 2013-12-20
Pages 442
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Mandelbrot is a world renowned scientist, known for his pioneering research in fractal geometry and chaos theory. In this volume, Mandelbrot defends the view that multifractals are intimately interrelated through the two fractal themes of "wildness" and "self-affinity". This link involves a powerful collection of technical tools, which are of use to diverse scientific communities. Among the topics covered are: 1/f noise, fractal dimension and turbulence, sporadic random functions, and a new model for error clustering on telephone circuits.

Dynamics in One Complex Variable AM 160

Dynamics in One Complex Variable   AM 160 Author John Milnor
ISBN-10 1400835534
Release 2011-02-11
Pages 320
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This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

Chaotic Modelling and Simulation

Chaotic Modelling and Simulation Author Christos H. Skiadas
ISBN-10 1420079018
Release 2008-10-20
Pages 364
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Offers Both Standard and Novel Approaches for the Modeling of Systems Examines the Interesting Behavior of Particular Classes of Models Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models. Using more than 500 graphs and illustrations, the authors show how to design, estimate, and test an array of models. Requiring little prior knowledge of mathematics, the book focuses on classical forms and attractors as well as new simulation methods and techniques. Ideas clearly progress from the most elementary to the most advanced. The authors cover deterministic, stochastic, logistic, Gaussian, delay, Hénon, Holmes, Lorenz, Rössler, and rotation models. They also look at chaotic analysis as a tool to design forms that appear in physical systems; simulate complicated and chaotic orbits and paths in the solar system; explore the Hénon–Heiles, Contopoulos, and Hamiltonian systems; and provide a compilation of interesting systems and variations of systems, including the very intriguing Lotka–Volterra system. Making a complex topic accessible through a visual and geometric style, this book should inspire new developments in the field of chaotic models and encourage more readers to become involved in this rapidly advancing area.

The Mis Behaviour of Markets

The  Mis Behaviour of Markets Author Benoit B. Mandelbrot
ISBN-10 9781847651556
Release 2010-10-01
Pages 352
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This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they have a shifting sense of time and wild behaviour that makes them volatile, dangerous - and beautiful. In his models, the complex gyrations of the FTSE 100 and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved.

The Colours of Infinity

The Colours of Infinity Author Nigel Lesmoir-Gordon
ISBN-10 1849964866
Release 2010-10-20
Pages 207
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A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory.

Chaos CNN Memristors and Beyond

Chaos  CNN  Memristors and Beyond Author Andrew Adamatzky
ISBN-10 9789814434812
Release 2013-01-02
Pages 564
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This invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first — cellular nonlinear networks, nonlinear circuits and cellular automata — deals with Chua's Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua's circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua's views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into ‘ancient memristors’, analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book. The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science. The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua's circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike. Contents:Cellular Nonlinear Networks, Nonlinear Circuits and Cellular Automata:Genealogy of Chua's Circuit (Peter Kennedy)Impasse Points, Mutators, and Other Chua Creations (Hyongsuk Kim)Chua's Lagrangian Circuit Elements (Orla Feely)From CNN Dynamics to Cellular Wave Computers (Tamas Roska)Contributions of CNN to Bio-Robotics and Brain Science (Paolo Arena and Luca Patané)From Radio-amateurs' Electronics to Toroidal Chaos (Otto E Rössler and Christophe Letellier)Analyzing the Dynamics of Excitatory Neural Networks by Synaptic Cellular Automata (V Nekorkin, A Dmitrichev, D Kasatkin and V Afraimovich)Dynamical Systems Perspective of Wolfram's Cellular Automata (M Courbage and B Kamińki)The Genesis of Chua's Circuit: Connecting Science, Art and Creativity (Francesca Bertacchini, Eleonora Bilotta, Giuseppe Laria and Pietro Pantano)Nonlinear Electronics Laboratory (NOEL): A Reminiscence (Chai Wah Wu)Bursting in Cellular Automata and Cardiac Arrhythmias (Gil Bub, Alvin Shrier and Leon Glass)Local Activity Principle: The Cause of Complexity and Symmetry Breaking (Klaus Mainzer)Explorations in the Forest of Bifurcation Trees: Route from Chua's Circuit to Chua's Memristive Oscillator (Łukasz Czerwiński and Maciej J Ogorzałek)Chua's Nonlinear Dynamics Perspective Cellular Automata (Giovanni E Pazienza)Application of CNN to Brainlike Computing (Bertram E Shi)Ideal Turbulence Phenomenon and Transmission Line with Chua's Diode (E Yu Romanenko and A N Sharkovsky)Chaos in Electronic Circuits: Chua's Contribution (1980–2000) (Christophe Letellier)Dynamical Systems and Chaos:Connectivity of Julia Sets for Singularly Perturbed Rational Maps (Robert L Devaney and Elizabeth D Russell)Structural Transformations and Stability of Dynamical Networks (L A Bunimovich and B Z Webb)Chua's Time (Arturo Buscarino, Luigi Fortuna and Mattia Frasca)Chaotic Neural Networks and Beyond (Kazuyuki Aihara, Taiji Yamada and Makito Oku)Chaotic Neocritical Dynamics (Walter J Freeman)Nonlinear Dynamics of a Class of Piecewise Linear Systems (M Lakshmanan and K Murali)Chaotic Mathematical Circuitry (R Lozi)Chua's Equation was Proved to be Chaotic in Two Years, Lorenz Equation in Thirty Six Years (Bharathwaj Muthuswamy)Toward a Quantitative Formulation of Emergence (G Nicolis)Controlled Synchronization of Chaotic Oscillators with Huygens' Coupling (J Peńa-Ramírez, R H B Fey and H Nijmeijer)Using Time-Delay Feedback for Control and Synchronization of Dynamical Systems (Kestutis Pyragas, Viktoras Pyragas and Tatjana Pyragiene)Models of Catastrophic Events and Suggestions to Foretell Them (Yves Pomeau and Martine Le Berre)Synchronization Propensity in Networks of Dynamical Systems: A Purely Topological Indicator (Stefano Fasani and Sergio Rinaldi)Further Progress in Partial Control of Chaotic Systems (Juan Sabuco, Miguel Sanjuan and Samuel Zambrano)Phase and Complete Synchronizations in Time-Delay Systems (D V Senthilkumar, M Manju Shrii and J Kurths)Symbolic Dynamics and Spiral Structures due to the Saddle-Focus Bifurcations (Andrey Shilnikov, Leonid Shilnikov and Roberto Barrio)Dynamics of Periodically Forced Mass Point on Constrained Surface with Changing Curvature (Yoshisuke Ueda)Solitons for Describing 3-D Physical Reality: The Current Frontier (Paul J Werbos)Thermal Solitons in 1D and 2D Anharmonic Lattices — Solectrons and the Organization of Non-Linear Fluctuations in Long-Living Dynamical Structures (M G Velarde, W Ebeling and A P Chetverikov)Global Optimizations by Intermittent Diffusion (Shui-Nee Chow, Tzi-Sheng Yang and Hao-Min Zhou)Memristors:How We Found the Missing Memristor (R Stanley Williams)Aftermath of Finding the Memristor (R Stanley Williams)The Singing Arc: The Oldest Memristor? (Jean-Marc Ginoux and Bruno Rossetto)Two Centuries of Memristors (Themistoklis Prodromakis)State Equations for Active Circuits with Memristors (Martin Hasler)Analytical Analysis of Memristive Networks (Torsten Schmidt, Willi Neudeck, Ute Feldmann and Ronald Tetzlaff)Hardware Memristor Emulators (Andrew L Fitch, Herbert H C Iu and Chi K Tse)Leon Chua's Memristor (Guanrong Chen) Readership: Graduate students, researchers and academics in all engineering disciplines as well as historians of science. Keywords:Memristors;CNN;Chaos;Dynamical SystemsKey Features:Unique personality of Leon Chua and enormity of his achievements underpins the structure of the bookConglomerate of hot topics: memristors, chaos, computationalOriginal papers from renown scholars and researchers as well as numerous tutorials and historical expositions on each of the topicsHigh pedagogical value makes the book a timeless referenceReviews: "It is a veritable kaleidoscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike." Zentralblatt MATH

Robust Chaos and Its Applications

Robust Chaos and Its Applications Author Elhadj Zeraoulia
ISBN-10 9789814374071
Release 2012
Pages 454
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Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.

Gaussian Self Affinity and Fractals

Gaussian Self Affinity and Fractals Author Benoit Mandelbrot
ISBN-10 0387989935
Release 2002
Pages 654
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A premier scientist in the field of fractal geometry focuses on a detailed study of fraction Brownian motions and presents the fractal themes of "self-affinity" and "globality." The book includes extensive introductory material and presents a number of striking new observations and conjectures. 50 illus.

The Mathematical Gazette

The Mathematical Gazette Author
ISBN-10 UCSD:31822032891137
Release 2005
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The Mathematical Gazette has been writing in one form or another for most of life. You can find so many inspiration from The Mathematical Gazette also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Mathematical Gazette book for free.

Fractals Graphics and Mathematics Education

Fractals  Graphics  and Mathematics Education Author Michael Frame
ISBN-10 0883851695
Release 2002-06-20
Pages 206
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Teaching resources for use with courses on fractal geometry, lecturers and interested readers.

The Fractalist

The Fractalist Author Benoit B. Mandelbrot
ISBN-10 9780307377357
Release 2012
Pages 324
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A personal account by the late research scientist who revolutionized visual geometry with his ideas about fractals traces his early life as member of a Lithuanian Jewish family in early 20th-century Warsaw, his broad education in Europe and America and his long-time affiliation with IBM, Harvard and Yale. 40,000 first printing.

An Eye for Fractals

An Eye for Fractals Author Michael D. McGuire
ISBN-10 UOM:39015056636197
Release 1991-01
Pages 165
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Offers an examination of fractals, discussing their discovery and their properties