The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Macmillan

ISBN: 9780716711865

Category: Juvenile Nonfiction

Page: 468

View: 7223

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.

The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Times Books


Category: Juvenile Nonfiction

Page: 468

View: 989

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.

The Misbehavior of Markets

A Fractal View of Financial Turbulence

Author: Benoit Mandelbrot,Richard L. Hudson

Publisher: Hachette UK

ISBN: 0465004687

Category: Mathematics

Page: 368

View: 1796

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change. In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again.

Measure, Topology, and Fractal Geometry

Author: Gerald Edgar

Publisher: Springer Science & Business Media

ISBN: 0387747494

Category: Mathematics

Page: 272

View: 2783

Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

Fractals, Graphics, and Mathematics Education

Author: Michael Frame,Benoit Mandelbrot

Publisher: Cambridge University Press

ISBN: 9780883851692

Category: Computers

Page: 206

View: 2775

Teaching resources for use with courses on fractal geometry, lecturers and interested readers.

Fractal Geometry in Architecture and Design

Author: Carl Bovill

Publisher: Springer Science & Business Media

ISBN: 1461208432

Category: Mathematics

Page: 195

View: 9095

na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.

Introducing Fractal Geometry

Author: Nigel Lesmoir-Gordon,Will Rood

Publisher: Totem Books

ISBN: 9781840461237

Category: Study Aids

Page: 174

View: 1298

Fractal geometry is the geometry of the natural world and is an extension of classical geometry.

Clouds Are Not Spheres: A Portrait Of Benoit Mandelbrot, The Founding Father Of Fractal Geometry

Author: Lesmoir-gordon Nigel

Publisher: World Scientific

ISBN: 1786344769

Category: Science

Page: 124

View: 4209

The time is right, following Benoît Mandelbrot's death in 2010, to publish this landmark book about the life and work of this maverick math genius. This compact book celebrates the life and achievements of Benoît Mandelbrot with the ideas of fractals presented in a way that can be understood by the interested lay-person. Mathematics is largely avoided. Instead, Mandelbrot's ideas and insights are described using a combination of intuition and pictures. The early part of the book is largely biographical, but it portrays well how Mandelbrot's life and ideas developed and led to the fractal notions that are surveyed in the latter parts of the book. CLOUDS PROMO from NIGEL LESMOIR-GORDON on Vimeo. Contents: ForewordPrefaceIntroductionThe Early YearsCaltech and to France Once MoreThe USA, France and IBMThe Birth of Fractal GeometryThe Mandelbrot SetThe Fractal Geometry of NatureThe Art of FractalsPractical FractalsIn RetrospectBenoit and NigelAwards and Publications Readership: Aimed at a general inquisitively-minded readership. It will appeal to those seeking to understand fractal geometry in particular and mathematics in general. The book will appeal to readers of all ages. It will not be technically difficult or demand a deep understanding of mathematics. It will find a wide readership as a popular science book as well as appealing to academics, who like to read about the lives, struggles and achievements of their fellow scientists. The book is written for a very broad audience with minimal scientific or mathematical background. It may interest those who have come across fractals or the Mandelbrot set in some context and who want to find out more about what fractals are and about their progenitor. Keywords: Benoît Mandelbrot;Fractal Geometry;Fractals;The Mandelbrot Set;Math;Geometry of NatureReview: "There's much to recommend in this text. Nigel's collection of quotations taken from interviews he conducted provide valuable insights, many unavailable in print in any other place. Also, Nigel has assembled nice examples in chapters 7 and 8, some are familiar, some are less well-known, some will surprise readers. His overall picture is a useful addition to the literature about one of the most creative scientists of the 20th century. I look forward to seeing it in print." Michael Frame Yale University "With its stunning pictures and lucid text, Clouds Are Not Spheres celebrates the works and the life of this remarkable man." Emeritus Professor Ian Stewart University of Warwick "It is a fine popular biography that will appeal to a far wider audience than any other book which focuses on Mandelbrot." Nathan Cohen Fractal Antenna Systems, Inc. "I read Nigel's Clouds Are Not Spheres and enjoyed it very much ... Benoît influenced a new generation of mathematicians and scientists for whom fractals are an integral part of their knowledge, vision, applications and enjoyment ... I recommend this publication." Michael Shlesinger Office of Naval Research, Arlington, USA "The book is clearly written and easy to read and the illustrations are well-chosen and helpful. The reader will com

The Colours of Infinity

The Beauty and Power of Fractals

Author: Nigel Lesmoir-Gordon

Publisher: Springer Science & Business Media

ISBN: 9781849964869

Category: Mathematics

Page: 207

View: 371

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.

Bildkompression mit Fraktalen

Author: Michael F. Barnsley,Lyman P. Hurd

Publisher: Vieweg+Teubner Verlag

ISBN: 9783322868299

Category: Technology & Engineering

Page: 232

View: 2558

Das Buch, ursprünglich 1993 in englischer Sprache erschienen, ist das Standardwerk zu einem der wichtigsten Kompressionsverfahren für Bilddateien, geschrieben von den Erfindern Michael Barnsley und Lyman Hurd. Es spannt den Bogen von den mathematischen Grundlagen, von der Modellierung von "Realweltbildern" bis hin zur Realisierung in einer höheren Programmiersprache, gewinnt vor dem Hintergrund neuer Multimedia- und Speicheranforderungen hohe Aktualität. Übersetzt wurde das Werk sowohl von einem Mathematiker wie einem Informatiker. Das Werk erscheint in der neuen Reihe des Verlages Vieweg: Multimedia-Engineering.

Fractal Surfaces

Author: John C. Russ

Publisher: Springer Science & Business Media

ISBN: 9780306447020

Category: Science

Page: 310

View: 7534

The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world.

Computers, Rigidity, and Moduli

The Large-scale Fractal Geometry of Riemannian Moduli Space

Author: Shmuel Bochner,Shmuel Weinberger

Publisher: Princeton University Press

ISBN: 9780691118895

Category: Mathematics

Page: 174

View: 8399

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.

The Pattern Book

Fractals, Art, and Nature

Author: Clifford A. Pickover

Publisher: World Scientific

ISBN: 9789810214265

Category: Computers

Page: 427

View: 2747

Although the patterns are computer-generated, the book is informal and emphasis is on the fun that the true pattern lover finds in doing rather than in reading about the doing.

Fraktale und Finanzen

Märkte zwischen Risiko, Rendite und Ruin

Author: Benoît B. Mandelbrot,Richard L. Hudson

Publisher: N.A

ISBN: 9783492248617

Category: Capital market

Page: 445

View: 8180


The (Mis)Behaviour of Markets

A Fractal View of Risk, Ruin and Reward

Author: Benoit B. Mandelbrot,Richard L. Hudson

Publisher: Profile Books

ISBN: 1847651550

Category: Business & Economics

Page: 352

View: 3180

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.

Fractals and Chaos

An illustrated course

Author: Paul S. Addison

Publisher: CRC Press

ISBN: 9780750304009

Category: Science

Page: 256

View: 8032

Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.

Fractals in Geophysics


Publisher: Birkhäuser

ISBN: 3034863896

Category: Juvenile Nonfiction

Page: 314

View: 3039

Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1

Fundamentals of Natural Computing

Basic Concepts, Algorithms, and Applications

Author: Leandro Nunes de Castro

Publisher: CRC Press

ISBN: 1420011448

Category: Science

Page: 696

View: 7529

Natural computing brings together nature and computing to develop new computational tools for problem solving; to synthesize natural patterns and behaviors in computers; and to potentially design novel types of computers. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications presents a wide-ranging survey of novel techniques and important applications of nature-based computing. This book presents theoretical and philosophical discussions, pseudocodes for algorithms, and computing paradigms that illustrate how computational techniques can be used to solve complex problems, simulate nature, explain natural phenomena, and possibly allow the development of new computing technologies. The author features a consistent and approachable, textbook-style format that includes lucid figures, tables, real-world examples, and different types of exercises that complement the concepts while encouraging readers to apply the computational tools in each chapter. Building progressively upon core concepts of nature-inspired techniques, the topics include evolutionary computing, neurocomputing, swarm intelligence, immunocomputing, fractal geometry, artificial life, quantum computing, and DNA computing. Fundamentals of Natural Computing is a self-contained introduction and a practical guide to nature-based computational approaches that will find numerous applications in a variety of growing fields including engineering, computer science, biological modeling, and bioinformatics.