The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Macmillan

ISBN: 9780716711865

Category: Juvenile Nonfiction

Page: 468

View: 880

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.
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The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Times Books

ISBN: N.A

Category: Juvenile Nonfiction

Page: 468

View: 9653

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.
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Measure, Topology, and Fractal Geometry

Author: Gerald Edgar

Publisher: Springer Science & Business Media

ISBN: 0387747494

Category: Mathematics

Page: 272

View: 5924

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.
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The Misbehavior of Markets

A Fractal View of Financial Turbulence

Author: Benoit Mandelbrot,Richard L. Hudson

Publisher: Basic Books

ISBN: 0465004687

Category: Business & Economics

Page: 368

View: 8395

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.
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Bildkompression mit Fraktalen

Author: Michael F. Barnsley,Lyman P. Hurd

Publisher: Vieweg+Teubner Verlag

ISBN: 9783322868299

Category: Technology & Engineering

Page: 232

View: 8217

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.
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Measure, Topology, and Fractal Geometry

Author: Gerald A. Edgar

Publisher: Springer Science & Business Media

ISBN: 1475741340

Category: Mathematics

Page: 231

View: 2799

From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
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Visualize This!

Author: Nathan Yau

Publisher: John Wiley & Sons

ISBN: 3527760229

Category: Statistics / Graphic methods / Data processing

Page: 422

View: 325

A guide on how to visualise and tell stories with data, providing practical design tips complemented with step-by-step tutorials.
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Die Wirklichkeit, die nicht so ist, ...

Eine Reise in die Welt der Quantengravitation

Author: Carlo Rovelli

Publisher: Rowohlt Verlag GmbH

ISBN: 3644052514

Category: Science

Page: 320

View: 3710

Was ist Wirklichkeit? Existieren Raum und Zeit tatsächlich, wenn wir uns anschicken, die elementarsten Grundlagen unserer Existenz zu erforschen? Wie viel davon können wir überhaupt verstehen? Carlo Rovelli beschäftigt sich seit vielen Jahren damit, die Grenzen unseres Verstehens zu erweitern. In diesem Buch nimmt er uns mit auf eine Reise, die von dem Realitätsverständnis der griechischen Klassik bis zur Schleifenquantengravitation führt. Ein großer Physiker unserer Zeit macht sich auf, uns ein neues Welt-Bild zu zeichnen: mit einem physikalischen Universum ohne Zeit, einer Raumzeit, die aus Schleifen und Körnchen besteht und in der Unendlichkeit nicht existiert. Einer Kosmologie, die ohne Urknall und Paralleluniversen auskommt und hier zum ersten Mal von einem ihrer «Erfinder» für ein breites Publikum einfach und ausführlich erklärt wird. Ein Buch über «die großen Herausforderungen der gegenwärtigen Naturwissenschaften, die all unser Wissen über die Natur in Frage stellen» (Rovelli).
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Das Technische Bild

Kompendium zu einer Stilgeschichte wissenschaftlicher Bilder

Author: Horst Bredekamp,Birgit Schneider,Vera Dünkel

Publisher: Walter de Gruyter

ISBN: 3050062193

Category: Art

Page: 231

View: 1252

Wissenschaftliche Bilder prägen die Ergebnisse und Einsichten, welche sie darstellen, immer auch konstruktiv. Die Wiedergabe einer Beobachtung mittels Bildern mag noch so mechanisch oder überindividuell in ihrer Erscheinung anmuten, immer zeigen sich in ihr auch Stile einer Zeit, eines Geräts, eines Denkens, eines Forscherkollektivs. Naturwissenschaftler, Mediziner und Techniker lassen ein spezifisches Wissen und Können in ihre Bilder einfließen, das auf Wirkung von Bildern und Erkenntnis durch sie, auf Evidenz angelegt ist und auf der originären Logik der bildlichen Form gründet. Das Buch zeigt einerseits, inwiefern kunsthistorische Methoden und Begriffe für eine Betrachtung wissenschaftlicher Bildwelten fruchtbar gemacht werden können. Andererseits werden die kunsthistorischen Ansätze anhand von Leitbegriffen und Methoden der aktuellen Wissenschaftsforschung überprüft und ergänzt. In der vielstimmigen Debatte der letzten Jahre um epistemische Bilder sucht der Band Begriffe zu entwickeln, die nicht theoretisch deduziert, sondern am Material der Bilder selbst entwickelt sind. Hierdurch erweist sich, wie unterschiedlich die Leistungsmerkmale von Bildern in den jeweiligen Zeiten, Disziplinen und Funktionen sind und welche vielfältigen Möglichkeiten sie liefern, Erkenntnisse, Beobachtungen oder Theorien sowohl zu erzeugen wie auch evident zu machen. Hierzu vereint der Band themenübergreifende Artikel, Begriffsbestimmungen und stichprobenartige Fallstudien zu einem Handbuch. Die Fallstudien zu fünfhundert Jahren Bildgeschichte in den Wissenschaften reichen von Sammlungszeichnungen des 16. Jahrhunderts über Darstellungen von Musikautomaten und frühe Röntgenbilder bis zur Nanomikroskopie und den Interfaces von Computern. Verfasst von der Forschergruppe "Das Technische Bild" der Humboldt-Universität zu Berlin, stellt der Band zugleich auch die Ergebnisse der im Jahr 2000 gegründeten Abteilung in gebündelter Form vor.
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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: 1127

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.
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The Pattern Book

Fractals, Art, and Nature

Author: Clifford A. Pickover

Publisher: World Scientific

ISBN: 9789810214265

Category: Computers

Page: 427

View: 576

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.
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Fractal Geometry in Architecture and Design

Author: Carl Bovill

Publisher: Springer Science & Business Media

ISBN: 1461208432

Category: Mathematics

Page: 195

View: 1033

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.
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Die Evolution des Auges - Ein Fotoshooting

Author: Georg Glaeser,Hannes F. Paulus

Publisher: Springer-Verlag

ISBN: 3642377769

Category: Science

Page: 214

View: 9153

Sehen und Gesehen werden Spektakuläre, großformatige Fotos auf Doppelseiten mit einem Erklärungstext machen die Leser neugierig auf das, was die Evolution im Bereich der Augen hervorgebracht hat: unabhängig bewegbare Augen, Stielaugen, Pigmentbecher, Lochkameraaugen, Komplexaugen, ... Das Buch kann in beliebiger Reihenfolge, Doppelseite für Doppelseite, gelesen werden. Querverweise sorgen für bequemes Umspringen auf andere Doppelseiten. Die Textpassagen sind zumeist - abgesehen von der fundierten Einleitung in jedem der 10 Kapitel - unabhängig voneinander und besprechen besondere Highlights im evolutionären Prozess. Ergänzt wird die Doppelseite mit Literaturhinweisen und Verweisen auf instruktive Internet-Seiten. Die Evolution des Auges in Bildern und Texten
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Fractals: A Very Short Introduction

Author: K. J. Falconer

Publisher: Oxford University Press

ISBN: 0199675988

Category: Mathematics

Page: 132

View: 8294

An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original.
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Benoit Mandelbrot: A Life In Many Dimensions

Author: Frame Michael,Cohen Nathan

Publisher: World Scientific

ISBN: 9814635537

Category: Mathematics

Page: 580

View: 6664

This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists, economists, and engineers, as expected; and also artists, musicians, teachers, an historian, an architect, a filmmaker, and a comic. Some articles are quite technical, others entirely descriptive. All include stories about Benoit.Also included are chapters on fractals and music by Charles Wuorinen and by Harlan Brothers, on fractals and finance by Richard Hudson and by Christian Walter, on fractal invisibility cloaks by Nathan Cohen, and a personal reminiscence by Aliette Mandelbrot.While he is known most widely for his work in mathematics and in finance, Benoit influenced almost every field of modern intellectual activity. No other book captures the breadth of all of Benoit's accomplishments.
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Phenomenology of Nature

Author: Young Ho Lee

Publisher: N.A

ISBN: 9783495456514

Category: Philosophy of nature

Page: 281

View: 3546

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Introducing Fractal Geometry

Author: Nigel Lesmoir-Gordon,Will Rood

Publisher: Totem Books

ISBN: 9781840461237

Category: Study Aids

Page: 174

View: 1221

Fractal geometry is the geometry of the natural world and is an extension of classical geometry.
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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: 4286

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.
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