The Fractal Geometry of Nature

Author: Benoit B. Mandelbrot

Publisher: Macmillan

ISBN: 9780716711865

Category: Juvenile Nonfiction

Page: 468

View: 4592

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 the Brain

Author: Antonio Di Ieva

Publisher: Springer

ISBN: 1493939955

Category: Medical

Page: 585

View: 8241

Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.

Measure, Topology, and Fractal Geometry

Author: Gerald A Edgar

Publisher: Springer Science & Business Media

ISBN: 1475741340

Category: Mathematics

Page: 231

View: 6541

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

Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 7485

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Chaos and Fractals

New Frontiers of Science

Author: Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe

Publisher: Springer Science & Business Media

ISBN: 1475747403

Category: Mathematics

Page: 999

View: 2220

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.

Fractals Everywhere

New Edition

Author: Michael F. Barnsley

Publisher: Courier Corporation

ISBN: 0486320340

Category: Mathematics

Page: 560

View: 3515

Up-to-date text focuses on how fractal geometry can be used to model real objects in the physical world, with an emphasis on fractal applications. Includes solutions, hints, and a bonus CD.

Exploring the Geometry of Nature

Computer Modeling of Chaos, Fractals, Cellular Automata, and Neural Networks

Author: Ed Rietman

Publisher: N.A


Category: Computers

Page: 197

View: 3836

The science of chaos attracts the attention of researchers in many disciplines. The idea: by following simple principles of randomness and disorder, patterns emerge. Here, users on their own PC's can construct mathematical models duplicating processes found in nature.

Fractals: A Very Short Introduction

Author: K. J. Falconer

Publisher: Oxford University Press

ISBN: 0199675988

Category: Mathematics

Page: 132

View: 5306

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.

Fractals and Chaos

The Mandelbrot Set and Beyond

Author: Benoit Mandelbrot

Publisher: Springer Science & Business Media

ISBN: 1475740174

Category: Mathematics

Page: 308

View: 7448

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.


Author: Jens Feder

Publisher: Springer Science & Business Media

ISBN: 1489921249

Category: Science

Page: 284

View: 7730

This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.

The Beauty of Fractals

Images of Complex Dynamical Systems

Author: Heinz-Otto Peitgen,Peter H. Richter

Publisher: Springer Science & Business Media

ISBN: 3642617174

Category: Mathematics

Page: 202

View: 8379

Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.

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: 1580

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.

Fractal Geometry

Mathematical Foundations and Applications

Author: Kenneth Falconer

Publisher: John Wiley & Sons

ISBN: 0470299452

Category: Mathematics

Page: 366

View: 1176

Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0 Please click here to download solutions to exercises found within this title:

The Fractalist

Memoir of a Scientific Maverick

Author: Benoit B. Mandelbrot

Publisher: Pantheon

ISBN: 0307377350

Category: Biography & Autobiography

Page: 324

View: 968

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.

Clouds Are Not Spheres

A Portrait of Benoit Mandelbrot, the Founding Father of Fractal Geometry

Author: Nigel Lesmoir-Gordon

Publisher: World Scientific Publishing Company

ISBN: 9781786344748

Category: Fractals

Page: N.A

View: 9204



The Patterns of Chaos

Author: John Briggs

Publisher: N.A

ISBN: 9781626543775


Page: 194

View: 4042

Fractals are unique patterns left behind by the unpredictable movement--the chaos--of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap--all are fractals. Learn to recognize them and the world will never look the same again.Fractals permeate our lives, appearing in places as tiny as the surface of a virus cell and as majestic as the Grand Canyon. From ancient tribal peoples to modern painters to Star Wars animators, artists have been captivated by fractals and have used them in their work. Fans of computer science and math whizzes are wild about fractals as well, for the interesting programming and math problems they present.In Fractals: The Patterns of Chaos, science writer John Briggs uses over 170 illustrations to clearly explain the significance and beauty of fractals. He describes how fractals were discovered, how they are formed, and the unique properties different fractals share. Fractals is a breathtaking guided tour of a remarkable frontier in art, science, and nature. It will revolutionize the way you see the world and your place in it.

Mathematical People

Profiles and Interviews

Author: Donald Albers,Gerald L. Alexanderson

Publisher: CRC Press

ISBN: 1439865175

Category: Mathematics

Page: 416

View: 8008

This unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introduction by Philip J. Davis.