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Measure, Topology, and Fractal Geometry

Author : Gerald A. Edgar
Publisher : Springer Science & Business Media
ISBN 13 : 1475741340
Total Pages : 252 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Measure, Topology, and Fractal Geometry by : Gerald A. Edgar

Download or read book Measure, Topology, and Fractal Geometry written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Fractal Geometry of Nature

Author : Benoit Mandelbrot
Publisher : Echo Point Books & Media, LLC
ISBN 13 : 9781648370410
Total Pages : 0 pages
Book Rating : 4.3/5 (74 download)

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Book Synopsis The Fractal Geometry of Nature by : Benoit Mandelbrot

Download or read book The Fractal Geometry of Nature written by Benoit Mandelbrot and published by Echo Point Books & Media, LLC. This book was released on 2021-07-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

The Science of Fractal Images

Author : Heinz-Otto Peitgen
Publisher : Springer Science & Business Media
ISBN 13 : 146123784X
Total Pages : 328 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Science of Fractal Images by : Heinz-Otto Peitgen

Download or read book The Science of Fractal Images written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, Heinz-Otto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by Heinz-Otto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudo-code or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.

Fractals: A Very Short Introduction

Author : Kenneth Falconer
Publisher : OUP Oxford
ISBN 13 : 0191663441
Total Pages : 153 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Fractals: A Very Short Introduction by : Kenneth Falconer

Download or read book Fractals: A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Fractal Worlds

Author : Michael Frame
Publisher : Yale University Press
ISBN 13 : 0300220707
Total Pages : 536 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Fractal Worlds by : Michael Frame

Download or read book Fractal Worlds written by Michael Frame and published by Yale University Press. This book was released on 2016-06-21 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.

Fractal Physiology

Author : James B Bassingthwaighte
Publisher : Springer
ISBN 13 : 1461475724
Total Pages : 371 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Fractal Physiology by : James B Bassingthwaighte

Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.

Alt.fractals

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Author : Eric Baird
Publisher : Chocolate Tree Books
ISBN 13 : 0955706831
Total Pages : 233 pages
Book Rating : 4.9/5 (557 download)

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Book Synopsis Alt.fractals by : Eric Baird

Download or read book Alt.fractals written by Eric Baird and published by Chocolate Tree Books. This book was released on 2011 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Where most books on fractals concentrate on mathematical theory, Alt. Fractals takes a graphical approach. starting with the fractal "standards"--The Sierpinski Triangle and Pyramid, Menger Sponge, Julia Mandelbrot sets - Alt. Fractals explores the world of variations one step removed from the usual textbook versions."--Back cover.

To Sleep in a Sea of Stars

Author : Christopher Paolini
Publisher : Tor Books
ISBN 13 : 1250762901
Total Pages : 848 pages
Book Rating : 4.2/5 (57 download)

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Book Synopsis To Sleep in a Sea of Stars by : Christopher Paolini

Download or read book To Sleep in a Sea of Stars written by Christopher Paolini and published by Tor Books. This book was released on 2020-09-15 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now a New York Times and USA Today bestseller! Winner of Best Science Fiction in the 2020 Goodreads Choice Awards! To Sleep in a Sea of Stars is a brand new epic novel from #1 New York Times bestselling author of Eragon, Christopher Paolini. Kira Navárez dreamed of life on new worlds. Now she's awakened a nightmare. During a routine survey mission on an uncolonized planet, Kira finds an alien relic. At first she's delighted, but elation turns to terror when the ancient dust around her begins to move. As war erupts among the stars, Kira is launched into a galaxy-spanning odyssey of discovery and transformation. First contact isn't at all what she imagined, and events push her to the very limits of what it means to be human. While Kira faces her own horrors, Earth and its colonies stand upon the brink of annihilation. Now, Kira might be humanity's greatest and final hope . . . The Fractalverse Series To Sleep in a Sea of Stars Fractal Noise At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

African Fractals

Author : Ron Eglash
Publisher :
ISBN 13 : 9780813526140
Total Pages : 258 pages
Book Rating : 4.5/5 (261 download)

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Book Synopsis African Fractals by : Ron Eglash

Download or read book African Fractals written by Ron Eglash and published by . This book was released on 1999 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

Fractal Cities

Author : Michael Batty
Publisher :
ISBN 13 : 9780124555709
Total Pages : 394 pages
Book Rating : 4.5/5 (557 download)

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Book Synopsis Fractal Cities by : Michael Batty

Download or read book Fractal Cities written by Michael Batty and published by . This book was released on 1994-01-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal Cities is the pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated throughcomputer graphics. The book explains how the structure of cities evolve in ways which at first sight may appear irregular, but when understood in terms of fractals reveal a complex and diverse underlying order. The book includes numerous illustrations and 16 pages full-color plates of stunning computer graphics, along with explanations of how to construct them. The authors provide an accessible and thought-provoking introduction to fractal geometry, as well as an exciting visual understanding of the formof cities. This approach, bolstered by new insights into the complexity of social systems, provides one of the best introductions to fractal geometry available for non-mathematicians and social scientists. Fractal Cities is useful as a textbook for courses on geographic information systems, urban geography, regional science, and fractal geometry. Planners and architects will find that many aspects of fractal geometry covered in this book are relevant to their own interests. Those involved in fractals and chaos, computer graphics, and systems theory will also find important methods and examples germane to their work. Michael Batty is Director of the National Center for Geographic Information and analysis in the State University of New York at Buffalo, and has worked in planning theory and urban modeling. Paul Longley is a lecturer in geography at the University of Bristol, and is involved in the development of geographic information systems in urban policy analysis. Richly illustrated, including 16 pages of full-color plates of brilliant computer graphics Provides an introduction to fractal geometry for the non-mathematician and social scientist Explains the influence of fractals on the evolution of the physical form of cities

The Baudelaire Fractal

Author : Lisa Robertson
Publisher : Coach House Books
ISBN 13 : 1770566023
Total Pages : 137 pages
Book Rating : 4.7/5 (75 download)

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Book Synopsis The Baudelaire Fractal by : Lisa Robertson

Download or read book The Baudelaire Fractal written by Lisa Robertson and published by Coach House Books. This book was released on 2020-02-04 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: The debut novel by acclaimed poet Lisa Robertson, in which a poet realizes she's written the works of Baudelaire. One morning, Hazel Brown awakes in a badly decorated hotel room to find that she’s written the complete works of Charles Baudelaire. In her bemusement the hotel becomes every cheap room she ever stayed in during her youthful perambulations in 1980s Paris. This is the legend of a she-dandy’s life. Part magical realism, part feminist ars poetica, part history of tailoring, part bibliophilic anthem, part love affair with nineteenth-century painting, The Baudelaire Fractal is poet and art writer Lisa Robertson’s first novel. "Robertson, with feminist wit, a dash of kink, and a generous brain, has written an urtext that tenders there can be, in fact, or in fiction, no such thing. Hers is a boon for readers and writers, now and in the future."—Jennifer Krasinski, Bookforum "It’s brilliant, strange, and unlike anything I’ve read before."—Rebecca Hussey, BOOKRIOT

Exploring Fractals on the Macintosh

Author : Bernt Wahl
Publisher : Addison-Wesley Professional
ISBN 13 :
Total Pages : 378 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Exploring Fractals on the Macintosh by : Bernt Wahl

Download or read book Exploring Fractals on the Macintosh written by Bernt Wahl and published by Addison-Wesley Professional. This book was released on 1995 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chaotic world of fractals meets the Macintosh for the first time in this expert exploration for users and programmers. This book examines the workings of these complex and intriguing mathematical models in a way that is accessible and engaging. Included are fully working versions of the acclaimed fractal applications FractaSketch and MandelMovie on 3.5" disk.

The Fractal Self

Author : John L. Culliney
Publisher : University of Hawaii Press
ISBN 13 : 0824866649
Total Pages : 257 pages
Book Rating : 4.8/5 (248 download)

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Book Synopsis The Fractal Self by : John L. Culliney

Download or read book The Fractal Self written by John L. Culliney and published by University of Hawaii Press. This book was released on 2017-07-31 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.

Fractals Everywhere

Author : Michael F. Barnsley
Publisher : Academic Press
ISBN 13 : 148325769X
Total Pages : 565 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fractals Everywhere by : Michael F. Barnsley

Download or read book Fractals Everywhere written by Michael F. Barnsley and published by Academic Press. This book was released on 2014-05-10 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals Everywhere, Second Edition covers the fundamental approach to fractal geometry through iterated function systems. This 10-chapter text is based on a course called "Fractal Geometry", which has been taught in the School of Mathematics at the Georgia Institute of Technology. After a brief introduction to the subject, this book goes on dealing with the concepts and principles of spaces, contraction mappings, fractal construction, and the chaotic dynamics on fractals. Other chapters discuss fractal dimension and interpolation, the Julia sets, parameter spaces, and the Mandelbrot sets. The remaining chapters examine the measures on fractals and the practical application of recurrent iterated function systems. This book will prove useful to both undergraduate and graduate students from many disciplines, including mathematics, biology, chemistry, physics, psychology, mechanical, electrical, and aerospace engineering, computer science, and geophysical science.

Fractals

Author : Oliver Linton
Publisher : eBook Partnership
ISBN 13 : 191270613X
Total Pages : 64 pages
Book Rating : 4.9/5 (127 download)

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Book Synopsis Fractals by : Oliver Linton

Download or read book Fractals written by Oliver Linton and published by eBook Partnership. This book was released on 2021-05-20 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.

Ergodic Theory and Fractal Geometry

Author : Hillel Furstenberg
Publisher : American Mathematical Society
ISBN 13 : 1470410346
Total Pages : 82 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg and published by American Mathematical Society. This book was released on 2014-08-08 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.

Fractal Geometry, Complex Dimensions and Zeta Functions

Author : Michel L. Lapidus
Publisher : Springer Science & Business Media
ISBN 13 : 1461421764
Total Pages : 583 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Fractal Geometry, Complex Dimensions and Zeta Functions by : Michel L. Lapidus

Download or read book Fractal Geometry, Complex Dimensions and Zeta Functions written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2012-09-20 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.