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Chaos and Fractals

Author: C.A. Pickover

Publisher: Elsevier

Published: 1998-08-03

Total Pages: 452

ISBN-13: 9780080528861

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Chaos and Fractals

Author: Heinz-Otto Peitgen

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 1013

ISBN-13: 1475747403

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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.

Applications of Fractals and Chaos

Author: A.J. Crilly

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 312

ISBN-13: 3642780970

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Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.

Fractals, Chaos, Power Laws

Author: Manfred Schroeder

Publisher: Courier Corporation

Published: 2009-08-21

Total Pages: 450

ISBN-13: 0486472043

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This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.

Fractal Physiology and Chaos in Medicine

Author: Bruce J. West

Publisher: World Scientific

Published: 2012

Total Pages: 345

ISBN-13: 9814417793

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This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics. In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs that have occurred in the intervening years are emphasized. The book provides a comprehensive overview of a nascent theory of medicine, including a new chapter on the theory of complex networks as they pertain to medicine.

Fractals and Chaos in Geology and Geophysics

Author: Donald L. Turcotte

Publisher: Cambridge University Press

Published: 1997-07-13

Total Pages: 424

ISBN-13: 9780521567336

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The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organized criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded, second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics.

Chaos and Fractals: The Mathematics Behind the Computer Graphics

Author: Robert L. Devaney

Publisher: American Mathematical Soc.

Published: 1989

Total Pages: 176

ISBN-13: 0821801376

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"Robert Devaney communicates his deep understanding as well as his enthusiasm for chaos, fractals, and dynamical systems. Starting at a level suitable for well-prepared high school students, he tells the mathematical story behind these fascinating topics. Equations and graphs are clearly shown with computer-generated characters, and Devaney's explanations are lucid and instructive. Illustrating the mathematics are forays into the colorful, unpredictable world of fractals and Julia sets. Devaney explains how the computer is used to generate the pictures and shows how the various colors are chosen for graphical representations ... Though the mathematical background required is elementary, those at the collegiate level and beyond will appreciate ... the clarity of exposition and the sheer beauty of the graphics."--Container.

Fractals and Chaos

Author: Benoit Mandelbrot

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 321

ISBN-13: 1475740174

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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.

Chaos and Fractals

Author: David P. Feldman

Publisher: Oxford University Press

Published: 2012-08-10

Total Pages:

ISBN-13: 0191637521

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This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations. The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.

Chaotic Dynamics and Fractals

Author: Michael F. Barnsley

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 305

ISBN-13: 1483269086

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Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.