Chaos And Fractals The Mathematics Behind The Computer Graphics

Author : Robert L. Devaney,Kathleen T. Alligood
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 50,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821801376

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Chaos and Fractals: The Mathematics Behind the Computer Graphics by Robert L. Devaney,Kathleen T. Alligood Pdf

"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.

Author : C.A. Pickover
Publisher : Elsevier
Page : 452 pages
File Size : 51,8 Mb
Release : 1998-08-03
Category : Computers
ISBN : 0080528864

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Chaos and Fractals by C.A. Pickover Pdf

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.

Author : American Mathematical Society
Publisher : Amer Mathematical Society
Page : 148 pages
File Size : 52,9 Mb
Release : 1989-12-31
Category : Computers
ISBN : 0821801422

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Chaos and Fractals: the Mathematics Behind the Computer Graphics + Chaos, Fractals and Dynamics: Computer Experiments in Mathematics, With Robert L. Devaney by American Mathematical Society Pdf

Author : A.J. Crilly,Rae Earnshaw,Huw Jones
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461230342

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Fractals and Chaos by A.J. Crilly,Rae Earnshaw,Huw Jones Pdf

This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. A fractal object is self-similar in that subsections of the object are similar in some sense to the whole object.

Author : Robert L. Devaney
Publisher : Addison Wesley Publishing Company
Page : 216 pages
File Size : 49,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015025153597

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Chaos, Fractals, and Dynamics by Robert L. Devaney Pdf

Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.

Author : Clifford A. Pickover
Publisher : Courier Corporation
Page : 416 pages
File Size : 47,8 Mb
Release : 2012-07-12
Category : Science
ISBN : 9780486151618

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Computers, Pattern, Chaos and Beauty by Clifford A. Pickover Pdf

Fractals and chaos theory lead to startling graphics in this book by a renowned scientist, inventor, and artist, who coordinates information from disparate fields. Over 275 illustrations, 29 in color.

Author : Clifford A Pickover
Publisher : World Scientific
Page : 466 pages
File Size : 44,9 Mb
Release : 1995-06-09
Category : Mathematics
ISBN : 9789814504034

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The Pattern Book: Fractals, Art And Nature by Clifford A Pickover Pdf

This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout.Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.)

Author : Karl-Heinz Becker,Michael Dörfler
Publisher : Cambridge University Press
Page : 420 pages
File Size : 46,7 Mb
Release : 1989-10-26
Category : Computers
ISBN : 052136910X

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Dynamical Systems and Fractals by Karl-Heinz Becker,Michael Dörfler Pdf

This 1989 book is about chaos, fractals and complex dynamics.

Author : John Briggs
Publisher : Simon and Schuster
Page : 196 pages
File Size : 50,6 Mb
Release : 1992
Category : Art
ISBN : 9780671742171

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Fractals by John Briggs Pdf

Explains the significance and beauty of fractals using over 170 illustrations.

Author : Michael Frame,Benoit Mandelbrot
Publisher : Cambridge University Press
Page : 232 pages
File Size : 45,7 Mb
Release : 2002-06-20
Category : Computers
ISBN : 0883851695

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Fractals, Graphics, and Mathematics Education by Michael Frame,Benoit Mandelbrot Pdf

Publisher Description

Author : Phillip A Laplante
Publisher : World Scientific
Page : 217 pages
File Size : 40,9 Mb
Release : 2023-07-26
Category : Mathematics
ISBN : 9789811273261

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Introduction To Chaos, Fractals And Dynamical Systems by Phillip A Laplante Pdf

This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems particularly focuses on natural and human phenomenon that can be modeled as fractals, using simple examples to explain the theory of chaos and how it affects all of us. Then, using straightforward mathematic and intuitive descriptions, computer generated graphics and photographs of natural scenes are used to illustrate the beauty of fractals and their importance in our world. Finally, the concept of Dynamical Systems, that is, time-dependent systems, the foundation of Chaos and Fractal, is introduced. Everyday examples are again used to illustrate concepts, and the importance of understanding how these vital systems affect our lives. Throughout the fascinating history of the evolution of chaos theory, fractals and dynamical systems is presented, along with brief introductions to the scientists, mathematicians and engineers who created this knowledge.Introduction to Chaos, Fractals and Dynamical Systems contains ample mathematical definitions, representations, discussions and exercises, so that this book can be used as primary or secondary source in home schooling environments.The book is suitable for homeschooling as a focused course on the subject matter or as a classroom supplement for a variety of courses at the late junior high or early high-school level. For example, in addition to a standalone course on Chaos, Fractals and Dynamical Systems (or similar title), this book could be used with the following courses:The text can also be used in conjunction with mathematics courses for undergraduates for non-science majors. The book can also be used for informal and lively family study and discussion.For each chapter, exercises and things to do are included. These activities range from simple computational tasks to more elaborate computer projects, related activities, biographical research and writing assignments.

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 49,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475747409

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Chaos and Fractals by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Pdf

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.

Author : Heinz-Otto Peitgen,Peter H. Richter
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 54,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642617171

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The Beauty of Fractals by Heinz-Otto Peitgen,Peter H. Richter Pdf

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.

Author : Manfred Schroeder
Publisher : Courier Corporation
Page : 450 pages
File Size : 41,5 Mb
Release : 2009-08-21
Category : Science
ISBN : 9780486472041

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Fractals, Chaos, Power Laws by Manfred Schroeder Pdf

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.

Author : P. Fischer
Publisher : CRC Press
Page : 282 pages
File Size : 48,8 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000154221

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Chaos, Fractals, and Dynamics by P. Fischer Pdf

This book contains eighteen papers, all more-or-less linked to the theory of dynamical systems together with related studies of chaos and fractals. It shows many fractal configurations that were generated by computer calculations of underlying two-dimensional maps.