Fractal Geometry And Computer Graphics

Author : Jose L. Encarnacao,Heinz-Otto Peitgen,Georgios Sakas,Gabriele Englert
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642956782

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Fractal Geometry and Computer Graphics by Jose L. Encarnacao,Heinz-Otto Peitgen,Georgios Sakas,Gabriele Englert Pdf

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with actual trends and topics of future research, are reported in the last section. The topics of the book are divides into four sections: Fundamentals, Computer Graphics and Optical Simulation, Simulation of Natural Phenomena, Image Processing and Image Analysis.

Author : Heinz-Otto Peitgen,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461237846

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The Science of Fractal Images by Heinz-Otto Peitgen,Dietmar Saupe Pdf

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.

Author : Clifford A Pickover
Publisher : World Scientific
Page : 466 pages
File Size : 47,8 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 : C.A. Pickover
Publisher : Elsevier
Page : 452 pages
File Size : 53,8 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 : Robert L. Devaney,Kathleen T. Alligood
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 49,8 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 : Michael E. Gaddis
Publisher : Unknown
Page : 0 pages
File Size : 47,8 Mb
Release : 1985
Category : Computer graphics
ISBN : OCLC:641007622

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The Fractal Geometry of Nature by Michael E. Gaddis Pdf

Author : Karl-Heinz Becker,Michael Dörfler
Publisher : Cambridge University Press
Page : 420 pages
File Size : 43,9 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 : Clifford A. Pickover
Publisher : World Scientific
Page : 474 pages
File Size : 44,7 Mb
Release : 1995
Category : Computers
ISBN : 981021426X

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The Pattern Book by Clifford A. Pickover Pdf

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.

Author : A.J. Crilly,Rae Earnshaw,Huw Jones
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 47,7 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 : Ronald Goldman
Publisher : CRC Press
Page : 592 pages
File Size : 45,7 Mb
Release : 2009-07-14
Category : Computers
ISBN : 9781439803356

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An Integrated Introduction to Computer Graphics and Geometric Modeling by Ronald Goldman Pdf

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with f

Author : Jibitesh Mishra,Sarojananda Mishra
Publisher : Elsevier
Page : 274 pages
File Size : 50,8 Mb
Release : 2007-01-08
Category : Mathematics
ISBN : 0080469388

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L-System Fractals by Jibitesh Mishra,Sarojananda Mishra Pdf

L-System Fractals covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Fractals generated from L-System including hybrid fractals Dimension calculation for L-system fractals Images and codes for L-system fractals Research directions in the area of L-system fractals Usage of various freely downloadable tools in this area

Author : Heinz-Otto Peitgen,Peter H. Richter
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 43,5 Mb
Release : 1986-07
Category : Computers
ISBN : 3540158510

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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 : John Briggs
Publisher : Touchstone Books
Page : 204 pages
File Size : 52,8 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015029074393

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Fractals by John Briggs Pdf

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

Author : Michael Batty,Paul Longley
Publisher : Unknown
Page : 394 pages
File Size : 41,9 Mb
Release : 1994-01-01
Category : Cities and towns
ISBN : 0124555705

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Fractal Cities by Michael Batty,Paul Longley Pdf

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

Author : Michael Mcguire
Publisher : Addison-Wesley Longman
Page : 184 pages
File Size : 51,9 Mb
Release : 1991-07-21
Category : Computers
ISBN : UOM:39015056636197

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An Eye For Fractals by Michael Mcguire Pdf

Fractional geometry posits that a natural visual complexity can arise from iteration of simple rules and simple shapes. An Eye for Fractals is a fascinating study of the converse premise: that nature's complexity implies an underlying simplicity that can be traced back to fractal geometry.The book effectively integrates art with science, illustrating the natural occurrence of mathematics and geometry in lava flows, kelp beds, cloud formations and aspen groves. The book is enhanced with more than 150 photographs and drawings, including some color illustrations. An Eye for Fractals is a beautiful introduction to fractal geometry, a graphic, visual approach that should appeal to all who feel the fascination of this artful mathematics.