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Fractals, Graphics, and Mathematics Education

By Michael Frame, Benoit Mandelbrot
Publisher: Cambridge University Press, 2002-06-20
Pages: 232
Language: en
ISBN_10:0883851695
ISBN_13:9780883851692
Subject: Computers

Fractals for the Classroom

Part One Introduction to Fractals and Chaos

$Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled.$

جزئیات و درخواست

By Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe
Publisher: Springer Science & Business Media, 2013-03-09
Pages: 468
Language: en
ISBN_13:9781475721720
ISBN_10:1475721722
Subject: Mathematics

Fractals for the Classroom

Part Two: Complex Systems and Mandelbrot Set

جزئیات و درخواست

By Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 513
Language: en
ISBN_13:9781461244066
ISBN_10:1461244064
Subject: Mathematics

Chaos and Fractals: The Mathematics Behind the Computer Graphics

The Mathematics Behind the Computer Graphics

$The terms chaos and fractals have received widespread attention in recent years. The alluring computer graphics images associated with these terms have heightened interest among scientists in these ideas. This volume contains the introductory survey lectures delivered in the American Mathematical Society Short Course, Chaos and Fractals: The Mathematics Behind the Computer Graphics, on August 6-7, 1988, given in conjunction with the AMS Centennial Meeting in Providence, Rhode Island. In his overview, Robert L. Devaney introduces such key topics as hyperbolicity, the period doubling route to chaos, chaotic dynamics, symbolic dynamics and the horseshoe, and the appearance of fractals as the chaotic set for a dynamical system. Linda Keen and Bodil Branner discuss the Mandelbrot set and Julia sets associated to the complex quadratic family z -> z2 + c. Kathleen T. Alligood, James A. Yorke, and Philip J. Holmes discuss some of these topics in higher dimensional settings, including the Smale horseshoe and strange attractors. Jenny Harrison and Michael F. Barnsley give an overview of fractal geometry and its applications. -- from dust jacket.$

جزئیات و درخواست

By Robert L. Devaney, Kathleen T. Alligood
Publisher: American Mathematical Soc., 1989
Pages: 176
Language: en
ISBN_13:9780821801376
ISBN_10:0821801376
Subject: Computers

Fractal Geometry and Computer Graphics

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

جزئیات و درخواست

By Jose L. Encarnacao, Heinz-Otto Peitgen, Georgios Sakas, Gabriele Englert
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 271
Language: en
ISBN_13:9783642956782
ISBN_10:3642956785
Subject: Mathematics

The Pattern Book: Fractals, Art And Nature

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

جزئیات و درخواست

By Clifford A Pickover
Publisher: World Scientific, 1995-06-09
Pages: 466
Language: en
ISBN_13:9789814504034
ISBN_10:9814504033
Subject: Mathematics

Chaos and Fractals

A Computer Graphical Journey

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

جزئیات و درخواست

By C.A. Pickover
Publisher: Elsevier, 1998-08-03
Pages: 469
Language: en
ISBN_13:9780080528861
ISBN_10:0080528864
Subject: Mathematics

Measure, Topology, and Fractal Geometry

$Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.$

جزئیات و درخواست

By Gerald Edgar
Publisher: Springer Science & Business Media, 2007-10-23
Pages: 293
Language: en
ISBN_13:9780387747491
ISBN_10:0387747494
Subject: Mathematics

Fractals for the Classroom: Strategic Activities Volume Two

$The same factors that motivated the writing of our first volume of strategic activities on fractals continued to encourage the assembly of additional activities for this second volume. Fractals provide a setting wherein students can enjoy hands-on experiences that involve important mathematical content connected to a wide range of physical and social phenomena. The striking graphic images, unexpected geometric properties, and fascinating numerical processes offer unparalleled opportunity for enthusiastic student inquiry. Students sense the vigor present in the growing and highly integrative discipline of fractal geom etry as they are introduced to mathematical developments that have occurred during the last half of the twentieth century. Few branches of mathematics and computer science offer such a contem porary portrayal of the wonderment available in careful analysis, in the amazing dialogue between numeric and geometric processes, and in the energetic interaction between mathematics and other disciplines. Fractals continue to supply an uncommon setting for animated teaching and learn ing activities that focus upon fundamental mathematical concepts, connections, problem-solving techniques, and many other major topics of elementary and advanced mathematics. It remains our hope that, through this second volume of strategic activities, readers will find their enjoyment of mathematics heightened and their appreciation for the dynamics of the world in creased. We want experiences with fractals to enliven curiosity and to stretch the imagination.$

جزئیات و درخواست

By Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, Evan Maletsky, Terry Perciante
Publisher: Springer Science & Business Media, 2013-06-29
Pages: 194
Language: en
ISBN_13:9781475752762
ISBN_10:1475752768
Subject: Mathematics

Fractals in Multimedia

$This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.$

جزئیات و درخواست

By Michael F. Barnsley, Dietmar Saupe, Edward R. Vrscay
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 271
Language: en
ISBN_13:9781468492446
ISBN_10:1468492446
Subject: Computers

The Science of Fractal Images

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

جزئیات و درخواست

By Heinz-Otto Peitgen, Dietmar Saupe
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 328
Language: en
ISBN_13:9781461237846
ISBN_10:146123784X
Subject: Mathematics

Introducing Fractals

A Graphic Guide

$Fractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protégé of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'$

جزئیات و درخواست

By Nigel Lesmoir-Gordon, Will Rood
Publisher: Icon Books Ltd, 2014-06-05
Pages: 429
Language: en
ISBN_13:9781848317833
ISBN_10:1848317832
Subject: Mathematics

The Beauty of Fractals

Six Different Views

$The Beauty of Fractals includes six essays related to fractals, with perspectives different enough to give you a taste of the breadth of the subject. Each essay is self-contained and expository. Moreover, each of the essays is intended to be accessible to a broad audience that includes college teachers, high school teachers, advanced undergraduate students, and others who wish to learn or teach about topics in fractals that are not regularly in textbooks on fractals.$

جزئیات و درخواست

By Denny Gulick, Jon Scott
Publisher: MAA, 2010
Pages: 107
Language: en
ISBN_13:9780883859711
ISBN_10:0883859718
Subject: Mathematics

Measure, Topology, and Fractal Geometry

$From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1$

جزئیات و درخواست

By Gerald A. Edgar
Publisher: Springer Science & Business Media, 2013-04-17
Pages: 252
Language: en
ISBN_13:9781475741346
ISBN_10:1475741340
Subject: Mathematics

Fractals for the Classroom

Introduction to fractals and chaos. 1

جزئیات و درخواست

By Heinz-Otto Peitgen
1992
Pages: 450
Language: en
OTHER:OCLC:716346306

Fractal Worlds

Grown, Built, and Imagined

$Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Frame—a close collaborator with Benoit Mandelbrot, the founder of fractal geometry—and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into less-known areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.$

جزئیات و درخواست

By Michael Frame, Amelia Urry
Publisher: Yale University Press, 2016-06-21
Pages: 536
Language: en
ISBN_13:9780300220704
ISBN_10:0300220707
Subject: Mathematics

Fractals and Chaos

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

جزئیات و درخواست

By A.J. Crilly, Rae Earnshaw, Huw Jones
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 278
Language: en
ISBN_13:9781461230342
ISBN_10:1461230349
Subject: Mathematics

Fractals

The Patterns of Chaos : a New Aesthetic of Art, Science, and...

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

جزئیات و درخواست

By John Briggs
Publisher: Simon and Schuster, 1992
Pages: 196
Language: en
ISBN_13:9780671742171
ISBN_10:0671742175
Subject: Art

Fun with Fractals

$This book/disk package presents over a dozen programs to enable DOS, Windows, and OS/2 users to create their own colorful fractal graphics. An introductory chapter explains the fundamental of fractals; subsequent chapters show readers how to use the accompanying programs.$

جزئیات و درخواست

By Judd Robbins
1993
Pages: 266
Language: en
OTHER:PSU:000022289599
Subject: Computers

Fractal Geometry

Mathematical Foundations and Applications

$An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.$

جزئیات و درخواست

By K. J. Falconer
1990-03-30
Pages: 320
Language: en
OTHER:MINN:31951D019352687
Subject: Mathematics

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