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Measure, Topology, and Fractal Geometry

Gerald A. Edgar
Measure Topology and Fractal Geometry Book PDF

Author : Gerald A. Edgar
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 55,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741346

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Measure, Topology, and Fractal Geometry by Gerald A. Edgar Pdf

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

Fractals: A Very Short Introduction

Kenneth Falconer
Fractals A Very Short Introduction Book PDF

Author : Kenneth Falconer
Publisher : OUP Oxford
Page : 144 pages
File Size : 48,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780191663444

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Fractals: A Very Short Introduction by Kenneth Falconer Pdf

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.

The Fractal Geometry of Nature

Benoit Mandelbrot
The Fractal Geometry of Nature Book PDF

Author : Benoit Mandelbrot
Publisher : Echo Point Books & Media, LLC
Page : 0 pages
File Size : 42,7 Mb
Release : 2021-07-16
Category : Electronic
ISBN : 1648370411

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The Fractal Geometry of Nature by Benoit Mandelbrot Pdf

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.

Fractals

Jens Feder
Fractals Book PDF

Author : Jens Feder
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 45,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489921246

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Fractals by Jens Feder Pdf

This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.

Chaos and Fractals

Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Chaos and Fractals Book PDF

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 55,6 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.

Fractals Everywhere

Michael F. Barnsley
Fractals Everywhere Book PDF

Author : Michael F. Barnsley
Publisher : Academic Press
Page : 565 pages
File Size : 49,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483257693

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Fractals Everywhere by Michael F. Barnsley Pdf

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

Oliver Linton
Fractals Book PDF

Author : Oliver Linton
Publisher : Wooden Books Us
Page : 64 pages
File Size : 50,7 Mb
Release : 2024-09-15
Category : Computers
ISBN : 1952178029

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Fractals by Oliver Linton Pdf

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. WOODEN BOOKS US EDITIONS. Small books, BIG ideas. Tiny but packed with information. "Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.

SuperFractals

Michael Fielding Barnsley
SuperFractals Book PDF

Author : Michael Fielding Barnsley
Publisher : Cambridge University Press
Page : 464 pages
File Size : 40,6 Mb
Release : 2006-09-07
Category : Computers
ISBN : 9780521844932

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SuperFractals by Michael Fielding Barnsley Pdf

SuperFractals, first published in 2006, describes mathematics and algorithms for the first time in book form, with breathtaking colour pictures.

Chaos and Fractals

C.A. Pickover
Chaos and Fractals Book PDF

Author : C.A. Pickover
Publisher : Elsevier
Page : 452 pages
File Size : 43,9 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.

Fractals and Chaos

Benoit Mandelbrot
Fractals and Chaos Book PDF

Author : Benoit Mandelbrot
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 52,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475740172

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Fractals and Chaos by Benoit Mandelbrot Pdf

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.

Fractals

Hendrik Adolf Lauwerier
Fractals Book PDF

Author : Hendrik Adolf Lauwerier
Publisher : Unknown
Page : 209 pages
File Size : 53,7 Mb
Release : 1991
Category : Mathematics
ISBN : 0691024456

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Fractals by Hendrik Adolf Lauwerier Pdf

Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations.

The Beauty of Fractals

Heinz-Otto Peitgen,Peter H. Richter
The Beauty of Fractals Book PDF

Author : Heinz-Otto Peitgen,Peter H. Richter
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 53,7 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.

Power of Patterns: Fractals

Theo Buchanan
Power of Patterns Fractals Book PDF

Author : Theo Buchanan
Publisher : Teacher Created Materials
Page : 48 pages
File Size : 54,6 Mb
Release : 2017-03-31
Category : Young Adult Nonfiction
ISBN : 9781480757301

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Power of Patterns: Fractals by Theo Buchanan Pdf

Fractals come in a huge variety of forms, but they are generally defined as shapes that exhibit self-similarity and high complexity. These shapes appear in many different forms throughout nature. Introduce students to the fascinating topic of fractals with this high-interest nonfiction book! Developed by Timothy Rasinski and featuring TIME content, this title includes essential text features like an index, captions, glossary, and table of contents. The intriguing sidebars, detailed images, and in-depth Reader's Guide require students to connect back to the text and encourage multiple readings. The Think Link and Dig Deeper! sections develop students' higher-order thinking skills. The Check It Out! section includes suggested books, videos, and websites for further reading. Aligned with state standards, this title features complex and rigorous content appropriate for students preparing for college and career readiness.

Power of Patterns: Fractals 6-Pack

Theo Buchanan
Power of Patterns Fractals 6 Pack Book PDF

Author : Theo Buchanan
Publisher : Teacher Created Materials
Page : 51 pages
File Size : 48,6 Mb
Release : 2017-03-31
Category : Young Adult Nonfiction
ISBN : 9781493837168

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Power of Patterns: Fractals 6-Pack by Theo Buchanan Pdf

Fractals are defined as shapes that exhibit self-similarity and high complexity. These shapes appear in many different forms throughout nature. This high-interest nonfiction reader introduces students to fractals, and teaches them new concepts and vocabulary terms including fractal compression, Mandelbrot set, constructual law, logarithmic spiral, Archimedean spiral, dendritic patterns, and venation patterns on leaves. Developed by Timothy Rasinski-a leading expert in reading research-this purposefully leveled text guides students to increased fluency and comprehension of nonfiction text. The complex text structure adds rigor and allows students to delve deeply into the subject matter. The images support the text in abstract ways to challenge students to think more deeply about the topics and develop their higher-order thinking skills. Informational text features include a table of contents, sidebars, captions, bold font, an extensive glossary, and a detailed index to further understanding and build academic vocabulary. The Reader's Guide and Try It! culminating activity require students to connect back to the text, and provide opportunities for additional language-development activities. Aligned with state standards, this text connects with McREL, WIDA/TESOL standards and prepares students for college and career. This 6-Pack includes six copies of this title and a lesson plan.

Biosensors: Kinetics of Binding and Dissociation Using Fractals

Ajit Sadana
Biosensors Kinetics of Binding and Dissociation Using Fractals Book PDF

Author : Ajit Sadana
Publisher : Elsevier
Page : 418 pages
File Size : 47,6 Mb
Release : 2003-12-17
Category : Science
ISBN : 0080528139

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Biosensors: Kinetics of Binding and Dissociation Using Fractals by Ajit Sadana Pdf

This title brings to the attention of researchers in the industry, and in academia, the application of fractals to help in modeling the analyte/receptor binding and dissociation kinetics on biosensor surfaces. The work builds on that done in Engineering Biosensors: Kinetics and Design Applications, published by Academic Press in 2002. In particular, more examples are provided of where biosensors may be effectively used. This sequel is extremely timely, given the anticipation that the applications and reliance on biosensors will increase due to the advances in miniaturization, (wireless) communications, and the development of new materials (especially biological and chemical). Other applications of biosensors on the increase can be found in: the protection of civilian structures and infrastructures; protection from possible biological and chemical threats; health care; energy; food safety; and the environment to name a few. Covers all areas of applications of biosensors No other book on biosensors describes the kinetics of binding Provides numerous examples of where biosensors may be used