Product Description
Applications of Fractals and Chaos presents new developmentsin this rapidlydeveloping subject area. The presentation ismore than merely theoretical,it specifically presentsparticular applications in a wide range of applicationsareas. Under the oceans, we consider the ways in whichsponges and corals grow; we look, too, at the stability ofshipson their surfaces. Land itself is modelled andapplications to art, medicineand camouflage are presented.Readers should find general interest in the range of areasconsidered and should also be able to discover methods ofvalue for their own specific areas of interest fromstudying the structure of related activities. ... Read more

Customer Reviews (1)

Interesting survey of the field
This book covers some of the many areas in which the study of fractals and/or chaos have found useful homes.It is written with the assumption of some level of scientific understanding on the part of the reader, but can serve as an interesting survey for someone who does not yet have the necessary scientific background and language. ... Read more

Product Description

This volume is the second edition of the highly successful Fractals Everywhere.The Focus of this text is how fractal geometry can be used to model real objects in the physical world.

This edition of Fractals Everywhere is the most up-to-date fractal textbook available today.

Fractals Everywhere may be supplemented by Michael F. Barnsley's Desktop Fractal Design System (version 2.0) with IBM for Macintosh software.The Desktop Fractal Design System 2.0 is a tool for designing Iterated Function Systems codes and fractal images, and makes an excellent supplement to a course on fractal geometry

* A new chapter on recurrent iterated function systems, including vector recurrent iterated function systems.
* Problems and tools emphasizing fractal applciations.
* An all-new answer key to problems in the text, with solutions and hints. ... Read more

Customer Reviews (12)

Way over my head!
Man, this got way too deep, way too fast. I have some algebra, some statistical analysis, some calc... This just took off running and left me in the dust. I was "fooled" by the "first course" title?

In fractal geometry we are concerned with the structure of subsets of various very simple "geometrical" spaces. Such a space is denoted by X. It is the space on which we think of drawing our fractals; it is the place where fractals live. What is a fractal? For us, for now, it is just a subset of a space. Whereas the space is simple, the fractal subset may be geometrically complicated.

So, why is *this* a fractal, but, *That*'s just a recursive function? Idunno, and I guess that I won't until I find another book?

This is a beautiful book. LOTs of graphics, TONs of information, but not for me.

The most intelligent and usefull book on fractals
I really enjoyed the author's style. It is not a typical mathematical book.So if you are into strict formal mathematics this is not for you. The author has deep understanding of fractals and he is an expert in Iterated Function Systems (IFS). The shadow theorem is one of the biggest hits on this book.
What I particularly like from this book is the illustrations. They let you understand fractals intuitively. It is definitelyan ideal book for engineers. Try also his other more advanced book SuperFractals
The only part of the book that is not very well developed is chaos, although the "chaotic dance" presented on the book is good starting point

A below average text book

Barnsley's book has a shortcoming common to many math text books -- it's poorly written.Barnsely's writing style is superfluous and rambling.What I learned from this book was in spite of Barnsley's writing, not because of it.

Furthermore, the book's illustrations are substandard.There are over five different fonts used in illustrations (including hand written text).This leads to confusion when you're unsure if the text in Barnsley's illustrations is referring to Greek letters or the conventional alphabet.Another shortcoming is that Barnsley intermingles end of chapter exercises with new concepts.You may have problems 1.1 to 1.5 reviewing what you've already learned, and then problem 1.6 introduces completely new material.This is a problem throughout the book, as important concepts are introduced in exercises or otherwise illogical locations.

On the positive side, solutions to most exercises are presented at the end of the book.Overall the book was useful, but learning the material was unnecessarily difficult due to the book's shortcomings.

Sometimes annoying but instructive
Although instructive, this book is sometimes annoying to read. The author seems to be playing his cards very close to the vest and not telling us everything.

For instance, there is little or no instruction on how to implement the IFS attractors presented as a panacea for data compression. This seems to be proprietary to his company. It also seems that hands-on manipulation is crucial to the images' production, contrary to the author's claims.

If you can understand the mathematics you may find the book useful, as I did when writing my book Fractals in MUsic.

A bad book for 7 th graders like me
this is a bad and very confusing book for a young student in, say... 7th grade, like me.The language is incomprehensible and there are no visual aids. ... Read more

Product Description
"It is only twenty-three years since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot Set. The graphics were state of the art, though now they may seem primitive. But how that picture has changed our views of the mathematical and physical universe! Fractals, a term coined by Mandelbrot, are now so ubiquitous in the scientific conscience that it is difficult to remember the psychological shock of their arrival. What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world. It is not just a book about a particular class of problems, but contains a view on how to approach the mathematical and physical universe. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. So read the book, look at the beautiful pictures that continue to fascinate and amaze, and enjoy! "

--From the foreword by Peter W Jones, Yale University This book provides a history of the Mandelbrot set of quadratic dynamics together with the authors hard-to-find early papers. It has extensive illustrations throughout and is divided into four sections: quadratic dynamics, klein groups, Minkowski measures, and Julia sets. Each section starts with introductory chapters giving historical context and background to the material. Benoit B Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T J Watson Research Center. He was awarded the Wolf Prize for Physics in 1993 and the Japan Prize for Science and Technology in 2003. ... Read more

Product Description
The authors present an unusual attempt to publicize the field of Complex Dynamics, an exciting mathematical discipline of respectable tradition that recently sprang into new life under the impact of modern computer graphics. Where previous generations of scientists had to develop their own inner eye to perceive the abstract aesthetics of their work, the astonding pictures assembled here invite the reader to share in a new mathematical experience, to revel in the charm of fractal frontiers. 184 illustrations in 211 parts, 88 in color. ... Read more

Customer Reviews (7)

A Beautiful Introduction To Fractals
Fascinating photos, although the instructional text is indeed "complex" as the book itself states.

Anna Marie Fritz, author of "Funny Feline Fotos" and other amazon books.

One of the first fractal books!
One of the first books on fractals that gave info on the mathematics to creating them and what parameters or sections of the set that yield some beautiful renderings. The math is for a math major but still interesting.

The Essence of Beauty
I spent all last evening reading snippets of The Beauty of Fractals (those few paragraphs that a layman could understand) and admiring the sheer beauty of the diagrams/maps.I had not realised there was an aesthetic component to mathematics, and I certainly did not know that aspects of what is generally thought of as a dry science can be so visually appealing, not to say stunning.

I cannot understand why some people would argue the intrinsic artistic merit of something computer-generated and 'unnatural', when the results speak for themselves.

Beauty, true, is perceived, and lies in the eye of the beholder. It can be very subjective. But there are certain aspects of visual appeal that go beyond that. One would think that a symmetry of form, the complementary use of colours, the balance of shape and form, light and shade, arcs and curves--all these combine to give an objective, irrefutable fact of beauty that transcends thought and emotions, if not the senses.

In a couple of the chapters, it was said, and here I paraphrase:

The two modes of analysis and intuition as human means of understanding the natual world--need they be considered at opposite poles? Do they not complement one another? Are the thinker and the dreamer not one?

I find that very intriguing, just as I find the idea of chaos and order existing together in natural, dynamic processes being actually TYPICAL of Nature.

The word 'Chaos' has such negative connotations, implying confusion and destruction, but if I were to replace it with the word 'Disorder', then things begin to fall into place.

There can be no Order if there were no Disorder, for how then would we know the difference? In fact, one of the writers go so far as to say that it is the very existence of Disorder within Order that confers the essence of beauty found in Nature.
That is so true. It is the very non-linear aspect of Nature, that which mathematics, up till Mandelbrot, have been unable to map, that is so appealing in the visual sense.

In Nature, which, apart from abhorring vacuums, also has no place for a straight line (oh, how the poor, innocent straight line is maligned in the preface), beauty is inarguable, irrefutable, and only after that does it have history and context, different to and for each beholder.

So both Chaos/Disorder and Order co-exist in Nature, hand in hand. Order alone, rigidly disciplined, artificially-imposed, seems to require Disorder to breathe life into it.

Taking this a step further, our perception of beauty in all things is affected by Nature.

In yet another chapter, someone quoted someone else and here I go
paraphrasing again.

Beauty in science is the same as beauty in other disciplines-art, music,literature, what have you.'A fog of events, and suddenly you see a connection. It expresses a complex of human concerns that goes deeply to you, that connects things that were always in you that were never put together before.'

The thinker and the dreamer co-exist within each person, just as the analytical and intuitive modes of thought co-exist, not at opposite poles,but complementing one another.

Intuition and analysis complement, rather than confound (or they should, gods-willing).

The artist and the scientist complement each other, i.e. Art and Science are not the opposing polarites of disciplines as some would have us think.

The thinker and the dreamer ARE one.

And this book has shown that the essence of beauty lies in the marriage of Art and Science.

(Disclaimer: Mere thoughts from a layman.)

Time goes by... the pictures fade
Amazon dot com gives no credit for my earlier reviews.... I wrote the first review without thinking or spell checking, fast.There are still parts of this book I can't duplicate! And parts that are just written so bad no one can understand them, but most of it stands the test of time, like Mandelbrot's article. This will probably be a classic in the future! I think the free Fractint documentation is probably better for a beginner or Hans Lauwerier's " Fractals".

Swirly
Although one of the earliest titles to bring fractals into the mainstream, 'The Beauty of Fractals' isn't as visually exciting as the follow-up, 'Chaos and Fractals', and it's a very dry read - in 1986 complex dynamics were an esoteric field of mathematics that had yet to transfer to student posters and rave videos. At this price it's restricted to people who absolutely need it, although along with 'Godel, Escher, Bach' it's one of the seminal hackish coffee-table books. ... Read more

Product Description
Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it. Introducing Fractal Geometry traces the development of this revolutionary new discipline. ... Read more

Customer Reviews (10)

NEVER in Stock!!!!!
I ordered this book in July, specifically, along with many other curious items since I was ordering this anyway; I was extremely anxious to receive it.Unfortunately, I NEVER received it but DID just (middle of October) receive word I never would and they cancelled the order.I would not have placed this order if I had known they would never get this in stock - EVER!!I never shop bait-n-switch stores OR any affiliate.I'm sure the book is great, but I would not order from Amazon since they are not able to obtain it.Try another book store!

Interesting book, Illogical progression
I bought this book because I wanted something that would introduce me to the topic, fractal geometry, without overwhelming me with technical jargon, and this book does do that. However, the way in which the book is constructed is quite convoluted. It has illustrations on every page, some of which are left without any description, that may or may not be related to the topic discussed on the page.

The book doesn't progress in terms of chapters, rather sort of chronologically. However, in doing this it just comes off disjointed. The paragraphs are jumpy and disconnected from short telegraphic sentences.
While reading the first 1/3 of the book, I had convinced myself that the book must have been written for an audience much, much younger than I. However, I don't see how that can be logical given the subject material. The latter 2/3 of the book also convinced me otherwise.
So in general, yes, you will learn from this book, provided you are able to follow the progression and are able to correctly interpret the meanings of the diagrams.

Excellent introduction to fractals
This book was an excellent introduction to fractals with clear writing and numerous illustrations.I'm ready for the next level!

disappointing, irregular

1.0 out of 5 stars mixed up, February 10, 2009
By Andres Amador "pickletruck" (san francisco, ca) - See all my reviews
(REAL NAME)
i'm not new to fractals by any means but i picked up this book in a bookstore and appreciated the simple way the ideas were being conveyed and with lots of graphics. after getting into it though, i was dismayed by it combination of simplicity and then sometimes dense detail. I mean, sometimes he would bring up something tantalizing, something ripe for expansion and then let it drop. and then other times he would go into detail that had me wondering if even HE knew what he was saying.

for a much better read with lots of great images, i highly recommend 'turbulent mirror' its a necessity for those curious is fractals and chaos.

loved it
Want to learn what fractal geometry is?Get this book, you'll know enough to be able to join in conversations on the topic. ... Read more

Product Description
Reprint from Pure and Applied Geophysics (Pageoph), Volume 157 (2000), No. 4. Contributions from the Third International Symposium on Fractals and Dynamic Systems in Geosciences, Stara Lesna, Slovakia, June 1997. Contains new ideas and applications of fractal geometry in diverse branches of geoscience. Softcover. ... Read more

Product Description
Benoit Mandelbrot's pioneering research in fractal geometry has affected many areas of mathematics, physics, finance and other disciplines. The papers reprinted in this third volume of his Selected Works center on a detailed study of fractional Brownian functions, best known as the mathematical tools behind the celebrated fractal landscapes. Extensive introductory material preceding the reprints incorporates striking new observations and conjectures. This book explores the fractal themes of "self-affinity" and "globality." The ubiquity of "wild" temporal and spatial variability led Mandelbrot, in the early 1960's, to conclude that those phenomena lie beyond the usual statistical techniques and represent a new state of indeterminism. New mathematical tools are needed, and this book contributes to their development. ... Read more

Product Description
For C programmers, this provides readers with the necessary background to investigate and create fractals on the PC. A source code for all the fractals discussed in the book is included. ... Read more

Customer Reviews (1)

Great Non-practicle experience
This is a real cool book, not really any application for me professionally, but it was fun to try to make the examples. It was a fun exercise in a completely different realm of C than I am used to. Kind of like a cross-word puzzle based on a genre you were totally unfamiliar with, but A fun learning process just the same. Had I seen the picture of the Author prior to purchasing this book I would have clearly known that this was a science text as he just has that "scientist" look about him. I would recommend this to any C programmer that has extra time on their hands, really loves C and wants to try something way out there more on the scientific side of C or if fractal programming does apply to your profession. ... Read more

Product Description
This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research. ... Read more

Customer Reviews (1)

Somewhat dated, but still a good introduction to chaos and fractals
This material is the collection of lecture notes used for a short course presented by the American Mathematical Society in 1988. Therefore, the material is somewhat dated. The topics are:

*) Dynamics of simple maps
*) Nonlinear oscillations and the Smale horseshoe map
*) Fractal basin boundaries and chaotic attractors
*) Julia sets
*) The Mandelbroit set
*) Introduction to fractals
*) Iterated function systems

However, despite the passage of almost twenty years, this material is still an excellent introduction to these subjects. At the time of the conference, the material was new, exciting and it seemed that new applications of chaos and attractors were being discovered on a daily basis. At the time, I was a regular reader of the weekly "Science News" magazine and hardly an issue went by without a mention of chaos or fractals. Since it was so new, the material had to be presented at a level that led to understanding. Therefore, the modern reader that is relatively ignorant of the topics can get a great deal of benefit from this book.
... Read more

Product Description
The combination of fractal geometry and stochastic methods can be used to create convincing models in many different areas of science such as biology, chemistry, computer science, mathematics and physics. The present book deals with the mathematical theory needed for this purpose. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the field. The contributors were the main speakers at the conference Fractal Geometry and Stochastics II held at Greifswald/Koserow, Germany, in August 1998.

The book is addressed to mathematicians and scientists who are interested in any of the following topics:

Fractal dimensions
Fractal measures and multifractals
Self-similar and self-affine fractals
Random fractals
Stable processes
Ergodic theory and dynamical systems
Harmonic analysis and stochastic processes on fractals

The readers will be introduced to the most recent results and problems on these subjects and also be treated to an overview of their historical development. Both researchers and graduate students will benefit from the clear expositions.

Series: Progress in Probability, Volume 46 ... Read more

Customer Reviews (1)

Pictures and math.
This is a very nice collection of papers: tutorials, and well written research presented to a wide audience. They cover stochastic aspects, geometry, analysis, iterated function systems, algorithms, to mention just a few. And they are written by authorities in the field. Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an exciting mathematical history. This very important book presents the subject in a way that it can be taught to students. Or it can be used for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. A recent example of this: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The authors have produced an attractive book on fractals. There are others, for example one by Falconer from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent. ... Read more

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Paperback ... Read more

Product Description
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods. ... Read more

Customer Reviews (3)

Ingenious Compilation of Essential Fractals
The Geometry of Fractal Sets by Falconer is an elegant composition of many necessary fractals, measures, projections, and dimensions.Included in the monograph are the most inspiring and applicable Besicovitch fractal sets, Kakeya fractal sets, the Appolonian packing fractal, osculatory packings,horseshoe fractals, Perron trees, hypercycloids, the Nikodym set, Lebesgue measure, Hausdorff dimension, sets of integral and non-integral dimension, sets in higher-dimensions, Borel measure, binary sets, Vitali coverings, polar reciprocity, Souslin sets, sigma-fields, tangents, net measures, the semicontinuity theorems of Golab and Vishtukin, osculatory packings, diophantine approximations, Fourier series, transforms and multipliers, Brownian motion, Grassmanian manifolds.......you name it this book explains and connects it all.

The text is written in full proper-fonting and contains many illustrations.Qualitatively the book should be of high value to researchers, graduates, and Phd's with the finest tastes.

Introduction to geometric measure theory
This book is devoted to the hausdorf measure and Hausdorff dimension of subsets of R^n and to an extensive study of their geometry: existence of tangency, projection, etc. Onechapter deals with Besicovich sets used for constructing counter-examples, especially in Harmonic analysis.

The book finish with a magnificent list of examples of haussdorff dimension computation: self-similar sets, Apollonian packings, number theory, Feigenbaum logistic map and Brownian motion.
The bibliography, of incredible quality, achieves to make the book a reference for anyone interested in fractals.

Advanced treatise on fractal geometry.
This text is a must-reading for anyone seeking advanced knowledge on fractal geometry. It is dense and deep, but clear and concise. It includes a lot of interesting material ranging from basic measure-theoretic conceptsup to the disprove of Vitushkin's conjecture. It's got an extensive list ofreferences, mostly to the original papers, making it a fundamental researchtool.

As it can be inferred from the preceeding paragraph, the book isnot for begineers; it was designed for graduate level courses. Undergradsand laymen should start with Edgar's "Measure, Topology, and FractalGeometry" and Falconer's "Fractal Geometry: MathematicalFoundations and Applications".

Please check my other reviews (justclick on my name above). ... Read more

Product Description

"Fractal" is a term coined by mathematician Benoit Mandelbrot to denote the geometry of nature, which traces inherent order in chaotic shapes and processes. Fractal concepts are part of our emerging vocabulary and can be useful in identifying patterns of human behavior, culture, and history, while enhancing our understanding of the nature of consciousness.

According to William J. Jackson, the more one studies fractals, the more apparent their connections to the humanities become. In the recursive patterns of religious music, in temple architecture in India, in cathedral structures in Europe and America, in the imagery of religious literature depicting infinity and abundance, and in poetic descriptions of the nature of consciousness, fractal-like configurations are pervasive. Recognition of this structure, which is also found in social organizations and ritual symbolism, requires only that one develop "an eye for fractals" by studying the work of researchers and observing nature. One then begins to see that the separation of humanities and science is convenient oversimplification, not an ultimate fact. Includes a DVD of animated fractals.

Customer Reviews (1)

sacred geometry
Before reading this book, fractals conjured in my mind, those trippy psychedelic posters. But Fractals are certainly a trippy subject, and the implications are beyond pop culture and trippy posters. Fractals reflect the ever unfolding but infinite patterns of the universe and nature. This book explores how humanity has innately picked up on the deep sense of order within the universe and human consciousness.

William Jackson takes us across cultures to explore the mysteries of the infinite.More interesting then reviewing the actual use of fractals as symbols is a discussion on the fractal experience. There is the sense that fractals as images are only reflective of existence and experience...The repeating pattern, the sense of infinity - there is certainly something to awe. And it seems that we humans have had a sense of it for some time. Jackson illustrates this point with an examination of poetry - Dante, Tennyson, and Dickinson all weighing in. Then there are the echoes of mathematicians, biologist, psychologist, and other scientist, philosophers, and mystics. The human psyche, culture, and personality all reveal the fractal condition. What other mysteries does fractal geometry reveal? - Divine consciousness, the inter-connectedness of all things?

- Look into the mirror and there is the universe
... Read more

Product Description
This book presents the analysis of textured images using fractal geometry, and discusses its application to imaging science and computer vision when modeling natural objects. The authors explore the methods which can be used to simulate, analyze, and interpret coherent images, and demonstrate a new approach which segments each image into regions of similarity that can be characterized by a random fractal with a given fractal dimension.
Fractal Geometry in Digital Imaging is based on a research project, but has been written with a broad coverage and user friendly math to make the book accessible to a wider audience. It includes real world experiences and applications using the techniques described.

* Discusses the analysis of textured images using fractal geometry
* Explores the methods used to simulate, analyze, and interpret coherent images
* Contains coverage of real world experiences and applications
* Written in a user friendly style ... Read more

Product Description
Fractal sets serve as excellent models in physics, chemistry, biology and other fields. However, the actual applications of these models are often unknown even to specialists in fractal theories. The communication of recent results utilizing fractal concepts in experimental and industrial engineering research was thus a major challenge to the above conference. The resulting proceedings which are published here are organized around five main themes: materials processing, flow, natural sciences, signal and image analysis and mathematical methods. Almost 50 papers are included in this volume. Besides the classical topics, the book introduces an important session on fractal signal and image analysis, a subject which is rapidly gaining recognition in computer science and engineering for its promising industrial applications. ... Read more

Product Description
Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field. ... Read more

Product Description
Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals. ... Read more

Product Description
Interest in image compression for Internet and other multimedia applications has spurred research into compression techniques that will increase storage capabilities and transmission speed. This tutorial provides a practical guide to fractal and wavelet approaches--two techniques with exciting potential. It is intended for scientists, engineers, researchers, and students. It provides both introductory information and implementation details. Three Windows-compatible software systems are included so that readers can explore the new technologies in depth. Complete C/C++ source code is provided, enabling readers to go beyond the accompanying software. The mathematical presentation is accessible to advanced undergraduate or beginning graduate students in technical fields.

Contents

- Preface
- Introduction
- Iterated Function Systems
- Fractal Encoding of Grayscale Images
- Speeding Up Fractal Encoding
- Simple Wavelets
- Daubechies Wavelets
- Wavelet Image Compression Techniques
- Comparison of Fractal and Wavelet Image Compression
- References
- Appendix A: Using the Accompanying Software
- Appendix B: Utility Windows Library (UWL)
- Appendix C: Organization of the Accompanying Software Source Code ... Read more

Customer Reviews (2)

Excellent as a tutorial !
This book is very good to be a tutorial or an introduction to this field. The presentation is simple and you can follow it easily.
I had project on this topic exactly, and I learned much from it.

This is book is on target
This book is on target for those who would like to learn the application of wavelet theory in image processing, which is an exciting field waiting for more people to explore. The applications of wavelet theory is numerous,but this is a hard-to-find book that concentrates on image processing, itworths a trial. ... Read more

Product Description
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling ? self-similarity, long-range dependence and multi-fractals ? are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space. ... Read more

Product Description
Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition.
* Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals.
* Each topic is carefully explained and illustrated by examples and figures.
* Includes all necessary mathematical background material.
* Includes notes and references to enable the reader to pursue individual topics.
* Features a wide selection of exercises, enabling the reader to develop their understanding of the theory.
* Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers.
Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. ... Read more

Customer Reviews (6)

The Basic Text For Understanding Fractals
Fractal Geometry:Mathematical Foundations and Applications by Kenneth Falconer(second edition)is one of the most important mathematical books of this beginning of the 21-st century.It is a book of high mathematical level which can be very useful to non-mathematicians possessing a reasonable mathematical instruction and a logical mind.Mathematicians will find in this book deep and sophisticated notions and proofsand non-mathematicians will find all the concrete applications of the theory of fractals(see e.g.the new paragraph dedicated to fractals in finance).Prof.dr.Ion Chitescu
Faculty of Mathematics and Computer Science
University of Bucharest

A rare find
I agree with all that was said by the other reviews here but add one important point. The physical layout, (typeface, drawings, whitespace etc.) of this book is brilliantly done. This is often overlooked by the producers of technical works who do it "on the cheap", but it is vital if one is to use the book day after day, as I have had to.

While the subject matter is not easy, this is an excellent book to motivate one to get stuck into the underlying mathematics. The reward is a little insight into the often beatiful theorems and practical results found in this stimulating field of study.

What every student should know about fractals.
Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

Theoretical as well as practical insight
The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.

Exposes fractal geometry as a real mathematical discipline.
I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basictopological concepts and then proceeds to develop the theory for severalpossible definitions of fractal dimension, showing the relations betweenthem. Then it explores deeply the local geometry of different kinds offractal objects, and studies some other geometrical situations, like thepojection of fractals (ever thought of a DIGITAL sundial? Here it isdescribed!).

The book also includes a lot of applications to other areasof mathematics and physics, a great amount of graphics, and muchmore.

The text is suitable from third year undergraduate school and on.It is a larger but lighter version of "The Geometry of FractalSets". ... Read more