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Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study. ... Read more

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Seems to be an unread classic
Some people might prefer an easy approach to fractals,
but long experience has taught me that Dr. Edgar is right in trying to develop fractals
in a systematic way. This book tries to lay a foundation
in traditional analysis, measure theoryand topology for the rough
self-similarity of sand piles and drainage basins.
The trajectories of Levy flights are shown on page 248,
but as in his other books Edgar seems to forget that you need concrete
generating function in complete analysis?
Combinatorial theory seems to be a bridge between analysis and fractal measures
and that is ignored in this book. The quantum mechanical
connection of fractals is also a more recent development,
but is shadowed in the product spaces herein. ... Read more

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"This delightful book illustrates beautifully the paradigm shift inphysics from writing equations and solving them to computer modeling andexperimentation." -- Greg Chaitin, author of The Limits ofMathematics

In this book Gary William Flake develops in depth the simple idea thatrecurrent rules can produce rich and complicated behaviors.Distinguishing "agents" (e.g., molecules, cells, animals, and species)from their interactions (e.g., chemical reactions, immune systemresponses, sexual reproduction, and evolution), Flake argues that it isthe computational properties of interactions that account for much ofwhat we think of as "beautiful" and "interesting." From this basicthesis, Flake explores what he considers to be today's four mostinteresting computational topics: fractals, chaos, complex systems, andadaptation.

Each of the book's parts can be read independently, enabling even thecasual reader to understand and work with the basic equations andprograms. Yet the parts are bound together by the theme of the computeras a laboratory and a metaphor for understanding the universe. Theinspired reader will experiment further with the ideas presented tocreate fractal landscapes, chaotic systems, artificial life forms,genetic algorithms, and artificial neural networks. ... Read more

Customer Reviews (17)

Not fun
Your eyes will glaze over. Fascinating subjects, but I don't feel they were explained very well.

A Waaaay Cool Book!
IMHO this book should be part of every US high school or undergradate Science/Math curriculum, and would be worth twice the price.The author's enthusiasm is infectious, his writing style very clear, and his material well cited.He also maintains a website with free software downloads that illustrate the many mind expanding (w/o drugs! (-:) concepts discussed. Although thanks to magazines like Wired (minus its aggressive leftist politics and more aggressive BB censoring)the sciences have become "cooler." Nevertheless, there is still A LOT of work to do, and damage to be undone, from academically inferior and unenthusiastic so called math/science "teachers" in US schools. I don't usually rate books five stars, but I am rating this one a big FIVE stars.

An enjoyable read
Granted you can find most of this info elsewhere but still this is a great read. Well written, a nice collection of material, and downloadable source code. I found it to be a very inspiring book.

Great book
This is an excellent book.I've been reading it for weeks.The chapters are not long, but the content is amazing. The author combines explanations and equations in a format that is demonstrative and repeatible.This is a very good book to study yielding the understanding necessary to penetrate many other advanced books on complexity theory. The author starts by examining whole numbers and real number problems.Next, he examine Godel's incomplete theory of predicate logic showing that no formal language is complete.Next, he examines fractals, self-similar patterns, low ordered with high compression and high order with low order compression, L-systems, and Juliet and Mandel-brot fractals. Fractals open up an emmense study into the complex pattern from simple rules and recursion. Next, he examines equations of strange attraction, chaos, and demonstrates stability behavior within complexity. Next, he looks at small universes created by running CA.NNs and GAs are examined in the last chapter. I was excited to write down many of the authors processes and run them using OpenGL and C.I believe this book to be an excellent book for college students. The material is easy to understand and the content very demonstratible.Cause and effect are very cohesive in this book.Even though the book seems simple, it covers an vast amount of topics necessary to understanding AI and AL.

Good first book on the subject of simulating natural phenomena
This is a good introductory textbook for college undergraduate mathematics and computer science students that attempts to combine the theory of computation with some mathematical concepts and in the end, manages to model virtual life by explaining basic concepts in chaos, adaptation, fractals, and complex systems. There are better books on all of these subjects, but few others do such a good job of tying together key concepts from each discipline into the one theme of this book. However, there is only enough room to outline the included subjects rather than investigate them thoroughly.

Also, the mathematics is elementary enough to be accessible to a mathematically mature high school student. The mathematics is concisely explained as it is needed, with just a page or two for each of calculus, linear algebra, affine transformations, complex numbers, vector calculus, and matrix algebra. Thus, the included mathematics makes a better refresher than a tutorial for the novice even though the author states in the preface that he wrote this book for a younger version of himself. This book teaches its subject matter mainly by demonstrating concepts through simulations that are expressed in dozens of programs which illustrate the points being made. Instructions on using the programs are scattered throughout the book. The source code is available for download on the web, along with selected excerpts from the book.

I would recommend this as a first book for those interested in simulating natural concepts, but it should not be your last if your goal is to truly grasp the concepts presented and produce simulations of your own. However, an even better book on this subject is "Mathematical Models in Biology", although it is an advanced text. A very accessible book that is also more advanced than this text is "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering". It clearly explains the mathematics while tying it into key concepts in nature. "Chaos and Fractals" by Peitgen is a good book on the subject for the layperson with a fascination for mathematics presented in some depth. The book also has various Java programs that illustrate key concepts. ... Read more

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From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a diskette where a selection of executable programs exploring the fractal concept can be found. ... Read more

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Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study. ... Read more

Customer Reviews (1)

A book that does Justice to both topics
I don't think there can be a price on this book. It offers discrete information that has the wieght of being both technical and general. It really puts the reader in the position to comfortably understand the topics. I can't see how anyone would ever want to sell this book, unless they memorized every page. It can be refrenced over and over again to get limtless information. Each chapter closes with suggestions for further reading,extending into every field: geology, physics, chemistry,etc. I found the book at the library, and just couldn't put it down. It smoothly transitions between a first section on fractals, then a middle area where both chaos and fractals intersect, and lastly a final chunk on chaos. The beauty is that you can start where ever you want in the book because each chapter builds independently, while tieing things together at the same time. A brilliant book published by the Institute of Physics. ... Read more

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New developments in computer science, biology, mathematics and physics offer possibilities to obtain deeper understanding of growth and forms of organisms. It is now possible to carry out simulation experiments in which the growth process can be simulated in virtual computer objects. In this book, methods from fractal geometry are applied to model growth forms. As a case study, a type of growth process is used which can be found among various taxonomic classes of organisms such as sponges and corals. The growth of these organisms is simulated with 2D and 3D geometrical objects. The models presented in the book provide a rendering method for natural objects which is based on the actual growth process. The models can be used, for example, to understand the amazing variety of forms to be found in a coral reef. Models which mimic the growth of forms and the environmental influence on the growth process are also useful for ecologists. A combination of simulation models and the actual growth forms can be used to detect the effects of slow changes in the environment. ... Read more

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This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.

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Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far reaching implications in a host of phenomena. This book describes diffusion and transport in disordered media such as fractals, porous rocks and random resistor networks. Part I contains material of general interest to statistical physics: fractals, percolation theory, regular random walks and diffusion, continuous time random walks and Levy walks, and flights. Part II covers anomalous diffusion in fractals and disordered media, while Part III serves as an introduction to the kinetics of diffusion-limited reactions. Part IV discusses the problem of diffusion-limited coalescence in one dimension. This book will be of particular interest to researchers requiring a clear introduction to the field. It will also be a valuable source to graduate students studying in areas of physics, chemistry, and engineering. ... Read more

Customer Reviews (1)

A fantastic introduction to the field...
I am a graduate student in statistical physics with a primary interest in diffusion-limited reactions. I have found the above book to be invaluable, so much so that I'm disappointed that I didn't know about it earlier, as I'm sure it would have accelerated my understanding. It is, in my opinion, the best introduction to the field of diffusion-limited reactions that I'm aware of and certainly makes the research literature in this area much more accessible. I have also found the other sections of the book to be particularly illuminating and essential background reading, with Part I covering many of the principles of statistical physics. Each chapter contains a list of exercises to enhance understanding of the material and a list of "Open Challenges" which provoke new avenues of research. I personally think that the book references the research literature extremely well (indeed the authors have themselves made substantial contributions to the field) which makes it easy to pursue further details on areas of interest. I regard the book as essential for anyone wishing to develop an understanding of anomalous diffusion in disordered media and to be particularly accessible to graduate students and young researchers. It has certainly made it easier for me to make the transition from student to researcher in this area of statistical physics. ... Read more

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This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics. ... Read more

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Orange Circle Studios, superior images, excellent color reproduction, and top quality materials make these wall calendars stand out from the rest! 16 month calendar, dimensions are 12 w x 12 h. ... Read more

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The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields.
The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications. ... Read more

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The authors describe mostly in non-technical language thedevelopment of a new scientific paradigm based on nonlineardeterministic dynamics and fractal geometry. The concepts from thesetwo mathematical disciplines are interwoven with data from thephysical, social and life sciences. In this way rather sophisticatedmathematical concepts are made accessible through experimental datafrom various disciplines, and the formalism is relegated toappendices. It is shown that the complexity of natural and socialphenomena invariably lead to inverse power law distributions, both interms of probabilities and spectra. This book tries to show how tothink differently about familiar phenomena, such as why the bell-shapecurve ought not to be used in teaching or in the characterization ofsuch complex phenomena as intelligence. ... Read more

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The use of fractals in engineering is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the growth in techniques available for the application of the ideas of fractals and complexity to a variety of engineering fields. The potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Signal and image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument.

Consisting of papers written by a world-wide pool of contributors, the multidisciplinary approach of "Fractals in Engineering" will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds.

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Science has begun to recognize the merit of studying complex phenomena in situ.Fractal geometry is one such approach, and this book discusses its application to complex problems in molecular biophysics. ... Read more

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This volume considers river basins and drainage networks in the light of their scaling and multi-scaling properties, and the dynamics responsible for their development. ... Read more

Customer Reviews (1)

Good overview of subject, lots of references
Easy to understand analysis of river systems.This is a good text for a graduate-level course.It is also a valuable reference for any geologist or hydrologist involved in work that deals with modern or ancient fluvial systems.CJD ... Read more

Customer Reviews (2)

The mathematics of fractals rather than their beauty
Most advances can be thought of as evolutionary, but in describing the contents of this book, one is tempted to add a soft r in front of the e.If fractal image compression lives up to its early promise, then the r should be made a very hard one.One seemingly inviolable law of computing is, ''Data will expand to fill all available memory, whether it be RAM, hard drive or floppy disk.It will also expand to exceed the capacity of any medium of data transfer''.As those who work with transferring large data sets understand, much of the recent success is due to the quality of the data compression algorithms rather then to improvements in the hardware.Compression utilities are now commonly bundled with many systems, for example, DOS 6.0.
To illustrate the potential impact offractal compression, we take the following paraphrased quote from the introduction to the book.'' Encarta is a multimedia encyclopedia on a single CD... .In addition to an exhaustive collection of articles it contains seven hours of sound, 100 animations, 800 color maps... more than 7,000 photographs... and all encoded in less than 600 megabytes of data.All of the pictures are stored using fractal compression techniques." The mathematics used to obtain such rates of compression is thoroughly explained, but it is not easy to understand.Presented in the standard form of theorem followed by proof, some background in real analysis and linear algebra is essential to understand the heavier ideas.But it is well worth it, as some of the results are truly astonishing.Most impressive is the ability to zoom in on the images without significant loss of clarity.C source code solutions to some of the problems are included.
There is no doubt in my mind that by the end of this decade, exposure to fractals will be an essential component of the undergraduate major in applied mathematics.The majority of pure math programs will also include some exposure.While futurists dispute the consequences, there is universal agreement that the rapid transfer of enormous amounts of data will be the driving economic and entertainment force of the next several decades.Fractal compression techniques appear to be the leading candidate to provide the necessary degree of compacting.
Suitable for a course in the mathematics of fractals or an advanced seminar in data compression, this book should be required reading for all applied mathematicians.It is truly one of the most fascinating books that I have ever encountered.

Published in Mathematics and Computer Education, reprinted with permission.

A Master Work of a Great Mathematician
With code and example Barnsley leads your through some very hard concepts. I really like that he has covered the topic of information compression so well for the traditional archiving methods. A must for anyone serious about fractals. Your unique Associates ID is:thefractaltransl. ... Read more

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Customer Reviews (4)

Science and art, together again
I was aware of fractals for some time and after watching a NOVA film "Hunting the Hidden Dimension" (2008). I went hunting for some of the many books by Benoit Mandelbrot. You can imagine my surprise with I tripped over this book, "An Eye for Fractals" by Michael McGuire.

Stacked up against other fractal works, this book has more stunning pictures both in quantity and quality. Even though the formulas are a tad complex with number lines and complex planes, the ideas on how to make and see fractals are quite clear.

If we were not enamored with fractal the book would stand on its own as great monochrome depictions of nature and monuments. There is one picture by Ansel Adams and the rest are by M McGuire. If you did not see the titles I challenge you to find the Adams picture.

Every time I read this book I get a different insight into the world of fractals and believe you will also.

Fractals: Hunting the Hidden Dimension (Blu-ray) [Blu-ray]

A good primer on fractals and an excellent introduction to their appearance in nature
Looking around in nature, it is easy to find examples of fractals. Individual plants, forests, volcanic activity, wind and water erosion, the flow of water and the movement of plants with the wind can all be described by an appropriate fractal function. Most of the pages of this book are taken up with spectacular images of such natural fractals. A few of the pages are devoted to the mathematical background used to generate the images. It is not rigorous; it was the author's intention to only give some of the general ideas rather than a complete description. They are understandable, even if your math background stops at algebra. Although it was written in 1991, this book is still an excellent primer on what fractals are as well as the large number of ways that they appear in nature.

beautiful BW photographs
I just got this book from the library. It many well printed BW photographs. There is some math discussion on fractals but there is no discussion of computer software for generating fractals pictures. Still a great book.

A beautiful journey through math and nature
One of the only fractal books available for non-mathematicians, An Eye forFractals interweaves beautiful photographs of natural scenes withexplanations of their fractal geometric characteristics.It gives enoughinformation about fractals for a beginner to understand what they are andhow they apply to nature.Its photography makes it a perfect book to leaveout on the coffee table.

Fractal geometry is revolutionizing the way thatscientists perceive the universe and its underlying order.Anyone canbenefit greatly from this understanding by reading this book. ... Read more

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Fractal analysis has rapidly become an important field in materials science and engineering with broad applications to theoretical analysis and quantitative description of microstructures of materials. Fractal methods have thus far shown great potential in engineering applications in quantitative microscopic analysis of materials using commercial microscopes.
This book attempts to introduce the fundamentals and the basis methods of fractal description of microstructures in combination with digital imaging and computer technologies. Basic concepts are given in the form of mathematical expressions. Detailed algorithms in practical applications are also provided. Fractal measurement, error analysis and fractal description of cluster growth, thin films and surfaces are emphasized in this book.
Image-Based Fractal Description of Microstructures provides a comprehensive approach to materials characterization by fractal from theory to application. ... Read more

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Fractal Geometry is a recent edition to the collection of mathematical tools for describing nature, and is the first to focus on roughness. Fractal geometry also appears in art, music and literature, most often without being consciously included by the artist. Consequently, through this we may uncover connections between the arts and sciences, uncommon for students to see in maths and science classes. This book will appeal to teachers who have wanted to include fractals in their mathematics and science classes, to scientists familiar with fractal geometry who want to teach a course on fractals, and to anyone who thinks general scientific literacy is an issue important enough to warrant new approaches. ... Read more

Customer Reviews (1)

See how fractals can be part of the math curriculum
When I teach computer programming, the sections that raise the greatest amount of interest are those that involve the manipulation of images. Therefore, it is natural to me that any mathematics that involves the manipulation of images would generate a great deal of student interest. I was a working mathematician when the concept of fractals hit the world, and like so many others was caught up in the excitement. I wrote programs to generate them and read all of the major books.
That was almost two decades ago, and the field has continued to expand. In this book, you will read about projects where math teachers have incorporated fractals into the curriculum. It is no surprise to me that it was almost universally a success, the sheer beauty of the fractal images guarantees interest and the increase in computing power has made the generation of images much easier. Many of the first images I created required overnight runs, something that can be done in minutes today.
The fact that the images do model much of the natural world also increases the interest. Nature is irregular and unpredictable in the micro sense, and fractals give us a way to describe and maybe understand it. The articles are all well written and easy to follow, and many different types of projects are demonstrated. Some of the papers describe the structure of courses in fractals, so if you have an interest in creating such a course, you can find your point of origin.
While fractals have occasionally suffered from the common malady of being oversold, they do provide a bridge between mathematics and the real world. Therefore, the study of fractals should be part of the mathematics curriculum, and in this book you can read about how many people have successfully done it. Another quality book on contemporary mathematics, it should be part of the next iteration of library purchases everywhere. ... Read more

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Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.

This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics — from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry. ... Read more