Product Description
Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications and introduces the fundamental concepts of fractal geometry and chaotic dynamics. In this new edition, Turcotte expands coverage of self-organized criticality and includes statistics and time series to provide a broad background for the reader. Topics include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection, and magnetic field generation. The author introduces all concepts at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics. He includes problems for the reader to solve. This book will appeal to a broad range of readers interested in complex natural phenomena. ... Read more

Customer Reviews (2)

Un libre excelente, an excellent book!
El Profesor Donald Turcotte desde principios de los 80 ha venido trabajando en el modelamiento de problemas geológicos con fractales y caos, y su libro es una de las mejores introducciones al tema.Desde su Capítulo1 se ve claramente el estilo concreto y práctico que lo caracteriza, y lamanera como introduce el concepto de la dimensión fractal por medio deejemplos sencillos es sin duda invaluable.El capítulo de fragmentaciónpresenta algunos modelos interesantes de este complejo fenómeno, y losejercicios son muy ilustrativos al respecto.El capítulo de sismicidad ytectónica presenta algunos de los más importantes resultados en lacaracterización de fallas y terremotos, aunque se queda un poco corto enlos avances recientes a nivel de evolución de sistemas de fallamiento.Elcapítulo de relación entre el tenor y el tonelaje para yacimientosminerales aún tiene su vigencia dado lo poco que se ha realizado en estecampo.Su relación con los procesos magmáticos de diferenciación es muyinteresante y se puede realizar mucha investigación al respecto.Sucapítulo de Geomorfología presente avances interesante como el concepto deordenamiento de tokunaga, pero también se queda un poco corto en losrecientes avances en este campo.El capítulo de fractales auto-afines esuna de las mejores introducciones a esta temática.El autor explica demanera clara algunos conceptos importantes como el exponente de Hurst,movimiento fraccionado browniano y cálculo de dimensiones fractales contransformada de fourier, además de introducir algunos conceptos de procesosestocásticos.El profesor Turcotte dedica algunos capítulos para hablaracerca de la teoría de sistemas dinámicos no lineales y sus posiblesaplicaciones en ciencias de la Tierra.Esta vez son las inversiones delcampo geomagnético y la convección en el manto los fenómenos que presentaneste tipo de comportamiento y sus implicaciones en la geología y lageofísica son profundas.Su capítulo de criticalidad autoorganizadapresenta claramente los conceptos fundamentales de lo que hoy en día hallegado a ser uno de los grandes paradigmas científicos.Este capítulopermite entender la manera como se aplican este tipo de ideas alentendimiento de los terremotos, y en un futuro se extenderá a muchos otroscampos de las ciencias de la tierra.Enhorabuena que el Profesor Turcottehaya publicado una obra como esta, que se convertirá en obra de referenciapara la futura generación de investigadores en ciencias de la Tierra.

Superb application and explanation of chaos and fractals
Dr. Turcotte explains and applies fractals to a wide variety of geological and geophysical phenomena.The writing is accessible to any educated reader who is willing to follow the mathematics.I have found it veryuseful in applying fractals and chaos to my own fields of study.Thesecond edition is a great improvement over the first:it is much expandedand clearer and begins at a more basic level.The book conveys a lapidaryconcision of thought that is impressive even in a pure theoreticalscientist.Dr. Turcotte is to be congratulated in this importantcontribution, which is so very useful to scientists in other fields. ... Read more

Product Description
Establishing a new genre of musical analysis, this book goes beyond the usual analysis of chord symbols and period forms to examine such topics as: Fibonacci number and golden mean proportions, Statistics for distinguishing among styles, Self-similarity in form. This second edition includes many new illustrations and concepts, including: Orbit drawings of attractors, Correlation coefficients, Melodic dimensions. It is intended for readers with little mathematical background and requires only algrebra and trigonometry. ... Read more

Customer Reviews (2)

helpful, easy to understand, straightforward
This book provides an excellent framework for understanding chaotic systems, whether for the novice or the experienced fractal scientist. The diagrams in particular helped elucidate the concepts presented. Sciencemade simple without being dummed down - well done!

Nice introduction to Chaos and Fractals!
This is a nice little book whose target audience is high school students, beginning undergraduates, and science teachers. Using many examples , Devaney leads the reader through ideas of iteration and dynamical system. The latter half of the book deals with the connection between chaos and the science of fractals. The readers are encouraged to explore the various facets of chaos and fractals using simple computer programs (many sample source codes are peppered throughout the book). In addition to the book, there is a couple of companion video tapes that are also highly instructive and serve as good introduction to chaos and fractals. The first video, Chaos, Fractals and Dynamics, bears the same name as the book and brings to life many of the examples mentioned in the book in a manner that is not possible via the static book format. The visual highlight occurs when Devaney shows beautiful animations of the Julia set. If this doesn't get the students excited, I don't know what will! The second video, Transition to Chaos, describes the period-doubling approach to chaos using the now standard quadratic map. There is a nice discussion about the relationship between the period-doubling bifurcation and the Mandelbrot and Julia sets. ... Read more

Product Description
This is a collection of informative extracts from Gardners' "Scientific American" column. Each brain-teasing article has been updated to include new mists, new ideas, and new solutions. Highlights include two new chapters-one on pi and poetry, one on minimal sculpture-and intriguing forays into time reversal, forms of fractions and magic, and an imaginary "Math Zoo" with its own publication, "ZOO-NOOZ". ... Read more

Customer Reviews (2)

profound masterpiece
Martin Garner is a genius, no doubt.However, he left no contact information for readers to report math errors.
On page 156, Figure 68, I hold the proof that 10 circles can be packed to a 3.81 density.In a clever disclaimer, at least Martin admits on the same page, that proofs exist for 1-9, but not 10.Martin, if you want my solution for 10 circles, circlepacker.afm@OrdinaryAmerican.net is my contact info.

Another work from the master of explaining mathematics
This book is another pillar holding up the banner that proclaims the author to be `the most ubiquitous man in the most ubiquitous of fields." He seems to have no mathematical weaknesses, attacking and explaining everytopic with charm, wit, grace and thoroughness. It there is such a thing asmathematical savoir-faire, Martin Gardner possesses it.
In this work,Dr. Gardner explains fractal music, the Bell numbers and their uses,Egyptian fractions, packing circles and squares, mathematical chessproblems, imaginary numbers, and tangent circles. He also discusses thecareer of Charles Saunders Pierce and the book Godel, Escher, Bach: AnEternal Golden Braid, by Douglas Hofstadter. Negative comments on minimalsculpture and psychic research methods are also included.
Informativeas well as entertaining, the works of this author should be part of everyliberal education.

Published in Journal of RecreationalMathematics, reprinted with permission. ... Read more

Product Description
The world of management is in crisis - the old remedies no longer work and organizations   are failing at an increasing rate. Although many talk of ‘joined up thinking’, few offer practical guidance on how to achieve this in organizations. The Fractal Organization sets down the practical implications of a well tested systemic approach to building organizations   that are capable of surviving and flourishing in these turbulent times.

“An excellent read…Many organizations fail at the mercy of their own ignorance. The author has done an excellent job in making ‘the science of effective organization’ accessible to management, providing them with a new knowledge to deal with the uncertainties that the markets place upon them.”

Stephen J. Brewis, Business Architect, British Telecom.

“.. one of the most interesting, thorough and rigorous guides to management that I have ever read, … introduces new insights in every chapter… carries a credibility which acts as a counterbalance to the sometimes difficult message which he conveys which is that a lot of mainstream management practice is at best ineffective and at worst downright destructive. I would recommend this book to anyone interested in management or systems thinking.”

Penny Marrington, Course Chair, Systems Group, Open University

“In my opinion this book manages to present sound academic theory that is relevant and helpful to the practitioner in the business. I experienced several A-HA moments.”

Pauline Marsh, Strategy Director, CS&S International, BAE SYSTEMS.

"The insights of the Viable System Model have been open only to a select few for much too long. Hoverstadt has gone furthest in bringing these ideas to a wider audience…Management books have too often been serious but not practical, or practical but not serious. This book is both brilliantly serious and practical, and often entertaining too.”

Prof. Peter Kawalak, Manchester Business School.

“Integrates mainstream management ideas with the systems ideas underpinning the VSM, and flows and reads well. As a starting point for developing understanding of the VSM in today’s world this book improves greatly on all books that have gone before, I would certainly recommend it to colleagues, clients, and students”. 

Dr. Robin Asby, Course Chair, Communication and Systems, Open University

... Read more

Product Description
Colene and her multi-dimensional allies must help fulfill a prophecy in Nona's male-dominated universe. But first, Nona herself must cross dimensions to a world more unpredictable than any she has encountered--a world called Earth. ... Read more

Customer Reviews (14)

Fractal Mode
Good story line... a bit harder to follow than most of Piers Anthony's books, but definitely worth the read.

Good Book
I liked the book. I'm reading the Chaos Mode now and they keep you intrigued.

Fractal Mode
This is a very good book as all the books in this series are. However, if the only thing you've seen of Piers Anthony is his Xanth series that is so popular, then you may want to screen this for the kids. All of these books deal with adult issues. You can judge whether someone is mature enough to read it, but all the books in this series follow a girl who is suicidal, the older man she loves and who loves her and their various companions. They deal with issues like suicide, rape, sex, etc... They do it in good way that is relevant and fits into the story. The story is about a girl Coleen, who was raped at a party once. Her father is an adulterer and her mother is a drunk. She puts on a good act and is a very popular girl on the outside, but cuts her self and frequently contemplates suicide, though she's very smart. One day on the way home from school, she comes across a man passed out in a ditch. Her suicidal nature leads her to take him home. After learning a little of each others language, he says that he's from another world/mode and that he wants to take her to be his wife there. She doesn't believe him and he disappears. She believes him and realizes she's made a mistake and he realizes he shouldn't have left. The method he takes is random though and the only way to reliably get back to Coleen is by invoking a virtual mode. The rest of the story is about how Coleen and Darren are trying to find each other and get back to his mode. They continuously encounter problems and solve them with the help of their friends from the other anchor modes. The whole time Coleen is trying to deal with her issues so that she can be with Darren in a health relationship. So there are many different things going on in this series and I have just gone over the general gist so that I don't give anything away. Everything is done in a tasteful manner, but as I said it contains very adult subject matter. Enjoy.

Fractured Mode of Boredom
This is the second novel of the mode series, and it is much worse than the first!The same cast of characters return here: Darius, Provos, Colene, and Seqiro, and a new one is added, Nona.The story features Nona predominently.
The mathematical concepts Anthony uses in Fractal Mode--the MandelbrotSet and the Julia Set--are not very well explained and do not lend themselves well to the imagination.The Fractal universe's construction was very confusing and it felt like an inept math professor was trying to shove their erroneous agenda down my throat.For those interested in fractals, check out the Mandelbrot Set, which is actually fairly simple to understand in math terms.In literature, not so much.
The rest of the story is awful.There are sections wherein the main characters are forced to breed with underground people.There are still further sections which seem to obsess over the female form.In this novel, Anthony mentions a woman followed by a "her sexy way", "in the manner of her sex", and similar ilk EVERY SINGLE TIME.I have no problem with the female form; gratuitous explanations of it in this book, however, are simply ridiculous.
The two-dimensional characters plod along on their relatively plotless adventure through a fractal universe where the BAD MALE MAGICIANS OF THE ANIMUS are oppressing the SERF MAGICIANS and only the FEMALE MAGICIAN OF THE ANIMA can bring order to the world.Huh?
The worst part of this is probably the writing.There are many times when Anthony's characters discuss a complex solution to a problem, how to implement it, and prepare to.Then there is a short sentence say "they did it."No explanation, no detail, nothing. In addition to that, the dialogue really makes you want to retch sometimes with how plainly stupid it is.There are also large, superfluous portions of the novel dedicated to side stories with almost nothing to do with the overall story. I can only hope that books three and four are better than this one.Anthony can do much better.

Amazing!How does he come up with this stuff?!
Like the first book in this series "Virtual Mode", this is another wonderful trip into an area never gone to before in a novel and a unique way of getting there.As a writer, Mr. Anthony never ceases to amaze me!He always entertains while educating you at the same time. ... Read more

Product Description
This insightful work explains Mandelbrot's fractal geometry and describes some of its most interesting applications. Fractal geometry exploits a characteristic property of the real world--self-similarity--to find simple rules for the assembly of complex natural objects.Beginning with the foundations of measurement in Euclidean geometry, the authors progress from analogues in the geometry of random fractals to applications spanning the natural sciences, including the developmental biology of neurons and pancreatic islets, fluctuations of bird populations, patterns in vegetative ecosystems, and even earthquake models.Written to enable students and researchers to master the methods of this timely subject, the book steers a middle course between the formality of many papers in mathematics and the informality of picture-orientated books on fractals. It is both a logically developed text and an essential "fractals for users" handbook.It is an essential resource for researchers and students in ecology, biology, applied mathematics, and plant and environmental sciences. ... Read more

Customer Reviews (2)

For mathematicians, not for beginners
The rise of fractal processes is the result of success and failure. It has been known for decades that continuous models were inadequate to simulate many phenomena. To paraphrase Benoit Mandelbrot, the father of fractals, "clouds are not spheres, mountains are not cones and trees are not lollipops." However, there were very few alternatives. Some early work on structures now recognized as fractal was done decades ago, but technical factors limited the scope. It was necessary for inexpensive computers and graphical devices to arise before fractals could truly be explored. The confluence of these two forces has led to a flood of work on fractals, the consequences of which will not be known for many years to come. However, it is clear that some knowledge of fractals is rapidly becoming a requirement in many disciplines, from physics to economics.
The authors here eschew a popular treatment of fractals, relying on mathematical explanations with few pictures. One immediately realizes that it is a scholarly work when a quick scan reveals that there are no color plates. Applications are used throughout. Earthquakes, pancreatic islets, temperature variations, rainfall data and vegetative ecosystems are some of the topics examined using fractals. But be prepared to perform some mathematics if you wish to understand.
And that is the outstanding feature of this book. There are a growing number of popular mathematics books that contain sections on fractals. Unfortunately, it is always more of the same. A description of the generation of the Mandelbrot and Julia sets, with color pictures. This book is designed to teach the working scientist the techniques needed to apply fractal models to their specific discipline. The mathematics is hard, complete and applicable. Listings of the many programs used to generate fractals are at the end of the book and the language is Turbo Pascal.
If your goal is to learn fractals for scientific applications, then this is the book for you. Otherwise, your best choice is one of the many popular books that use verbal explanations.

Originally published in School Science and Mathematics, reprinted with permission.

not for the beginner
It's an odd book.

According to the book's review is in between the formality of many papers and a picture oriented book.

The first two lines of its table of contents are:

chapter. 1 Our view of nature page. 7...chapter. 2 Fractals and power law scaling 15...36

The chapter 1 is whatany picture intended book on fractals has. The chapter 2, where the funbegins and basic concepts as "power law", "fractaldimension" are introduced is incomprehensible.

Nevertheless it seemsto be an interesting book about applications of fractals. I'm talking about"Part III", page > 80 to 233 (the end).

It's curious andinconsistent book at the beginning: it talks to beginners in a way that isincomprehensible for a beginner!.

If you are a beginner in fractals as Iam, you need another book!. ... Read more

Product Description
Fractal patterns have emerged in many contexts, but what exactly is a pattern? How can one make precise the structures lying within objects and the relationships between them? This book proposes new notions of coherent geometric structure to provide a fresh approach to this familiar field. ... Read more

Product Description

Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.

Customer Reviews (4)

Typical Mandlebrot
The good side of Mandlebrot is that he is always entertaining, and this is no exception. The downside is that this entire book is based on a complete false premise. Even the most cursory glance at the literature of mathematical finance shows that the mainstream of financial mathematics is perfectly aware of the fact that distributions of returns are non-normal, but Mandlebrot pretends that this is some sort of great insight on his part and proceeds to attack the nonexistent misconception that things are otherwise.

Secondly, on the question of self-similarity and scaling: tick data at various level of scale do not look the same. At the scale of seconds or sub seconds the data look dramatically different to longer scales and it seems silly to suggest that this is truly fractal.

A clear warning to all those financial analysts using N(0,1)
This book deserves to receive 6 stars.Mandelbrot serves up overwhelmingempirical,statistical,and historical evidence that financial decision makers are dead wrong in assuming,contrary to the available evidence, that a normal probability distribution describes the outcomes accurately in financial markets .In fact,the Cauchy distribution is substantially more relevant than the normal distribution.Mandelbrot's work simply means that the standard theoretical models taught in all colleges and universities,the CAPITAL ASSET PRICING MODEL(CAPM) and the BLACK-SCHOLES equation,give correct answers if and only if the relevant probability distributions about the movement of prices in financial markets over time are all normal.However, the evidence shows that they are NOT normal.Mandelbrot confirms ,by massive data analysis, Keynes's original 1921 objections to the misuse in application of (by merely assuming the applicability of such a distribution without examining the actual data)the normal probability distribution made in chapters 29 and 30 of the A Treatise on Probability(1921).Unfortunately,it appears that little,if any ,of Mandelbrot's scientific approach and analysis is being integrated into economics and finance.

scientific way of evaluating price movement
in this book, Mandelbrot is trying to prove that first, the price movement's distribution is scaling invariant, meaning a security's log price-change's distribution is same as with its 5-min's or with its daily's(or even monthly); second, price movement is not purely random/normaldistribution/brownian/random walk on street(they are all same description), meaning if u use normal distribution as one of ur bases for ur model, u will not only be theoretically wrong, but also be punished in real-life trading, such as the case of long-term capital. third, price movement does have cycle, but it length can not be determined in trading time, meaning u will not be able to decide when those cycles are going to start or end; fourth, changes of price movements do concentrate, meaning big moves will happen continouesly, or very closely to each other. the major implication to me is that many current financial theories are wrong, specially, those using normal distribution(such as option model) as basic assumption for security price movement. it also may prove that some of current price-based models(such as some trend following system) have some merit. but manay systems based on channel(such as bollinger bands)will not work in long-run. with those in mind and many available mathematical tools, one should be able to build a good financial model.

A book to make you think differently about the markets
To read this book you need truly to understand math and the markets. There is no questions that Mandelbrot is one of the greatest figures of our time. What he claimed based on his studies on cotton trading in the early 60s might not be close to the reality of today, but the way he approached it makes you think twice about the markets. Cotton trading is so different from stock market trading because it is either spoting trading or futures trading, and it is based on margins. The market usually has poor liquidity and with few players in it. The conclusions the book made could poorly extend to the general markets. The hard-to-follow math notations kept distracting me from following the main subjects. Anyway, this book will teach you something new, but you have to understand math and the markets, deeply. ... Read more

Product Description
Fractals and chaos are currently generating excitement across various scientific and medical disciplines. Biomedical investigators, graduate students, and undergraduates are becoming increasingly interested in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This accessible text lucidly explains these concepts and illustrates their uses with examples from biomedical research. The author presents the material in a very unique, straightforward manner which avoids technical jargon and does not assume a strong background in mathematics. The text uses a step-by-step approach by explaining one concept at a time in a set of facing pages, with text on the left page and graphics on the right page; the graphics pages can be copied directly onto transparencies for teaching. Ideal for courses in biostatistics, fractals, mathematical modeling of biological systems, and related courses in medicine, biology, and applied mathematics, Fractals and Chaos Simplified for the Life Sciences will also serve as a useful resource for scientists in biomedicine, physics, chemistry, and engineering. ... Read more

Customer Reviews (1)

Excellent! Make it a permanent part of your Library!!
This book is amazing. It should be a requisite book of anybody who is interested in Fractals and Chaos Theory, whether they be a student in High School or an expert in rigorous mathematics. The book jumps right to the important points and conclusions of this beautiful area of mathematics, and develops intuition without resorting to mathematical rigor, which is a boon to any beginner.

This book makes a solid introduction to Fractals and Chaos Theory, and should allow any motivated student in this area to later jump to more mathematically/technically rigorous textbooks later. For students in biological and medical sciences, whom may only have limited mathematical training compared to students of other disciplines (Physics, Mathematics, Computer Science, etc..), this should be a required book to read. More and more current research is indicating that biological systems - Immune system, Heart Dynamics, Vision - are fundamentally ruled and described by chaos and fractal based processes. The book goes over several biological applications, and does a great job of calibrating the student to the promise that this area of mathematics will revolutionize our understanding of biology and medicine in addition to highlighting specific open research questions to help focus the thoughts of the motivated student.

Overall, get this book ASAP!!!!! ... Read more

Product Description
Everything You’ll Need to Create Thousands of Fractals!

Fractals are the name given to certain types of iterated equations that produce very strange results and are capable of creating unusual and beautiful patterns. Creating Fractals describes the characteristics and mathematical background of fractals and shows the reader how the accompanying fractal-generating program is used to produce thousands of different kinds of fractals, to enlarge them, to color them, and to save them—without any knowledge of computers or programming. The program works with any computer using Windows. In addition to producing artistic effects, the reader can gain an understanding of how each type of fractal is created and how it might be used to treat natural phenomena, e.g., the turbulence of liquids, the behavior of the stock market, and the compression of graphic images. Mathematical terminology is explained in elementary terms.

KEY FEATURES:* Includes a fractal-generating program on the CD-ROM that is capable of producing and modifying thousands of fractals* Describes the mathematics (in elementary terms) involved in creating different types of fractals* The CD-ROM has over 100 example fractal images and includes all of their source code, permitting modification of the program to add new fractals, or change the program to meet specialized requirements ... Read more

Customer Reviews (4)

Creating Fractals
The software included inthis book is retro 20 century, lame.
Images are strictly low-res (600x400); interface pedantic: no retrace, wouldn't save bmp images on XP. wasted money!

Disappointing book creates but does not teach fractals
I really expected better from Roger Stevens. In the past he has written some truly excellent books on computer graphics that included working code. This particular book is very elementary with only the bare bones of the mathematics of fractals being given. Most of the book just shows a picture of each type of fractal covered, a screenshot of the included application and what you should type into the application to get the resulting fractal, and some text without equations on each fractal. If you really want to learn the mathematics behind fractals you should read "Chaos and Fractals" by Peitgen, and the older "Science of Fractal Images" by the same author. Both books are accessible yet go into sufficient mathematic detail that you could write working code. The authors even offer up code examples of their own. The second book I mentioned on fractal imaging has some great code samples and mathematics for creating beautiful realistic natural scenes of forests and lakes that are completely computer generated. I notice Amazon does not show the table of contents so I do that here:
1.Introduction
2.What are Fractals?
3.The Lorenz and Other Strange Attractors
4.What you can do with L-System Fractals
5.The Snow Flake and other Von Koch Curves
6.Peano Curve
7.Generators with Different Sized Line Segments
8.The Hilbert Curve
9.FASS Curves
10. Trees
11. Creating your own L-System Fractals
12. Newton's Method
13. What you can do with Mandelbrot-Like and Julia-Like Fractals
14. The Mandelbrot and Julia Sets
15. Working With Colors
16. Fractals with the Logistic Equation
17. Fractals using Transcendental Functions
18. Fractals using Orthogonal Polynomials
19. Creating your own 2nd-order to 7th-order Equations
20. Phoenix Curves
21. The Mandela and Pokorny Fractals
22. Fractals Using Circles
23. Barnsley Fractals
24. Iterated Function Systems
25. Midpoint Displacement Fractals

Dissaponted
I got this book to learn how to generate fractals and use the included programm to generate large images for printing. While the programm is very flexible in terms of what it generates, maximum resolution is something like 600x400. There are better books that bescribe what fractals are. This book will not help you to set up calculations on you own and it's fractal generation programm is useless for anything other that on screen display.

Introducing the Mathematics of Fractals
Fractals were originally considered to be a rather messy offshoot of conventional mathematics. They required entirely too much arithmetic to be useful before the age of computers. But with computers the whole concept of fractals became something that could indeed be studied.

A bit of time goes by and all of a sudden the people doing fractals begin to discover that using the right kind of mathematics can be used to produce a lot of images that begin to look like things in nature. These drawings began to look like things such as trees, mountains, clouds, explosions. And all of a sudden there was an interest beyond those of the mathematician just drawing cute geometric patterns, it's called game development.

This book is not on gaming, it's on the basics of fracticals. It includes software to generate fractals, and it gives the mathematics of how these fractals are created. It's a basic, beginners book to computer graphics at the mathematical level. ... 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 study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.

The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.

The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing, University of Johannesburg.

Contents: Nonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Neural Networks; Genetic Algorithms; Gene Expression Programming; Optimization; Discrete Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic. ... Read more

Customer Reviews (5)

Exact same content as the cheaper and sturdy paperback version
Overall, this is a good book on the various subjects it covers, but I have to wonder - why would you buy this expensive hardcover version when the paperback version costs a little more than half what this hardcover costs? The contents are the same, the publication date is the same, and having had my softcover copy for two years and made heavy use of it, it seems to be standing up to the wear and tear just fine.

This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the passage of time there are now tools and mathematical models at our disposal that make for a much more concise model of many systems. This workbook tries to touch on all of those mathematical tools.

The first six chapters of the book has to do with modeling such complex systems in general, and the rest of the book is a survey of the tools needed to perform complex modeling. The book's format is that of briefly explaining a concept in a few pages, and then presenting a computer program that demonstrates the concept just explained. The explanations are very clear and concise, there are plenty of equations shown, and the accompanying code is well commented. If you want to really drill deeply into any of the concepts then you are going to need some other books. I suggest that for further reading for the mathematically inclined that you pick up "Chaos: An Introduction to Dynamical Systems" by Kathleen Alligood. For scientists that want to see specific problems that can be solved by dynamical systems I suggest the excellent "Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering" by Strogatz. The only real complaint I have against this book is that there is uneven coverage of different tools. For example, the author has a great deal to say about neural networks and fuzzy logic, but has very short chapters covering discrete wavelets and cellular automata. More material would have been great, since it is hard to find good books on discrete wavelets and cellular automata in particular. Some readers may also be annoyed that much of the book are code listings of the various demonstration programs.

Overall, I would highly recommend this as one of several books that anyone interested in dynamical systems should definitely own. In particular, those individuals interested in the techniques of algorithmic composition of music might find this book a good jumping off point for studying the tools and techniques that make such compositions possible.

explains many key ideas
Here is a text of advanced nonlinear dynamics. Geared towards the intensive use of computers to perform the necessary grungework. Steeb hits on many important ideas that have emerged in recent decades. He shows the interrelation between chaotic phenomena and fractals, and how fractals can be used to describe the onset to chaos.

The Hidden Markov Models have proved to be the key idea in current Automatic Speech Recognisers. A tribute to the practical nature of this idea.

Steeb's discussion of neural networks and genetic algorithms is enough to get you started in this field. Ideas like forward and back propagation for feedback are clearly explained.

The sample code should be welcomed. It lets you see for yourself on your own computer, and to tinker with the various parameters. Though I am unsure about the choice of code in Symbolic C++. Unlike C++ or Java, this is a rarely used language.

Good overview of nonlinear dynamics
This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the passage of time there are now tools and mathematical models at our disposal that make for a much more concise model of many systems. This workbook tries to touch on all of those mathematical tools. The first six chapters of the book has to do with modeling such complex systems in general, and the rest of the book is a survey of the tools needed to perform complex modeling. The book's format is that of briefly explaining a concept in a few pages, and then presenting a computer program that demonstrates the concept just explained. The explanations are very clear and concise, there are plenty of equations shown, and the accompanying code is well commented.If you want to really drill deeply into any of the concepts then you are going to need some other books. I suggest that for further reading for the mathematically inclined that you pick up "Chaos: An Introduction to Dynamical Systems" by Kathleen Alligood. For scientists that want to see specific problems that can be solved by dynamical systems I suggest the excellent "Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering" by Strogatz. The only real complaint I have against this book is that there is uneven coverage of different tools. For example, the author has a great deal to say about neural networks and fuzzy logic, but has very short chapters covering discrete wavelets and cellular automata. More material would have been great, since it is hard to find good books on discrete wavelets and cellular automata in particular. Some readers may also be annoyed that much of the book are code listings of the various demonstration programs. Overall, I would highly recommend it as one of several books that anyone interested in dynamical systems should definitely own. In particular, those individuals interested in the techniques of algorithmic composition of music might find this book a good jumping off point for studying the tools and techniques that make such compositions possible.

Helpful in some sections
The topics covered in this book are all important from the standpoint of applications in physics, engineering, computer science, financial engineering, and computational biology. It is written for the person just getting started in these topics, and the author does a fairly good job of discussing them. Readers should not expect, and they will not get, in-depth discussions on these topics, as this would swell the book to 10 times the size. They will however get preparation for moving on to more advanced and complete treatments.

Nonlinear and chaotic maps are considered in chapter 1, with elementary definitions given and six different examples of maps discussed. In discussing the calculation of numerical trajectories of maps, the author deals with the problem of large initial values for the maps and how to implement these in SymbolicC++ and Java. He also shows how to write/read data to a file using C, C++, and JAVA. The exception handling capability of JAVA comes out nicely, but no performance comparison between the three languages for simulating the maps is given by the author. The language REDUCE is used to discuss the stability of the fixed points of the logistic equation, but the code would be useless to the reader who did not have REDUCE since some of the function calls are hidden from the reader. Useful programs are given for calculating the Lyapunov and autocorrelation functions. In addition, C++ programs are given for evaluating the correlation integral for the Henon map. The programs he develops in this chapter can serve as a quick benchmark for one's own programs that calculate the same quantities.

In chapter 2, the author discusses methods for studying time series, including the Lyapunov and Hurst exponents. These two quantities are of enormous importance in the study of dynamical systems, financial data, and network performance. The C++ program that the author gives for calculating the Hurst exponent will not work for arbitrary time intervals. This is followed in the next chapter by a consideration of autonomous systems of ordinary differential equations. The classification of fixed points is considered, and the important concept of a homoclinic orbit. The author gives a nice JAVA program that finds the homoclinic orbit of an anharmonic differential equation using the Lie series technique. The phase portrait of the Van der Pol oscillator is calculated using the Runge-Kutta technique in a C++ program, along with the Lotka-Volterra system from mathematical biology.

Hamiltonian mechanics is discussed in chapter 4, with the important Henon-Heiles model from astrophysics is discussed and JAVA programs given for studying its behavior using the Poincare section technique. Newcomers to this technique will appreciate seeing it done here explicitly.Integrability of Hamiltonian systems using the Lax representation and Floquet theory are also treated, but only at a very rudimentary level. Dissipation is included in the next chapter, and the author discusses the classification of fixed points according to their stability. Lyapunov exponents are again brought into the picture, and the phenomenon of hyperchaos is discussed. Some bifurcation theory is introduced with an example of the Hopf bifurcation. Chapter 6 studies nonlinear driven systems, with the Duffing oscillator treated, and the author gives a useful program for calculating the autocorrelation function of this system. The controlling of chaos with feedback and non-feedback controls is the subject of the next chapter, mostly in the context of difference maps. Fractals finally get introduced in chapter 8, with iterated function systems defined but proofs of their properties omitted. The author gives programs for calculating various popular fractals, such as the dragon, Sierpinski gasket, Koch curve, the Mandelbrot set, and the Julia set. The main disappointment in this chapter is that the author does not give programs for calculating the Hausdorff dimension or capacity, quantities that are notoriously difficult to get a meaningful computational handle on.

The author switches gears in the next chapter and discusses cellular automata, which have recently made a comeback, especially in research on quantum computation. The discussion is too brief however, and does not allow the reader to gain an appreciation of the properties of these important objects. Chapter 10 gives a brief overview of some techniques for solving differential equations, such as the Euler method and the Lie series technique. The latter is not commonly treated in beginning books so its inclusion here is helpful. Symplectic integration is also discussed briefly, but the author does not discuss how to check the integrators using backward integration, which is commonly used in conservative systems modeled by symplectic maps.

Chapter 11, covering neural networks, is the most well-written in the book, and the newcomer to the field will get a fairly decent introduction to the subject. The supplied programs serve to illustrate some of the important concepts in neural networks, such as the Hopfield model, the Kohonen network, the perceptron learning algorithm, and the back-propagation algorithm.

Chapter 12 is an introduction to genetic algorithms, and I find this one particularly nice also, as it does give a rudimentary introduction to what evolutionary algorithms are all about, and gives some elementary genetic programs that find the maximum of one- and two-dimensional maps. He also discusses simulated annealing, and gives a useful program that allows the reader to see clearly how this technique works.

The last chapter covers fuzzy sets and fuzzy logic, which has also taken on importance in recent years, especially in data mining and financial engineering. The programs given to illustrate the concepts are particularly interesting from the standpoint of coding in C++, as the author uses friend functions and operating overloading in some of them. The reader gets a good overview of fuzzy reasoning and fuzzy rule-based systems.

Useful information, poor presentation
The information was useful & approprate to the topic.I'd rank it as an average quality refence but a very poor text book.

The text is poorly written.The code is simple and easy to understand, but not very objectoriented.There is not enough explanation of the code.The code is notelectronically available.

The treatment was very mathematical but lackingin explanation & application examples.There were plenty ofdeffinitions, but not enough examples. ... Read more

Product Description

A specialized presentation of fractal analysis oriented to the social sciences

This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior.

Key Features

• Detailed examples help readers learn and understand the analytical methods presented.
• Matlab codes for programs allow users to implement, on their own, some of the techniques described in the text. Visit http://www.ccs.fau.edu/~liebovitch/larry.html for more details.
• Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material.

This is the only book designed to introduce fractal analysis to a general social science audience.

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
Seventeen articles explore the challenges of using computer-generated fractals in education, art, music, fashion, chess, and medicine. Despite a handy glossary and a first chaptercalled "Conquering the Math Bogeyman," the collection is definitely geared toward mathemeticians, scientists, and techn ... Read more

Product Description
This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers.While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C.Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST. ... Read more

Product Description

Fractal geometry is the formal study of mathematical shapes that display a progression of never-ending, self-similar, meandering detail from large to small scales. It has the descriptive power to capture, explain, and enhance one's appreciation of and control over complex diversity. Natural shapes and rhythms, such as leaves, tree branching, mountain ridges, flood levels of a river, wave patterns, and nerve impulses, display this cascading behaviour. These fractal concepts are found in many fields, from physics to musical composition.
Architecture and design, concerned with control over rhythm, and with such fractal concepts as the progression of forms from a distant view down to the intimate details, can benefit from the use of this relatively new mathematical tool. Fractal geometry is a rare example of a technology that reaches into the core of design composition, allowing the architect or designer to express a complex understanding of nature.
The exposition of the book is at a level suitable for applied scientists, architects, and students with a modest background in mathematics. It is well illustrated and has numerous examples from which to learn the underlying concepts and their applications. Thus the book is addressed to a wide audience with a multiplicity of interests in new compositional ideas.

Customer Reviews (1)

Only book I've seen that understands both subjects
Bovill does a good job of explaining the principles of fractal geometry in layman's terms for those not already familiar with them. I was particularly impressed with his understanding of how fractal dimension varies with scaleand which scales are important for architecture. However, I wasdisappointed that there were no references made to structural properties offractals and how they might have excellent strength to weight ratios for awide range of scales. Everything was taken from a design perspectiveconcerned with texture. ... Read more

Product Description

From reviews of the first edition:

"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...the book also contains many good illustrations of fractals (including 16 color plates)."

Mathematics Teaching

"The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples."

Christoph Bandt, Mathematical Reviews

"...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out."

H.Haase, Zentralblatt

About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.

Customer Reviews (4)

some new material->same approach
I bought the first edition of this in the early 90's
and was disappointed that it didn't have the Mandelbrot or other complex dynamics
in it. Dr. Edgar has updated the older book with Julias, multifractals
and Superfractals, but has stayed true to his topological measure theory
Hausdorff space approach. He never updates his Biscovitch-Ursell functions
to 2d and 3d parametrics or the unit Mandelbrot cartoon method.
Some of his definitions are still so minimal
that duplicating the fractals needs much more information?!
The text is still the good place to begin, but
it is a shame that Dr. Edgar has not kept up
with many of the developments in the field. Zipf and Per Bak
are left out, but my double V L-system made the index as a picture.

A nice book
I liked this book because it provided me with a new perspective on metricspaces, in using them as a basis learning about fractals. I think it servesas a nice book for an undergraduate to read and get enthused about studyingfractals at a higher level.

Good starting point to study fractal geometry.
This book could be used as a bridge between traditional books on topology-analysis and the speciallized treatises on fractal geometry. More a catalog of definitions, methods, and references than a course text, itcovers the fundamental topological and measure-theoretic concepts needed tounderstand the principles of some of the different dimension theories thatexist. But warning: the book is far away of being a complete exposition onany of the subjects it includes.

Suitable for 3rd-year undergrads.Interesting examples and exercises. Extensive bibliography.

Please checkmy other reviews in my member page (just click on my name above).

A difficult but worthy book!
The programs are in LOGO: don't let the turtles fool you, this is the real stuff by a master teacher. It is hard and the examples are even harder. The problem sets are at times impossible, but in the end Dr. Edgar delivers: understanding! Your unique Associates ID is:thefractaltransl. ... Read more

Product Description
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

Customer Reviews (1)

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