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1. The Essence of Chaos (The Jessie
2. Chaos: A Very Short Introduction
3. Chaos Theory Tamed
4. Does God Play Dice? The New Mathematics
5. Nonlinear Dynamics And Chaos:
6. Chaos And Complexity: Implications
7. Chaos and Fractals: New Frontiers
8. Indra's Net: Alchemy and Chaos
9. 24 Declassified: Chaos Theory
10. Introducing Chaos: A Graphic Guide
11. Applied Chaos Theory: A Paradigm
12. Fractal Market Analysis: Applying
13. Chaos and Order: Complex Dynamics
14. Complexity: Life at the Edge of
15. Chaos, Complexity, and Sociology:
16. Simply Complexity: A Clear Guide
17. Chaos and Fractals: The Mathematics
18. Chaos: The Making of a New Science
19. Nonlinear Dynamics and Chaos
20. Chaos

1. The Essence of Chaos (The Jessie and John Danz Lecture Series)
by Edward N. Lorenz
Paperback: 227 Pages (1996-04)
list price: US$14.95 -- used & new: US$8.00
(price subject to change: see help)
Asin: 0295975148
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field.
Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals.
As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time. ... Read more

Customer Reviews (10)

2-0 out of 5 stars Good info but long-winded and poorly written
In my opinion this book is poorly written and long-winded. The author could have explained everything in a book half the size. His explanations are not entertaining either.

The author is obviously well versed in chaos theory but lacks the ability to write a good book. For a good read on a similar topic that is much better written try The Black Swan by Taleb or The (MIS)Behavior of Markets by Mandelbrot.

4-0 out of 5 stars Introductory examples of chaos
Chaos is not randomness and randomness is not chaos. Ed Lorenz, one of the founding fathers of chaos theory, has produced a book aimed at explaining chaos theory to the public, starting and ending on the same point- common usage has incorrectly rendered "chaotic" and "random" to be synonyms. Randomness implies that there are no equations to govern the evolution of a system, while chaos implies that the system is incredibly sensitive to its initial conditions, but there are equations behind the curtain. A pinball machine, flipping coins, tossing dice, and the global weather are all examples of chaotic systems, despite what your math teachers might have told you. Along the way you get a small dose of the history of the field and the relevant higher-level mathematics.

Lorenz does, I think, a pretty good job of explaining the subject. The more mathematically inclined reader will find all the details and differential equations in the appendix of the book, but for the most part you do not need to have that much of a mathematical background to understand the main points of the book. Sometimes the explanations do get a little hairy, and might require a second read. Lorenz makes analogies with simple systems and everyday occurrences (such as a pinball machine and skiing down moguls) in engaging language mostly free of jargon. I would recommend this book if you are interesting in learning about the basics of chaos theory. I haven't yet read Gleick's famous Chaos: Making a New Science, but this seems like an excellent place to start.

5-0 out of 5 stars Great review of chaos by one of the founding fathers
Edward Lorenz is credited with "discovering" chaos theory based on his meteorological work.In The Essence of Chaos, Lorenz does a great job describing the historical background of chaos theory and its implications for the natural world.Well-written with some interesting graphics.

5-0 out of 5 stars Very Good Introduction
I read this book when it was snowing outside in the Sierras. I was immediately able to correlate this book with the chaotic snow fall.

Extremely good read.

4-0 out of 5 stars This is the book if you're looking for a chaos primer
If your interest in Chaos was piqued by Gleick's book on the subject, you may have found it unsatisfying. While it conveyed a enthusiasm for chaos, it only superficially answered questions about what characterizes a chaotic system. "The Essence of Chaos" is a much better book for gaining an understanding of chaos, mainly because it includes a discussion of the mathematics. Both authors strive to avoid mathematics as much as possible, but in the end, I believe Lorenz achieves a better balance. He only touches lightly on the math, but without that, it's impossible to understand what makes a system chaotic. He doesn't quite go so far as to show a practical application of chaos theory, but a clear and concise example of that probably doesn't exist yet. But, he does achieve the goal of demonstrating and examining the fascinating characteristics of a chaotic system. ... Read more

2. Chaos: A Very Short Introduction (Very Short Introductions)
by Lenny Smith, Leonard Smith
Paperback: 176 Pages (2007-04-16)
list price: US$11.95 -- used & new: US$6.39
(price subject to change: see help)
Asin: 0192853783
Average Customer Review: 4.0 out of 5 stars
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Chaos exists in systems all around us. Even the simplest system can be subject to chaos, denying us accurate predictions of its behavior, and sometimes giving rise to astonishing structures of large-scale order. Here, Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible math and physics to explain Chaos Theory, and points to numerous examples in philosophy and literature that illuminate the problems. This book provides a complete understanding of chaotic dynamics, using examples from mathematics, physics, philosophy, and the real world, with an explanation of why chaos is important and how it differs from the idea of randomness. The author's real life applications include the weather forecast, a pendulum, a coin toss, mass transit, politics, and the role of chaos in gambling and the stock market. Chaos represents a prime opportunity for mathematical lay people to finally get a clear understanding of this fascinating concept. ... Read more

Customer Reviews (5)

4-0 out of 5 stars Physics Introductions
I am a physicist with a PhD who likes reading almost anything on physics, astronomy, and mathematics.These "...very short introductions" are concise, entertaining, and for the most part instructive.I recommend these books to researchers in these fields as a good review and to those seeking a more detailed educational experience than most popularizations sans equations.

3-0 out of 5 stars Unsuitable as an introduction to chaos
This book starts out promising but, as one goes along, it drifts farther and farther from what an introduction to chaos should be.

In particular, the book turns out to be largely a discussion of modeling and forecasting, with some emphasis on the relevant implications of chaos.Moreover, most of the examples and applications relate to weather and climate, which becomes boring after a while (especially considering the abundance of other options).Smith's bio reveals that this is exactly his specialty, so the book appears to be heavily shaped by his background and interests, rather than what's best for a general audience.As a result, many standard and important topics in chaos theory recieve little or no mention, and I think the book fails as a proper introduction to chaos.

A further problem is that much of Smith's discussion is muddled, especially in the later chapters.It's as though he wants to probe deeply, but can't take time to really spell things out, so he winds up being unclear.This lack of clarity is exacerbated by his bending over backwards to avoid writing out even the simplest equations, which is cumbersome and annoying, not to mention out of place given Smith's efforts to present some fairly sophisticated material.

Considering all of this, I can recommend the book only to people who are particularly interested in modeling, forecasting, and the relevant implications of chaos, especially as this relates to weather and climate.In this context, Smith's discussion of the differences between mathematical, physical, statistical, and philosophical perspectives is particularly insightful and useful.

However, I can't recommend the book for a general audience, and I would definitely recommend against it as a first book on chaos.It's simply too incomplete and unbalanced for that purpose.

5-0 out of 5 stars Great, simple book
I like the book. It is really easy to read and includes so so much information.

5-0 out of 5 stars A Great Introduction
A very readable introduction for anyone interested in nonlinear dynamics, time series, weather forecasting or climate modelling.

There are very few concise introductions to chaos and its applications, so this one is well worth reading.

3-0 out of 5 stars Confusing and Humbling
I really struggled in trying to rate this book, as I really want to be fair and equitable in all my reviews.Perhaps it is a very good book and I have "short-changed" it, but I cannot really say because, after reading it, I feel just about as confused and bewildered regarding mathematical chaos as I did before I launched into it.Well, I do not suppose that reading it "hurt" me!But, in my humble opinion, this condensed, compressed "cutting edge" stuff is not for "beginners"!

It seems like I would have a "fighting chance" to readily comprehend the content of this little book, given that I am what many people would call a "well-read" and intelligent person (and I even have a graduate degree with a "minor" in multivariate statistics from a respected university).But no way!I was confused early on in trying to decipher this book on my own.I really needed a patient teacher to hold my hand.Maybe I am basically dense, stupid, below average in IQ, and/or just getting old -- who knows?But, while I endeavored to read this "very short introduction", I found myself thinking that, at least for the average person, it may be possible, but not probable, that they will grasp much of the content beyond perhaps a few vague intuitive notions.Otherwise, I learned a few new impressive words, what a "vole" is, a little about "Olbers' paradox", and that Edgar Allan Poe was seriously interested in cosmology (for example, see his essay entitled, "Eureka"). ... Read more

3. Chaos Theory Tamed
by Garnett P. Williams, A Joseph Henry Press book
Hardcover: 520 Pages (1997-10-08)
list price: US$34.95 -- used & new: US$20.00
(price subject to change: see help)
Asin: 0309063515
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

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Williams uses lists, graphics, examples, and friendly language to help readers understand the vocabulary and significance of chaos theory. The book will help scientists and students outside mathematics to use the concepts of chaos in working with data and will help interested lay readers grasp the fundamentals of chaos theory Pub: 9/97. ... Read more

Customer Reviews (18)

1-0 out of 5 stars Requires detailed understanding of mathematics
Do not order this book unless you have a strong mathematics background. The entire book hinges upon mathematical argument.

2-0 out of 5 stars Get in print, not Kindle
This is an excellent book in print. As a Kindle book, no. The conversion process has converted all subscripts and superscripts to regular type, and all Greek and math symbols to english text. Inserted formulas are so small they are only legible when magnified. Buy the paper edition.

5-0 out of 5 stars Fantastic Book
This book was my first introduction to chaos thoery.

I found it to be an excellent primer with the right amount of technical details. This book will provide a good reference in the future.

5-0 out of 5 stars Outstanding!
I would have to echo those who say this is an outstanding book. Maybe because the author is not a mathematician or engineer he doesn't overwhelm you with abstract mathematics and concepts and expect you to know these as a matter of course.

He also doesn't assume your an idiot so the material is not over simplified, it's not a casual read but if you're interested in the subject and have the motivation the book is definitely accessible.

He slips into difficult topics like say Fourier Analysis in such a way as to really impart a level of understanding of the process again without oversimplifying nor overwhelming.

A first rate author and an outstanding instructor I highly recommend this book.

5-0 out of 5 stars Brilliant
Garnett Williams is my hero.He takes what seems like a complicated topic and makes it seem simple.Williams never assumes anything about the reader's prior understanding of any topic - he patiently and carefully explains what you need to know to understand his point.He reiterates, summarizes and gives examples so that even when you are occaisionally feeling like you might get lost, he reels you right back in.

He includes a glossary and chapter summaries which are very helpful.He also does a great job of refreshing important concepts from prior chapters as they again become relevant.

The layman's challenge in understanding scientific literature, even books written for lay audiences, often results from a minor oversight or assumption on the author's part.One little detail that, upon omission, makes the picture unclear.Williams covers every detail; he was thorough and consistent throughout.

I'd highly recommend this book for anyone trying to understand Chaos Theory or build a better foundation for the understanding of Complexity and other related sciences. ... Read more

4. Does God Play Dice? The New Mathematics of Chaos
by Ian Stewart
Paperback: 416 Pages (2002-03-05)
list price: US$24.95 -- used & new: US$17.58
(price subject to change: see help)
Asin: 0631232516
Average Customer Review: 4.5 out of 5 stars
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"You believe in a God who plays dice, and I in complete law and order."Albert EinsteinThe science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner. Perhaps God plays dice within a cosmic game of complete law and order.Does God Play Dice? reveals a strange universe in which nothing may be as it seems. Familiar geometrical shapes such as circles and ellipses give way to infinitely complex structures known as fractals, the fluttering of a butterfly's wings can change the weather, and the gravitational attraction of a creature in a distant galaxy can change the fate of the solar system.

This revised and updated edition includes three chapters on the prediction and control of chaotic systems. New information regarding the solar system and an account of complexity theory is also incorporated. It is a lucid and witty book which makes the complex mathematics of chaos accessible and entertaining.Amazon.com Review
We'd better get used to chaos because it certainly isn't going anywhere. Mathematician Ian Stewart--who is also a very talented writer--shares his insights into the history and nature of the highly complex in Does God Play Dice: The New Mathematics of Chaos. While his delightful phrasings will draw in nearly every reader, those with a strong aversion to figures and formulae should understand that it will be slow going. Chaos math suffuses everything from dreaming to the motion of the planets, and Stewart's words can never match the precision of his numbers. Persistence pays off, though; there are so many "aha" moments of insight herein that it almost qualifies as a religious text. The second edition has been partially revised in the wake of 1990s research, and three exciting new chapters report on prediction and other applications of chaos mathematics. --Rob Lightner ... Read more

Customer Reviews (18)

4-0 out of 5 stars Very good book with a few minor flaws
An interesting and fun introduction to chaos. Stewart writes very well and often makes keen and insightful observations. I learned a great deal and was inspired to read other books on this fascinating topic. There were a few things I didn't like, but to be honest they are not major: 1) The deliberate avoidance of mathematical detail in this book, which does indeed present some very deep mathematical concepts, is very odd and sometimes unhelpful. Odd, for example, as when in the midst of a chapter on quantum theory Stewart takes time to painstakingly tell the reader what an absolute value is. Or, when he's describing how to perform calculations to generate chaos he stops for a paragraph to explain what it means to square a variable. Is it really possible that readers who lack such rudimentary math skills would be reading this book?? 2) For my tastes, there's way too much God talk in this book. Stewart clearly is not doing this for any religious reason - but it's odd because I have no idea why he finds it necessary to so often toss in sentences about God doing this or God thinking that, or God blah blah blah. By the end - especially at the literal end and the stupid joke in the epilogue - it really gets tiresome.

3-0 out of 5 stars Excellent book, VERY small print
I am a college-educated, non-math major, numbers-oriented senior citizen who wanted to find out what Chaos Theory is.I got this book out of my local library to see whether I should purchase it. It reads easily, even entertainingly, so I decided to order it.

However, the newest edition in paperback has very very fine print--even with reading glasses!I returned this edition, and am trying again with the older edition in hardback (same ISBN as the library book).

As others have noted, this book does not go into the "deep" mathematics of Chaos.However, the material IS challenging.

5-0 out of 5 stars This is an excellent book.
Ian Stewart accomplishes the near impossible; he describes an extremely difficult area of math and science in an intelligible manner.He writes with humor and in a straightforward manner, devoid of the pedantic convolutions that often make many math and science books boring and incomprehensible.He writes as if he were sitting next to you, trying his best to get you to understand what he is presenting, rather than (as some authors often due) trying to show how smart he is and how awfully difficult the subject is. This book is aimed at the general reader, and while it is about a very advanced mathematical subject it contains very few equations or the abstract symbolism that make mathematics so intimidating to many people.This book is not a textbook on non-linear dynamics (the underlying cause of chaotic behavior), and it does not provide enough information to solve problems that go beyond the simple examples that are used to describe the basic concepts.However, I did get a very good feeling for how Chaos Theory evolved, what it explains and why it is so important to many problems.This book is a very good choice for someone studying Chaos Theory in a more formal manner as it does an excellent job of providing an overview of the subject.The book is also an excellent choice for someone, like myself, who wants to know what Chaos Theory is all about but is not ready (or able) to study the subject in detail.While no mathematics, beyond that discussed in high school, is required, the reader should have enough of a mathematics and physics background to know what a differential equation is and some elementary mechanics, such as that involved with a simple pendulum.

The first 20% of the book reviews the inherent problem of non-linear dynamics and why it was ignored for so long.Professor Stewart points out that an apparently simply problem, such as the dynamic behavior of three bodies, is only solvable in for a finite number (but very large) number of revolutions when assumptions are made that obscure the true non-linear nature of the problem.He focuses on Henri Poincare's attempt to answer what most people would not have even thought was question; is the solar system dynamically stable (i.e., will the planets someday cease to follow the path laid out by conventional Newtonian dynamics).Poincare's approach laid the foundation of a powerful approach to solving problems in non-linear dynamics.(By the end of the book there is a tentative answer to the question.)After providing this background, Professor Stewart lays out the basic ideas and approaches to solve the non-linear problems that can give rise to chaotic behavior, where the evolution of a dynamic system depends so critically on the initial conditions.This is best seen in the application of Chaos Theory to weather forecasting.In a completely deterministically determined system, the definition of the initial conditions leads to a completely predictable outcome.But when the system is governed by non-linear dynamics (as the weather is) accurate predictions cannot be made for more than a few days, perhaps ten days to two weeks with only limited accuracy.This is not a problem of computing power, but rests with the very nature of the system. Professor Stewart provides many applications for Chaos Theory and shows how powerful this approach can be in describing the nature of the dynamical system and providing bounds for the solutions, even if the nature of chaos prevents the exact evolution of the system from being determinable.I particularly liked the section on the applications to Quantum Mechanics. He proposes that Chaos Theory may be a way out of the conundrums currently posed by Quantum Mechanics.

Professor Stewart answered a question that I have always had regarding non-linear dynamics.I have always wondered if the problem was only that our mathematics have not been formulated in the correct manner and with mathematical approaches an exact, non-chaotic, solution could be found.In other words, is chaos a problem of math or nature?Professor Stewart provides many examples where nature exhibits chaos, so chaos is real, not a mathematical artifact.

3-0 out of 5 stars A low level introduction
This book disappointed me - it is written at such a low technical level, with virtually no math.An opportunity squandered.

4-0 out of 5 stars Great if you are new to the study of chaos
This is a good book for those who are either starting to learn about chaos and nonlinear dynamics or those who would just like an overall view of what the subject is about without getting bogged down into heavy-duty math. This book has two distinct themes. One is to explain the mathematical concept of chaos, and why it is both natural and inevitable. The other is to ask the rather long question "Does the mathematical model of chaos exist in the real world, and does it help us understand some of the things that we see?".

This book covers a variety of subjects that might at first seem unrelated - mathematical history, various chaotic models, weather patterns, applications - but by the end of the book everything comes together to give you a good overall view of the field. This second edition is mainly different from the first in the added three chapters on applications. These chapters cover prediction in chaotic systems, the control of chaotic systems, and then there is a speculative chapter that attempts to explain how the concept of chaos might lead to a new answer to Einstein's famous question which is also the title of this book.

This book requires more imagination and an ability to visualize than a talent for mathematics, and it makes a good introduction to more technical books on the subject such as "Nonlinear Dynamics and Chaos" by Strogatz. Of course, that book requires much more in the way of mathematical maturity. This book looks more at the forest, the Strogatz book looks more at the trees. ... Read more

5. Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity)
by Steven H. Strogatz
Paperback: 512 Pages (2001-01-19)
list price: US$57.00 -- used & new: US$39.60
(price subject to change: see help)
Asin: 0738204536
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

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An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples. Softcover. ... Read more

Customer Reviews (38)

4-0 out of 5 stars How can you compare that which has not rivals?
This is an excellent book , I bought this book for a course at Boston University titled "non linear dynamics and chaos".
Up to chapter 5 is ordinary differential equations, nothing more nothing less. It does teach you a lot of basics in diff eq however if you have no idea about diff eq this is not the book of choice.So in order to be able to surf through this book you need to have a good understanding of ordinary differential equations because things that you'll face in this book are weird but amazing. I loved course and I loved the book and if you are committed you can study this book by yourself. I couldn't find a solution manual for it but it has the answers for odd questions just like every math book.
Strogatz is a great professor at Cornell University and if you want to get an insight to the mind that wrote this book just go to [...] type his name and watch the short presentation that he gives about non-linear dynamics.
Remember this is no a bed time read. This is a serious and a rigorous course that requires a pencil, huge amount of paper and your undivided attention. Enjoy

4-0 out of 5 stars Pretty Good Applied Math Book
If you're a mathematician this book is probably not for you, its not very formal and is driven by physical applications and examples more than theory and rigor.Also it doesn't quite go as deep as other books that I've read on the subject which were written more for mathematicians and more advanced students studying the subject.However, after reading other books on the subject one can still perhaps gain a lot from this book.This book isvery good at presenting physical applications and a different perspective on the subject of dynamical systems that would probably not be discussed in a more mathematically driven book.For example I've read books on the subjects of ODE's and dynamical systems in which the only examples given were either proofs of lemma's and theorems or just "Here's a nondescript system, and here's how we solve it."So I can definitely appreciate what this book has to offer.While understanding that this is a very applied mathematics book, my only big criticism is that the presentation of the material seems a little scatter-brained and a somewhat superficial throughout(which is fine if you're just an undergraduate, but not really suitable for anyone more advanced).
In other words I recommend buying this book for the examples and perspective, but learning the theory elsewhere.

5-0 out of 5 stars Great read, even casually
Strogatz is a great writer and makes reading this even for pleasure very enjoyable!
I especially loved the section where he talked about fireflies.

I did cover some of these topics in a class, and it helped greatly. I understood the topics probably more than anyone else in the class. And Strogatz makes it very easy to learn, with his casual writing style. Best math-related book I've ever boughten. I wish all books were so great!

4-0 out of 5 stars Excellent introductory text in this topic
This is one of the best, most easy to read introductory texts on the topic of non-linear dynamics....
Must read for students who want to enter this area.

5-0 out of 5 stars A must have for researchers in the area
Easy and fun to read while covering the area widely. There are examples provided in the book that help a lot to understand the topic. This is my area of research and I found this book as a must in this field. Even of you are doing research in other related areas, this book provides a very good perception of this field. ... Read more

6. Chaos And Complexity: Implications For Psychological Theory And Practice
by Michael R. Butz
Hardcover: 271 Pages (1997-09-29)
list price: US$109.95 -- used & new: US$94.62
(price subject to change: see help)
Asin: 156032418X
Average Customer Review: 5.0 out of 5 stars
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The nature of this book is to emphasize the inherent complexity and richness of the human experience of change. Now, the author believes there to be an acceptable "scientific" explanation for this phenomona. Explored here are 30 years of studies to describe nonlinear dynamics, today termed either chaos theory or complexity theory. The connotations of both theories are discussed at length. Offering social scientists validation in their attempts to describe and define phenomona of a previously ineffable nature, this book explores chaos' implications for psychology and the social sciences. It describes the benefits psychology can glean from using ideas in chaos theory and applying them to psychology in general, individual psycho-therapy, couples therapy, and community psychology, and also considers possible directions for research and application. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Cutting Edge Social Science
This book is truly at the cutting edge of social science. Although chaos theory has supposedly already had its day and been dismissed as the latest intellectual flavor of the month by many in the hard sciences, it has onlymoved into psychology and the social sciences over approximately the lastdecade. Those in the social sciences who have studied chaos theory havefound something of immeasuarable worth: "nothing less thanvalidation," as Dr. Butz stresses in his preface.

I don't think thatanyone can read this book and not realize that chaos theory is far from afad but rather represents a new way of thinking about all of reality. Thisis an important book that deserves to become a standard introduction tochaos theory for those in the social sciences for years to come. Many willnot need to go further. Those who do will find ample material to point themfurther on their individual explorations. ... Read more

7. Chaos and Fractals: New Frontiers of Science
by Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe
Hardcover: 864 Pages (2004-02-03)
list price: US$89.95 -- used & new: US$53.08
(price subject to change: see help)
Asin: 0387202293
Average Customer Review: 4.5 out of 5 stars
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For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals.Amazon.com Review
Fascinating and authoritative, Chaos and Fractals: NewFrontiers of Science is a truly remarkable book that documentsrecent discoveries in chaos theory with plenty of mathematical detail,but without alienating the general reader. In all, this text offers anextremely rich and engaging tour of this quite revolutionary branch ofmathematical research.

The most appealing aspect about Chaos andFractals has to be its hundreds of images and graphics (withdozens in full-color) used to illustrate key concepts. Even themath-averse reader should be able to follow the basic presentation ofchaos and fractals here. Since fractals often mimic natural shapessuch as mountains, plants, and other biological forms, they lendthemselves especially well to visual representation.

Early chaptershere document the mathematical oddities (or "monsters") such as theSierpinski Gasket and the Koch Curve, which laid the groundwork forlater discoveries in fractals. The book does a fine job of placingrecent discoveries about chaos into a tradition of earliermathematical research. Its description of the work of mathematicianslike Pascal, Kepler, Poincaré, Sierpinski, Koch, and Mandelbrotmakes for a fine read, a detective story that ends with the discoveryof order in chaos. (For programmers, the authors provide shortalgorithms and BASIC code, which lets you try out plotting variousfractals on your own.)

This is not, however, only a book of prettypictures. For the reader who needs the mathematics behind chaostheory, the authors in no way dumb down the details. (But because thericher mathematical material is set off from the main text, thegeneral reader can still make headway without getting lost.)

Therehave been advances in the field since this book's publication in 1992,but Chaos and Fractals remains an authoritative generalreference on chaos theory and fractals. A must for math students (andmath enthusiasts), Chaos and Fractals also deserves a place onthe bookshelf of any general reader or programmer who wants tounderstand how today's mathematicians and scientists make sense of ourworld using chaos theory. --Richard Dragan

Topicscovered: Overview of fractals and chaos theory, feedback andmultiple reduction copy machines (MRCMs), the Cantor Set, theSierpinski Gasket and Carpet, the Pascal Triangle, the Koch Curve,Julia Sets, similarity, measuring fractal curves, fractal dimensions,transformations and contraction mapping, image compression, chaosgames, fractals and nature, L-systems, cellular automata basics,attractors and strange attractors, Henon's Attractor, Rössler andLorenz Attractors, randomness in fractals, the Brownian motion,fractal landscapes, sensitivity and periodic points, complexarithmetic basics, the Mandelbrot Set, and multifractal measures. ... Read more

Customer Reviews (13)

4-0 out of 5 stars This book is a dream come true.
This book is a dream come true.
No other publication comes close to such complete coverage of the subject.
It is highly readable even for a novice like myself.
It has been a great joy to me.
Many thanks to the authors for doing such a great job.

5-0 out of 5 stars It's all true: Best single source on fractals-but get the 1st ed.
Thanks to S.J. Will for the tip: Get the FIRST edition (used), as I did and save more than half the price, even of a used copy of this newer edition. Can't compare the two (having not seen the new one) but I can say the color images are very sharp in the older book. As far as content, I too have looked at and bought several books trying to understand fractals. (I am not math-literate, beyond high school algebra.) I found this book most helpful, but NOT easy for the general reader, beyond the first few, introductory pages. As other reviewers have noted, most of it is WAYYYY over the head of anyone who's not a college math major, but skipping through the examples and exercises (some of which are very rewarding if you can stay with it), I found the general explanations, the excitement of the authors, the broader significance of fractals all to be well-worth the price. -- And hey: at over 900 pages ( ! ) and with FORTY color plates, this book is an astounding bargain. Strongly recommended, even for novices.

"The Colors of Infinity," based on the video documentary by Arthur C. Clarke is a good introduction to fractals. An enjoyable DVD is included of the original TV program, especially if you learn better by watching and listening. The accompanying animated fractals are fascinating, but frustratingly poor resolution. For a more philosophical approach to fractals, I highly recommend "Heaven's Fractal Net" by William Jackson.

3-0 out of 5 stars Compare the editions
I found the 1992 edition of this book at my local public library, and was (like all the other reviewers here) very impressed at the quality. The book deals with a highly technical subject, but does it in a way that you can follow even if you don't have advanced math training. The numerous color plates were also very beautiful. And to top it all off, there were "do it yourself" exercises at the end of the chapters, showing you how to program your computer to run these figures! OK, they use the old BASIC language, but still the code is clear enough that you can follow it and see what's really going on with these equations.

So I was so pleased to see a copy of the updated edition at a bookstore. In particular, I was eager to see if they'd updated those "do it yourself" exercises for use with EXCEL. However, as I read through it I was disappointed to notice two changes from the previous edition: first, all of the programming examples had been eliminated; second, the print quality of the color plates was noticeably poorer. And I didn't see much new material added - in fact one of the reviews above observes that the text itself is virtually unchanged. Considering the steep price of this tome, these were significant points to consider. Used copies of the old edition cost under 20 bucks, and IMHO are a better deal (I ended up buying one). So if you're ready to buy, just do yourself (and your wallet) a favor and compare the two editions first.

5-0 out of 5 stars Excellent tutorial on nonlinearity
At least 50% of this book can be well understood by any 1st year, exact science student. There are a couple of mathematical issues that are more senior-like, but never mind. With the appropriate teaching or guidance, a lot of practical, advanced tasks can be tackled down.I could use this book all along for giving examples for college (university), undergraduate students of almost every mathematical subject: numerical analysis, calculus, linear algebra, group theory, algorithm theory, visualization in 2 and 3 dimensions, topology...you name it, after reading this book. No fuzzy theory or wavelets or any other advanced statistical method for dynamical systems is formally mentioned, though. However the concept of measure is very well introduced and described with examples. For physics is not bad for dynamical systems theory. Although no Hamiltonian or Lagrangian formalism is mentioned, the description on how to obtain Lyapunov exponents out of a set of differential equations is very good. Engineers get their share too: useful examples are given about, e.g., feedback and control theory (mind you, it is not a book specialized in, say, robotic control using chaos theory, but it is a good start). For philosophers and the layman there are quite a few pages as well. The foreword from Mitchel Feigenbaum, just to give an example, tells us a kind of summary which "warms up" the reader and "exorcises away" the possible fantasies an unprepared reader could have regarding (or against or in favor of) the word "chaos". Nice color plates for those with artistic inclinations and the graphics are just so very well printed, you can practically "follow" their computation. Not a bad book at all for your personal (or institutional) library, I may say.

4-0 out of 5 stars A good introduction
Chaos as a physical theory began essentially in the 1970's, but as a mathematical field it has existed since the early 1900's. This book covers only the mathematical study of chaos, and is addressed to those readers who have a fairly strong background in undergraduate mathematics. A knowledge of dynamical systems and measure theory would help in the appreciation of the book, but are not absolutely necessary. The application of fractals and chaos to finance is now legendary, but other applications, such as to packet networks and surface physics are not so well-known. Current research in chaos is done predominantly in the context of information theory, wherein the goal is to understand the difference between chaos and noise, and develop mathematical tools to quantify this difference. The BASIC code in the book gives away its age, but can be easily translated to one of the symbolic computing languages available now, such as Maple or Mathematica.

This is a sizable book, and space prohibits a detailed review, but some of the more interesting discussions in it include: 1. The video feedback experiment, which can be done with only a video camera and a TV set. This is always a crowd pleaser, at whatever level of the audience it is presented to. 2. The comparison between doing iteration of a chaotic map on two different calculating machines: a CASIO and an HP. The difference is very dramatic, illustrating the effect of finite accuracy arithmetic. 3. The pictures illustrating the Chinese arithmetic triangle and Pascal's triangle as it appeared in Japan in 1781. 4. The space-filling curve and its relation to the problem of defining dimension from a topological standpoint. This discussion motivates the idea of covering dimension, which the authors overview with great clarity. They also give a rigorous definition of the Hausdorff dimension and discuss its differences with the box counting dimension. 5. The many excellent color plates in the book, especially the one illustrating a cast of the venous and arterial system of a child's kidney. 6. The difficulty in measuring power laws in practice. 7. Image encoding using iterated function systems, which has become very important recently in satellite image analysis. This leads into a discussion of the Hausdorff distance, which is of enormous importance not only in the study of fractals but also in general topology: the famous hyperspaces of closed sets in a metric space. 8. The relation between chaos and randomness, discussed by the authors in the context of the "chaos game." 9. L-systems, which are motivated with a model of cell division. 10. the number theory behind Pascal's triangle. 11. The simulation of Brownian motion. 12. The Lyapunov exponent for smooth transformations. 13. The property of ergodicity and mixing for transformations, the authors pointing out that true ergodic behavior cannot be obtained in a computer where only a a finite collection of numbers is representable. 13. The concept of topological conjugacy. 14. The existence of homoclinic points in a dynamical system. These are very important in physical applications of chaos. 15. The Rossler attractor and its pictorial representation. 16. How to calculate the dimensions of strange attractors. 17. How to calculate Lyapunov exponents from time series, which is of great interest in many different applications, especially finance. 18. The Julia set, which the authors relate eventually to potential theory. ... Read more

8. Indra's Net: Alchemy and Chaos Theory as Models for Transformation
by Robin Robertson
Paperback: 196 Pages (2009-06-30)
list price: US$16.95 -- used & new: US$9.79
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Asin: 083560862X
Average Customer Review: 4.0 out of 5 stars
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In this clear, engaging book, Robin Robertson draws parallels between alchemy and chaos theory and shows how to apply them to our inner development. He is not proposing they replace traditional spiritual paths, but rather that they reflect deep structures in the psyche that any inner journey awakens. The model they provide necessarily underlies all paths of spiritual transformation and describes a framework for the stages through which any seeker goes. No matter what your particular calling, these insights enrich understanding of the transformative process, whether outside in the world, or within your life.
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Customer Reviews (1)

4-0 out of 5 stars tools of transformation
Self-transformation is the most important challenge we face as humans. The growing complexity of modern crises require a new breed of human thinking that few are willing to embrace. Because of these challenges, I was intrigued by the idea of Dr. Robin Robertson's Indra's Net, combining the mathematics of chaos theory and the mythological language of alchemy to serve as models for an individual transformational path. Few embark on this path and many who do are bogged down by approaches that are too often steeped with pseudoscience or empty metaphors. In walking my own path, I've tried to focus on readings that pay special attention to the development of the higher self while avoiding the language of "self-help" or scientific concepts evoked with little understanding. Much of the mystique surrounding our modern perception of alchemy is primarily because we view alchemy as a primitive ill-informed version of chemistry. By dispelling this myth early on in Indra's Net, Robertson removed my concerns that his book would be innocuous commentary on the human condition decorated with fanciful mysticism. Even Isaac Newton, who viewed the scientific world as one of absolutes, used alchemical models to reveal the dynamic processes defining our world. Alchemy has always been a process of transforming Man, a constant process of refining the individual to reveal the "golden" potential, not transforming Pb into Au. While alchemy was an ancient method of modeling the dynamics of the human condition, chaos theory is the modern equivalent of modeling dynamic realities. When combined, alchemy and chaos math reveal many nuances critical to our growth as we seek to express our authentic human nature. The use of mythological symbols are highly relevant because they represent the mechanisms of the unconscious as much now as they did in the past.

I was particularly struck by Robertson's description of the uroboros, the deeply ingrained archetype of the snake eating its own tail, to represent the process of feeding back information into the individual for a constant transformational process. The uroboros represents that the end is contained within the beginning, all too often we transform over a lifetime to find our inner child looking right back at us in the mirror. Additionally, when examining feedback as a model for transformation we see that there is no short way to subtend the process, we must work over the same issues a a deeper and deeper level. By seeking to transcend our current broken state we fail to probe the depths of human existence. Trying to amputate the dark sides of our nature we are like a rope that continually cuts its end off, the rope gets shorter and shorter, and as a human we become shallower and shallower. The full spectrum of human existence must be appreciated in its entire context.

In addition to feedback, Indra's Net adapts emergence onto the path of personal challenge. Striving to adapt our lives to specific equations for success is a common focus for modern humans. Go to college + get a job + gain skills = make more and more money. Yet at some undetermined point everything can, and usually does change without any specific reason. Building a network of probability through interactions with an external world only increases the opportunity for our inner self to emerge at a spontaneous point. If we think life will continue down a pre-determined route, ignoring the little dissatisfaction accumulating underneath, they eventually emerge into a devastating climax. This manifests commonly as the stereotypical midlife crisis in American culture but we all undergo many such crises (but at smaller magnitudes) on a frequent basis.

I was impressed with Robertson's writing and the succinctness of his message, at 147 pages Indra's Net covers all its bases but doesn't drone on unnecessarily like many books in the genre of self-work. At a time when many in the US have opportunities to re-evaluate their presence at 40+ hour a week jobs where making money means doing something with little fulfillment, Indra's Net can provide the tools for recognizing the inner self. ... Read more

9. 24 Declassified: Chaos Theory
by John Whitman
Mass Market Paperback: 336 Pages (2007-06-01)
list price: US$6.99 -- used & new: US$2.89
(price subject to change: see help)
Asin: 0060842296
Average Customer Review: 4.0 out of 5 stars
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A brilliant madman dedicated to anarchy has dark plans for the U.S. In twenty-four hours, America will be plunged into chaos—the result of an unthinkable assassination to be carried out flawlessly—and the government has no inkling of the catastrophe that is about to occur.

Only one man can prevent the nightmare: disgraced rogue CTU operative Jack Bauer. But Bauer's been cut loose, is wanted for murder, and is running from the police, who have orders to shoot to kill. And there's no one he can turn to for help—because a high-level traitor in CTU wants Jack Bauer dead.

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Customer Reviews (10)

4-0 out of 5 stars Another Thriller
Another 24 Thriller but sometimes harder to follow. I have found all of the 24 Declassified books GREAT but this one was somewhat harder to follow at times. It was still a great book and kept me interested the entire time. Jack has everyone at CTU questioning what is going on in this one so it keeps the reader in doubt at all times too. It is another great book by Whitman. I recommend all of the 24 Declassified books.

4-0 out of 5 stars A Good 24 Hours
Of all the 24 books, I think this one has the best beginning.Right from the start we are thrown back into Jack Bauers world as he is in a place not quite expected with only a few who know the truth of his situation.What happens within the first few hours of the book makes you think of the movie Face-Off and Nicholas Cages character...without the actual face off thing.Loyalties are tested and some broken.The action is good but the final confrontation wasn't as strong as I would have liked.One thing I really enjoyed was the twist at the end that starts to set up events in Season 5.I hope Mr. Whitman continues that angle in his next book due out this Spring.

2-0 out of 5 stars Eh, nothing special (and beware the F-bomb)
Writing's nothing special. And unlike the TV show and other 24 books, Chaos Theory has profanity. (Page 33:) "You gonna get F***ked blondie," Oscar said as he was led away.

"Well you're not gonna be doing it," Jack said.

Ugh. It's not that I'm a prude. I just don't like bad writing. I think the author was struggling to give us tough-guy talk and action ala Lee Child, but Child rises above shallow action. Chaos Theory never does. It's lousy writing that leans on cliché after cliché.

Jack's in prison for the first 100 pages of this book, primarily beating up a series of stock Latino characters. And there's pretty much nothing here I haven't already seen in a dozen prison movies. There's even a requisite prison shower scene (oh boy). Where's the cleverness? The originality? The tech-savvy strategy and commando daring? When Bauer finally gets out of prison, the plot's pretty much a predictable yawn after that.

I just didn't feel this was up to the standards set in the earlier entries in the 24 book series, which rocked when it came to originality in their elements and plotting, not to mention better writing (and no F-bombs).

If you want to read something that's very much like this (lone ex-military man thrown in prison) but done a thousand times better, I'd highly recommend the bestselling title Killing Floor by Lee Child, a real master at thriller writing. And there are certainly other titles in the 24 series that are worth checking out. Almost all of them had better stories than this one.

4-0 out of 5 stars The best of the 24 novels
This is not only the best--by far--of the 24 series of novels, it is also better than Day 6 of the television series.

I was really disenchanted by the other books in the series, and almost didn't pick this up from the library, but I needed some light reading and I figured it would serve its purpose.However, I actually enjoyed the story.The author had a solid grasp of the characters and created a solid, twisting plot line (even if you could see one of the ending twists coming a mile away).He also introduced some background elements that would play out in Days 1 and 5 of the television series, although I'm not sure that I like what came out of that.

I didn't think that much of Whitman's other 24 novels (although they were better than Cerasini's) but this one I can recommend to fans of the show and action novel readers in general.

4-0 out of 5 stars Jack Bauer:Wild Card
I'm a big fan of Kiefer Sutherland's Jack Bauer character on the television show 24. I like the way Bauer is driven to get the job done no matter what, no matter who gets hurt.It sets him up asgreat flawed hero among his family and peers, but all of us who love the character know the price he's paying to stop the bad guys.

I also have to admit that I can't stand waiting from week to week for episodes of the new season. I have to make a deal with myself. I don't watch the first-run showing of the seasons. After they're finished, I wait until the DVD sets come out and buy those. I watch those straight through, more or less. It's easier on me than having to wait every week. I know there are some people who enjoy getting together to watch the episodes and then rehashing the twists and turns of the plot as well as making predictions about what's going to happen. I tried that it first, and it drove me crazy.

When I first found out Harper Collins paperbacks was going to be releasing new books set in the series, I was excited and dismayed at the same time. I was glad to get the extra Bauer adventures, but I didn't know how the books were going to pull off the immediacy of the television episodes.

Nor did I want anyone to try to sandwich books between the ongoing series seasons. Bauer's life changes from season to season and I prefer that that be shown within the television world.

Fortunately, with the tight driving plot lines of the series, publishers weren't willing to risk trying to elaborate on stories set between the seasons. They elected to go back to earlier in Jack's career and call the series 24 Declassified. This way we get to see the first season CTU (Counter Terrorist Unit) team in action all over again.From time to time, though, a few mishaps with canon will occur, or the characterization will not quite seem right.

One of the biggest problems in the book series is the fact that all of the television fans who read them know what Nina is really like. We know that she was not a good person, yet the authors of these books have to portray her as decent and professional. But no attempt can be made to evoke a lot of sympathy for character because we won't buy it.

John Whitman and Marc Cerasini together have written six books in the 24 Declassified novel series so far. CHAOS THEORY is the latest in the successful run.

The book opens with Bauer interrupting a poker game and shooting one of the man dead. This prologue is set a few weeks prior to the opening hour of the next 24-hour run. It sets the plot into motion and raises questions. Two pages later, we learn that Bauer is in prison awaiting trial for murder of a man he shot in the prologue. Questions arise immediately, but they take back seat to the action that begins with a bang. Within minutes, Bauer is attacked by an Hispanic street gang in the shower. He has no idea why he's been targeted, but he knows something has gone drastically wrong.

It isn't long before the reader understands that Bauer is in jail because he wants to be. He has a mission on the inside. However, his cover has been blown because someone has taken out all three people that know he's innocent. Bauer has no choice, as usual, but to take matters into his own hands and move events directly toward critical mass. This is typical, great Bauer action.

The plot is convoluted and multi-layered. The CTU team all have parts to play. Whitman does an excellent job of "seeding" events that lead up to betrayals and double-crosses that play out in the television series. This foreshadowing works well and doubles down on the pleasure the reader receives because not only is a new mission unfolding, the fans get to see some of the other pieces of the television series' twists and turns fall into place.

The title, CHAOS THEORY, relates to the action in the book and a lot of ways. Everybody seems to take some part in the chaos that eventually unravels. Nobody's plans, not Bauer's or the villain's, go as intended. Some of the twists and turns can be predicted, and some of the action is a little over the top, but there are some surprises.

I read the book on the plane on the way to San Diego Con this past weekend. With three hours of flight time ahead of me, I wanted something familiar to read that would easily grasp my attention and immerse me in a world other than the airplane. By the time I reached San Diego, I was totally engaged in the book.After arriving at my hotel, I settled in, put my feet up, and finished the read rather than going exploring. For me, that's a sign of a good book.

Now I know there are five other Jack Bauer adventures awaiting me that I'll probably be able to cram into my schedule before Season Six arrives on DVD. If you're a 24 fan, and like to read, these books are for you. If you don't like to read but love the show, I'd recommend giving these books a try. If the others are like this one, they are lean and mean and move with the same blistering bullet speed as the television series. You may find the book interface seems to disappear completely as Bauer's adventures come to life inside your mind.

If the rest of the books are like this one, they're just sheer good fun.
... Read more

10. Introducing Chaos: A Graphic Guide
by Ziauddin Sardar
Paperback: 176 Pages (2004-12-15)
list price: US$9.95 -- used & new: US$5.10
(price subject to change: see help)
Asin: 1848310137
Average Customer Review: 2.5 out of 5 stars
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"Introducing Chaos" explains how chaos makes its presence felt in many varieties of event, from the fluctuation of animal populations to the ups and downs of the stock market. It also examines the roots of chaos in modern mathematics and physics, and explores the relationship between chaos and complexity, the new unifying theory which suggests that all complex systems evolve from a few simple rules.This is an accessible introduction to an astonishing and controversial theory that could dramatically change our view of the natural world and our place in a turbulent universe. ... Read more

Customer Reviews (11)

4-0 out of 5 stars Solid background
This is a well-reasoned, carefully thought out book that allows for a good introduction of the subject of Chaos. I wish that the volume was a bit more of a "populist" volume (like Larry Gonick used to write and draw), but that might be a bit too much to ask these days.

3-0 out of 5 stars OK, but something missing...
I'm a fan of the Introducing series.I don't want to be too critical of this book, but I was a bit disappointed.I did learn a little more than I knew before I read it, but as many of the reviews say, the organization is a bit "chaotic" to the point where you feel you're never given a true overview of the subject.An introduction to any topic should at least try to leave you with some framework of organization for the topic as a whole.

You can probably learn as much about Chaos theory by reading the Wikipedia article.If I'm going to buy a book, I want something more.Perhaps a deeper exploration into one practical application of Chaos theory that shows it as a real science with a purpose.One is almost left with the impression that Chaos theory is more a post-modern criticism of western science rather than a true alternative explanation of phenomenon.

5-0 out of 5 stars Great book
This was the book that got me hooked on the Introducing... series.I wanted to get a nice overview of Chaos Theory, and this book provided it.

4-0 out of 5 stars Introducing Chaos Adequate
I've read a number of books on Chaos/Complexity, and found this one to be fine.I think my favorite was the one by Mitchell M. Waldrop "Complexity: the Emerging Science at the Edge of Order and Chaos."

At any rate, for the audience for which the book is intended, which is someone who wants an easy-to-read introduction on chaos, I think the book is perfectly adequate.

1-0 out of 5 stars "Chaos" (not Chaos theory) is all this book introduces you.
I was looking for an easy-to-understand book on Chaos Theory for some non-English speakers (say, some Japanese students) to read, and I personally like "Introducing Fractal Geometry", so I got my hand on this book...

It was a mistake.

I would not say much about this. The author did introduce Chaos, not really Chaos theory, to the readers. He tried his best, I believe, to make things easy to understand by simplifying things... However, in doing so, he had just created Chaos.

Hence, this book is probably one of the best examples of "How Simplicity creates Complexity and Chaos"... a simple scheme found in Complex systems (like complex Cellular Automata which emerged from a simple set of rules).

One thing, while a lot of names (technical terms) were introduced, almost all of them are left unexplained. And I think only "introducing" is never enough. (Well, it was the name of the book afterall... this book wasn't named "Explaing Chaos" :)

There are other good books on Chaos for layperson. And, in fact, "Introducing Fractal Geometry" did a far better job than this one. ... Read more

11. Applied Chaos Theory: A Paradigm for Complexity
by Ali Bulent Cambel
Hardcover: 246 Pages (1992-11-19)
list price: US$88.95 -- used & new: US$17.70
(price subject to change: see help)
Asin: 0121559408
Average Customer Review: 4.0 out of 5 stars
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Product Description
This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but also as themes for theses, dissertations, and research proposals.

Key Features
*Includes laboratory experiments Includes applications and case studies related to cell differentiation, EKGs, and immunology
* Presents interdisciplinary applications of chaos theory to complex systems
* Emphasizes the meaning of mathematical equations rather than their derivations
* Features reader friendly presentation with many illustrations and interpretations
* Deals with real life, dissipative systemsIntegrates mathematical theory throughout the text ... Read more

Customer Reviews (3)

5-0 out of 5 stars Soft but scientific introduction to chaos theory
This is more like a historical perspective of the development of the concepts of chaos theory than a deep coverage of chaos theory. Emphasis is on introducing the concepts for allowing interested people to get into advanced theoretical developments (and practical too). However there are some scientific prerequisites (physics, dynamical systems...).

Writing is very good, intuitive, does not assume any particularmathematical background or practice with tools for simulating chaotic systems. Exposition is rather short because of a scientific writing style, it's not about scientific popularization (don't feel this is pedantic, writing is concise and not meant to be crowded with examples). In its approach, i think it's the smoothest scientific introductory book on the subject. For example Schroeder's (Fractals chaos and power laws) is overly mathematical as an introduction. Williams' (chaos theory tamed) on the other hand has a similar approach to this one but it is longer, more general and with less emphasis on the applied side of chaos theory (the analytic side). From an economical point of view, William's is cheaper while covers more about chaos theory, but this volume is scientifically better and more useful than Williams', which is too "generalistic".

In summary : a very good self-contained and short introduction to chaos theory. But for a first book on chaos theory go to Williams, it's easier to read.

2-0 out of 5 stars Recommended only if you don't need it!!
The book has some fine features.But it doesn't explain anything.So, if you already know about chaos and want to read a brief review then probably it is ok (but read ahead). If you don't know about chaos you'll get lost.

The book is too expensive for what it offers!!.

5-0 out of 5 stars Cogently Written
Not a bad survey.Well written and easy enough for any layman to understand.This is a survey that puts the author's uniqique synthesis ofsomerather broad and difficult fieldsinto words and he doesa good jobof it.After reading this book you will not only have a good handle onwhat chaos is or isn't but how it has emerged from seemingly dipsaratefields of science. ... Read more

12. Fractal Market Analysis: Applying Chaos Theory to Investment and Economics
by Edgar E. Peters
Hardcover: 336 Pages (1994-01-12)
list price: US$95.00 -- used & new: US$58.99
(price subject to change: see help)
Asin: 0471585246
Average Customer Review: 3.5 out of 5 stars
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A leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena. ... Read more

Customer Reviews (9)

4-0 out of 5 stars Gets you up and running with chaos theory for time series
This book includes a very detailed description of how to apply some chaos theory techniques - primarily R/S analysis - to time series data.With this technique, one can gauge whether a time series is completely random, completely predictive, or a mixture of these.

This book glosses over some conceptual topics such as Efficient Market Theory and the Fractal Market Hypothesis in favor of details to perform a rigorous statistical analysis.These conceptual topics are better covered in Peters' earlier work "Chaos and Order in the Capital Markets".

For the analytically oriented reader, there can be much frustration as equations are often initially presented in sloppy and unusable forms with undefined parameters (hence 4 of 5 stars).However, these are subsequently broken down and presented in a step-by-step manner that will allow most readers to implement his techniques.

Overall, this is an excellent introductory book for the practitioner or economist, not so great for the non-technical reader.

1-0 out of 5 stars This book is a disappointment
As a market analyst for an oil company, I spend considerable effort in trying to find new ways and theories to "decode" the markets and overcome uncertainty. I had hoped Mr. Peters book would offer a model of analysis to test and hopefully use.

Unfortunately, the deeper you get into the "meet and potatoes" of this text, the more disappointing it gets. This book offers nothing. Readers less skilled in the subject matter might attribute this to their shortcomings or lesser math skills. Readers well-versed in this subject matter will easily determine that this text is a waste of time...

4-0 out of 5 stars Good for newcomers to FMA
I have found Mr. Peters book excellent. I am no mathematician and still I found it easy to read. I was interested in learning about fractal market analysis and I found what I needed in this book.

3-0 out of 5 stars Almost useless
In this book, Peters explains general capital market in an interesting way; but when he gets into the Fractals - the main theme of the book, he seems to just pick things up from previous research papers and condensesthem. At the end of the day you will be wondering if it is worthwhile topurchase and read the book after all.

On the editing side, I think Wileycould have done better. The math in the book is typeset in a programminglanguage style and you have to give extra effort in order to readthem.

The three stars is for being one of the very few works available inthis field.

4-0 out of 5 stars simple as possible intro to fractals and markets
The title only indicates part of the true subject matter of this book.The book teaches about fractal analysis of any data set, and uses financial markets as special cases to illustrate the concepts involved in fractalanalysis.He begins with a brief, but facinating history of fractals, andyou learn the concepts you will need to form your own trading strategies.Mr. Peters demonstrates an easy familiarity with fractals, and this servesto keep the book interesting through its most difficult mathmaticalpassages. ... Read more

13. Chaos and Order: Complex Dynamics in Literature and Science (New Practices of Inquiry)
Paperback: 316 Pages (1991-08-13)
list price: US$27.50 -- used & new: US$9.99
(price subject to change: see help)
Asin: 0226321444
Average Customer Review: 4.0 out of 5 stars
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Product Description
The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines, including the humanities.In this volume, fourteen theorists explore the significance for literary and cultural studies of the new paradigm of chaotics, forging connections between contemporary literature and the science of chaos.They examine how changing ideas of order and disorder enable new readings of scientific and literary texts, from Newton's Principia to Ruskin's autobiography, from Victorian serial fiction to Borges's short stories.

N. Katherine Hayles traces shifts in meaning that chaos has undergone within the Western tradition, suggesting that the science of chaos articulates categories that cannot be assimilated into the traditional dichotomy of order and disorder.She and her contributors take the relation between order and disorder as a theme and develop its implications for understanding texts, metaphors, metafiction, audience response, and the process of interpretation itself.Their innovative and diverse work opens the interdisciplinary field of chaotics to literary inquiry. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Completely different from the norm
What shocked me was when the book started by talking about chaos andbuddhist philosophy. This is not a book that will teach you the basics onfractals, nor is it an advanced book that will teach you how to run anexperiment on chaos. I don't really know what this book is but whatever itis, it is INTERESTING. I was not expecting such a different topic base.Apparently, this book is a collection of essays, all based on chaose butfrom non-mathematical perspectives. ... Read more

14. Complexity: Life at the Edge of Chaos
by Roger Lewin
Paperback: 242 Pages (2000-02-15)
list price: US$18.00 -- used & new: US$13.76
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Asin: 0226476553
Average Customer Review: 4.0 out of 5 stars
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"Put together one of the world's best science writers with one of the universe's most fascinating subjects and you are bound to produce a wonderful book. . . . The subject of complexity is vital and controversial. This book is important and beautifully done."—Stephen Jay Gould

"[Complexity] is that curious mix of complication and organization that we find throughout the natural and human worlds: the workings of a cell, the structure of the brain, the behavior of the stock market, the shifts of political power. . . . It is time science . . . thinks about meaning as well as counting information. . . . This is the core of the complexity manifesto. Read it, think about it . . . but don't ignore it."—Ian Stewart, Nature

This second edition has been brought up to date with an essay entitled "On the Edge in the Business World" and an interview with John Holland, author of Emergence: From Chaos to Order.

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Customer Reviews (9)

5-0 out of 5 stars Intriguing and thought provoking.
This was a very intriguing book.The author's method of discussing the topic is by interviewing the various individuals involved in complexity research.It is sometimes a little difficult to follow because it's difficult to decide who is doing the questioning and who the answering, but once past that, the reader will find that the author follows a very coherent outline of the topic.

In general Lewin starts with the inception of the concept by its various originators and the way that they have developed methods (largely computerized programs) to test their hypotheses.He also discusses the difficulty which these individuals met in trying to promote their ideas of complexity, chaos, and self-organizing criticality to the various academic departments to which they were attached.The author interviews a number of the best known scientists for their impressions of the output of the research into complexity.Some meet it with great skepticism while others, though cautious, seem to think that complexity theory has a great deal to say about dynamic complex systems.

Those of you unfamiliar with complexity but have read something on chaos theory or self-organizing criticality (particularly Per Bok's how nature works: The Science of Self-Organized Criticality (Copernicus)) will realize that this is simply another component of the dynamic system, another way of putting mathematics and computer generated programs to use in understanding things like evolution of species and ecosystems, of financial, business, and economic systems, and natural physical phenomena, even historic events (such as the abandonment of the Chaco Canyon Pueblo system.

I found especially interesting the appendices, particularly that dealing with global economics and business.It was interesting to see what the predictions were and what the author and his sources thought businesses should do to make their particular market share more stable in a world economy that is forever changing not only within a specific region or a specific business type but within an entire suite of interacting businesses world wide.

Very worthwhile reading.

4-0 out of 5 stars Fascination at the edge of chaos.
Before I read this book I had no idea what Complexity theory was. I picked up a sentence or two in another book about it, and decided to investigate. While Roger doesn't really state what complexity *is*, it is suffice that he tells you what it's all about.

I liked that the book was written as a journey into complexity, rather than throwing data at you. It flowed much more easily than anticipated, so much so I'd recommend it to my less academic friends.

If you're looking for a good introduction to complexity - especially in the field of biology, then pick up nothing other than this book. If you're looking for a more advanced insight into the science, I'd suggest you find something else. Although a magnificent intro, it's not in-depth enough for you to start adapting the idea to your field in my opinion.

5-0 out of 5 stars Engagingly Written Science
Roger Lewin engagingly writes of his discussions with leaders in the field of complexity, the study of non-linear, dynamical systems in the life sciences.Studies in 'chaos' theory and related fields like cellular automata have led to new formulations of self-organization and non-vitalistic emergence in living systems.Although still considered a fringe element by some of their colleagues, people like Stuart Kauffman, Chris Langton, Norman Packard and others are exploring models of "...common dynamical patterns in the realms of physics, biology, and society..." (193) which may radically change our understandings of evolution and consciousness.A cheering trend toward non-aristotelian directions.

5-0 out of 5 stars Why read complexity?
I am not a scientist. I am, however, interested in a wide variety of subjects and fascinated by complexity. I am not referring now to the book, or the subject but the expression in the real world of all that there is to know and understand. How can anyone live and not recognise at the deepest levels of their understanding that everything that exists does so in dependence on other things that exist and that this interdependence, because of the number of dynamic variables, cannot be described otherwise than a complex system. It is at this point that anyone who has read the book or who is a part of this book will protest that I have missed the point. I have not. This book isn't about a vague subjective comprehension of all things being related. It is much more scientific than that. I have started off this way because I am aware that in the hustle of everyday life-the place where most readers of books reside-the subject of the science of complexity is beyond even the periphery of what might occur to them as a topic to take an interest in, let alone find relevant.Having a general, non-expert appreciation for the immense complexity of which we are a part is an appropriate mindset to bring to any reading of the subject. The book is deserving of a wider appeal than for just new wave idea groupies.

I find Lewin strikes the right balance with his reader presenting difficult concepts with elegant clarity yet providing enough detail to challenge the reader. To make the material too simple would leave the concepts incoherent-to provide too much would leave the reader behind. He also presents a balanced view of the subject. There are detractors in the scientific community. They are heard from.Lewin develops various concepts directly related to complexity rather cleverly. We are given a piece of concept that is added onto later in a different context providing us with a kaleidoscopic way of thinking of the material. It is all connected but our focus shifts slightly giving us a new view of the subject.In the beginning there were Boolean Networks. Other concepts follow: edge of chaos; complex adaptive systems; emergence.If anyone has ever wondered even in passing why is it that discrete bits of biota or data that do not amount to much in themselves can produce not only something more complex when put together but something that is more than the sum of its parts then Complexity is of interest to you.

This book doesn't have to be the final authority or explain it all to be a very good read.And, in reference to other reviews, novel new ways of approaching scientific inquiry don't come from just anyone. Personalities matter. Putting the subject of complexity in the context of those who have been pursuing its secrets is not only acceptable but adds to our understanding. The implications for the opening up of new ways of seeing what we've heretofore been looking at `through a glass darkly' are incredible. I can see why some of the leading scientists might find the subject worth their time and energy. So many things we wish to fix about how we operate within the system that supports us have proved intransigent to change. Perhaps this is because up to now we have been hampered by a too narrow view of what dynamics are relevant to a particular line of inquiry.

Lewin has presented complexity as a good mystery novel. It is a non-fiction mystery novel the ending of which has yet to be written.

4-0 out of 5 stars A fine SECOND book on Complexity
The scope of complexity science is vast, encompassing many disciplines.This book focuses on how the new idea of complexity relates to biology by discussing the idea with many leading biologists of the day.Other reviewers were put off by the book's lack of definition of what complexity is, and the lack of resolution as to what terms such as "edge of chaos" mean.But that is exactly the point.These terms do not have clear definition today.Complexity is a very immature field, frequently pursued at the visceral level.It is hard to define what it *is*, but frequently easy to identify it where it exists.I can understand the other reviewers' concerns with the lack of definition, and can only suggest that because of the narrower focus (biology), this is an appropriate second book on complexity.

As a second book, narrowly focused on the question of complexity in biology, it is outstanding.Specifically, the question is one of how self-organization (complexity) relates to evolution and what this means for natural selection.Complexity is frequently talked up as the unifier of the sciences.Lewin takes a balanced approach, taking the time to talk to complexity theorists and understand their ideas, then talking to mainstream biologists to see how the ideas relate.His conclusion shows no inherent bias.Where other books on complexity show extreme (perhaps undue) enthusiasm, Roger Lewin's concusion is decidedly "wait and see".I found his insights to be on target and relevant.

I mentioned that this is a good second book.For an introduction to complexity, read John Holland's "Hidden Order".For a history of the Santa Fe Institute and some of the personalities there, read Mitchell Waldrop's "Complexity".Either or both of these would serve as an adequate introduction to this book. ... Read more

15. Chaos, Complexity, and Sociology: Myths, Models, and Theories
Paperback: 360 Pages (1997-06-12)
list price: US$70.95 -- used & new: US$59.54
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Asin: 0761908900
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Chaos theory has firmly established itself in many of the physical sciences, such as geology and fluid dynamics. This edited volume helps locate this revolutionary theory in sociology as well as the other social sciences.

The contributors provide a timely collection of articles which examine the emerging myths and theories surrounding the study of chaos and complexity. In the second part methodological matters are considered. Finally, conceptual models and applications are presented.

... Read more

16. Simply Complexity: A Clear Guide to Complexity Theory
by Neil Johnson
Paperback: 256 Pages (2009-10-16)
list price: US$15.95 -- used & new: US$9.08
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Asin: 1851686304
Average Customer Review: 4.5 out of 5 stars
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What do traffic jams, stock market crashes, and wars have in common?They are all explained using complexity, an unsolved puzzle that researchers believe is the key to predicting - and solving-everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion. Scientists can predict shopping habits, patterns in modern jazz, and the growth of cancer tumors. Considered by many to be the single most important scientific development since general relativity. ... Read more

Customer Reviews (7)

5-0 out of 5 stars An interesting approach to the complexity
There is a proposition in this book that is really important for the evolution of the mathematical economy: "The system as a whole manages to self-organize itself in such a way that the fluctuations are smaller than for the case where everyone tosses a coin".(pag. 84) This means that an economy founded on the rules of Black-Scholes is less apted to understand than a theory of complexity integrated with the game theory. This fact allows to the researchers to have a better preview of the phoenomena.

4-0 out of 5 stars An interesting walk down a single narrow path
Complexity science is a broad field with vague boundaries, so no single book can cover the whole field in depth.In this book, Neil Johnson focuses on a definition of complexity associated with a particular class of computational models, and he describes these models and their resulting behaviors at a level suitable for the general reader (somewhat detailed descriptions, but essentially no formal math).He has a PhD in physics and has himself done considerable research on these types of models (see the references at the end of the book), so his knowledge in this area is fairly authoritative.

For Johnson, a complex system has the following characteristics:

(1) A population of multiple (at least three) interacting objects or "agents" which typically form a network.These objects may be very simple, but they don't have to be.

(2) Competition among the objects for limited resources.As part of this overall competition, there can also be local cooperation within the system.

(3) Feedback processes, which give the system memory and history.

(4) Ability of the objects to adapt their strategies in response to their history.

(5) Ability of the system to interact with its environment.

(6) Self-organization of system behavior, without the need for a central controller.

(7) Emergence of non-trivial patterns of behavior, including a complicated mixture of ordered and disordered behavior.This can include chaotic behavior, as well as extreme ordered behavior (eg, traffic jams, market crashes, human diseases and epidemics, wars, etc.).

Johnson gives many examples of complex systems, and a jazz band is among the most interesting of these examples (the jazz performance is the behavior of the system).

Here are some of the key results from the models he describes:

(1) Even if the objects comprising the population of the system are complicated and heterogeneous (eg, people), this variability tends to "average out" in a way that allows the objects to be modeled as being fairly simple and homogeneous (at least as a first approximation).

(2) Due to competition, the population of objects will often become polarized into two opposing groups (eg, bears and bulls in financial markets, opposing political parties, etc.).This competition tends to reduce fluctuations in the behavior of the system.

(3) It's sometimes possible to steer the behavior of a system by manipulating a subset of the system's objects.

(4) Network structure tends to make complex systems more robust.

(5) The overall behavior of a system, and the ability of individual objects in the system obtain resources, depends on both the amount of available resources and the level of connectivity (network structure) between objects.When resources are only moderate, adding a small amount of connectivity widens the disparity between successful and unsuccessful objects, whereas adding a high level of connectivity reduces this disparity.By contrast, when resources are plentiful, adding a small amount of connectivity is sufficient to increase the average success rate and enable most objects to be successful.These patterns are consistent with what I've observed in the competition among engineering firms over the years (including during the current recession, a time of reduced resources).

(6) The behavioral outcomes of complex systems often follow a power law distribution, with smaller events being most common, but with extreme events also occurring more often than one might expect.

One of my main motivations to read this book was to get insight into how malignant tumors might be modeled as complex systems, with the hope that such models might provide clues regarding more effective ways to treat cancer.I was pleased to see that Johnson does discuss cancer at several points in the book, but I was disappointed to find that his discussion of cancer modeling is relatively superficial.Nevertheless, I'm firmly convinced that cancer is best modeled as a complex system, so I believe that much more research along these lines is (urgently) needed.

Overall, I do recommend this book.Johnson is qualified to write it, and it works well as an easily understood introduction at a level of detail suitable for general readers.However, again, keep in mind that the scope of the book is fairly narrow, so many important topics aren't mentioned at all.As a result, the book provides a good understanding of some of the trees in the forest of complexity science, but not much sense of the overall forest.For a broader introduction to complexity science, I recommend Complexity: A Guided Tour by Melanie Mitchell.

4-0 out of 5 stars A good intro
I found this book interesting and engaging for the intelligent person who is a novice with complexity theory. It helps you appreciate the world from yet another perspective.Entertaining & thought provoking. I didn't feel floored, but I did keep with it.

5-0 out of 5 stars A fine introduction to what Complexity is all about.
If you are unfamiliar with Complexity Theory ("The Science of Sciences") then this is a great book to start with. Neil Johnson has done an impeccable job of keeping the intricacies of Complexity within a very manageable framework that any layman can understand. Take this quote for example: "Complexity can be summed up by the phrase "Two's company, three is a crowd." In other words, Complexity Science can be seen as the study of the phenomena which emerge from a collection of interacting objects - and a crowd is a perfect example of such an emergent phenomenon, since it is a phenomenon which emerges from a collection of interacting people." The real strength of this book lies in Johnson's unsophisticated and plain approach towards Complexity Science which he couples with many real world examples. But neither does Johnson leave anything out; Self-Similarity, Fractals, Power-Laws, Networks, etc. - it's all here.

My only complaint about this book comes on page 100. Here, Johnson explains how the "six degrees of separation" network was conceived by Stanly Milgram in 1967. I am sure that Johnson knows that this was debunked by later research, but Johnson fails to mention this in the book (one only has to look to Wikipedia, Complexity: A Guided Tour by Melanie Mitchell or The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics, and inLife for confirmation. I do not fault Johnson here because given the 'basic' level at which this book was written, he probably didn't feel like complicating the issue - the point he was trying to make was satisfied - and he therefore surely didn't feeling like going into the whole mess by upending the urban legend. So, with that aside, I do recommend this book as a great introduction to Complexity and recommend Complexity: A Guided Tour by Melanie Mitchell for the interested reader as a great book to continue learning about Complexity Science.

3-0 out of 5 stars Ok, but I suspect there are better books on the subject
I enjoyed this book well enough.The subject matter was interesting and the author genuinely seems to have a way of making complex (no pun intended) subject matter very easy to understand.This is readily apparent upon reading his simple explanation of quantum physics for the lay person, which is among the best I have read (rivaling Stephen Hawking).

Where this author really has trouble is with his writing style.I'm not sure if he edited his own book, but I can't imagine this manuscript made it past a decent editor.The author uses the expression "In other words" with felonious frequency.He also uses other pet phrases, like "In particular", "It turns out", and "In short" way too often, though not as often as his all-time favorite "In other words."After a while this grated on my brain like fingernails on a chalkboard.I began finding myself mentally rewriting his sentences to make them less annoying, rather than enjoying the subject matter.

Just for kicks, I did a search for his pet phrases using the Amazon preview tool (which I am sure didn't give me all the occurrences - only the ones in the preview).The results were 111 "In other words", 120 "In particular", 66 for "It turns out", and 36 for "In short".I'd say there are easily twice this many instances of each of these.I counted "In other words" three times on one page.

Bottom line:There was nothing so compelling or unique in this book that would cause me to recommend it in spite of its shortcomings.In particular (ha!) the writing style keeps the book from being enjoyable.In short (ha ha!), I'd recommend finding a different book on Complexity Theory that gives the same information in a much less annoying way.In other words (ha ha ha!), don't buy it unless you find repetitive, useless phrases entertaining.

... Read more

17. Chaos and Fractals: The Mathematics Behind the Computer Graphics (Proceedings of Symposia in Applied Mathematics)
by Robert L. Devaney
Hardcover: 208 Pages (1989-07)
list price: US$32.00 -- used & new: US$4.49
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Asin: 0821801376
Average Customer Review: 4.0 out of 5 stars
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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)

4-0 out of 5 stars 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

18. Chaos: The Making of a New Science
by James Gleick
Hardcover: 360 Pages (1987-10-29)
list price: US$22.95 -- used & new: US$11.77
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Asin: 0670811785
Average Customer Review: 4.0 out of 5 stars
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James Gleick explains the theories behind the fascinating new science called chaos. Alongside relativity and quantum mechanics, it is being hailed as the twentieth century's third revolution. 8 pages of photos.Amazon.com Review
Few writers distinguish themselves by their ability to writeabout complicated, even obscure topics clearly and engagingly. JamesGleick, a former science writer for the New York Times, residesin this exclusive category. In Chaos, he takes on the job ofdepicting the first years of the study of chaos--the seemingly randompatterns that characterize many natural phenomena.

This is not apurely technical book. Instead, it focuses as much on the scientistsstudying chaos as on the chaos itself. In the pages of Gleick's book,the reader meets dozens of extraordinary and eccentric people.Forinstance, Mitchell Feigenbaum, who constructed and regulated his lifeby a 26-hour clock and watched his waking hours come in and out ofphase with those of his coworkers at Los Alamos NationalLaboratory.

As for chaos itself, Gleick does an outstanding job ofexplaining the thought processes and investigative techniques thatresearchers bring to bear on chaos problems. Rather than attempt toexplain Julia sets, Lorenz attractors, and the Mandelbrot Set withgigantically complicated equations, Chaos relies on sketches,photographs, and Gleick's wonderful descriptive prose. ... Read more

Customer Reviews (115)

2-0 out of 5 stars Anecdote and Science
"Chaos" is far too much opinionated anecdote and far too little science. All the stories of brilliant mathematicians who worked out the theory, and all the silly physical scientists who couldn't see it was explaining their world, can't cover up the fact that nowhere does Gleick actually explain either the math or the physical science.

I came away with the view that there certainly are physical realities (in biology, hydrodynamics, electronics, etc.), that are explained by Chaos Theory, but no idea what the explanation is or how it works.

Poor book.

4-0 out of 5 stars Intelligent, tantalizing, brisk popular science
Gleick traces the genesis of chaos theory by emphasizing the key personalities involved: Edward Lorenz in research meteorology; Stephen Smale, Benoit Mandelbrot, and Mitchell Feigenbaum in mathematics; and the experimental researchers in physics and biology who recognized some implications of and applications for the emerging theory.

Gleick's work has two central themes. First and primary is the description of chaos theory. Gleick begins by noting that chaotic systems, which are deterministic but which are not predictable, undermine the supposedly customary assumption of deterministic predictability and thereby revolutionizes physics. Gleick indirectly describes this chaos theory, observing its chief properties including sensitivity to initial conditions, damping and driving processes, global, or macro-scale stability despite local, or micro-scale, instability, representation through frequently unsolvable non-linear equations, and modeling through visualization, fractal geometry, and multi-dimensional Poincare maps.

Gleick's second and auxiliary theme is his critical commentary on the scientific and research process. Gleick suggests that interdisciplinary science produces innovative theories. Similarly, he suggests that scientists' tendencies to isolate themselves within their respective disciplines and to disregard, undervalue, or remain disinterested in results from foreign disciplines impedes scientific progress. Finally, Gleick favorably contrasts the contributions of experimenters with those of theorists and suggests that the former are more likely to address interesting, rather than merely conventional or solvable, problems.

Gleick's text feels brisk and intelligent. The author introduces many scientific ideas and personalities. Although the lay target audience of the book and its brevity preclude detailed discussion, Gleick tantalizes and supports further investigation with extensive source notes. Nevertheless, Gleick's work may frustrate readers who have knowledge sufficient to understand (and desire) more technical detail but who lack the experience or breadth of knowledge necessary to identify the general scientific or mathematical concepts alluded to. Finally, Gleick's non-chronological progression, sometimes rapid alternation between personalities, and occasional mention of names and concepts that are either not explained nearby or not at all may further frustrate readers.

4-0 out of 5 stars Good
Gleick does a great job of chronicling the many (many) intersting characters who contributed to the study of chaos and simplifies itenough to make it understandable. However, I think even a hardcore mathmetician/physicist/whatever would find it goes deep enough into the material to be interesting. Throughout the book he continually refers back to other people from earlier in the book. If you are anything like me you will not be able to keep these people straight and it gets confusing. I lost steam reading this thing about five times but eventually got through it. It was enlightening but not always riveting. If you are interested in chaos and learning about people much smarter than you, this is the book for you.

5-0 out of 5 stars Great Introduction
There are very few books on any field of science that can be read from cover-to-cover by a layman.This book captured my attention from the beginning and introduced a new way of thinking about science.

The math sections, whether discussing fractals, bifurcations, or attractors, where presented in very clear language that I could follow without advanced math education.

Other topics were presented with the same clarity and easy to follow language that made this book a rare treat.

If you are interested in learning about Chaos theory or any of its associated elements, I cannot recommend a better book!

4-0 out of 5 stars Good narrative history of Chaos/Complexity
Mr. Gleick delivers to the reader a concise and approachable narrative of the history, science, and mathematics of chaos theory. Much as he did with his biography of Richard Feynman, Gleick managed to make the complex understandable for a non-scientist and manage to keep the reader engaged/interested. If the reader has an interest in chaos, this would one of the first books to read. Highly recommended (just sorry it took me 20 years to getting around to it!). ... Read more

19. Nonlinear Dynamics and Chaos
by J. M. T. Thompson, H. B. Stewart
Hardcover: 460 Pages (2002-04-15)
list price: US$260.00 -- used & new: US$201.40
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Asin: 0471876453
Average Customer Review: 5.0 out of 5 stars
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Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos.

  • Expands on the bestselling, highly regarded first edition

  • A new chapter which will cover the new research in the area since first edition

  • Glossary of terms and a bibliography have been added

  • All figures and illustrations will be 'modernised'

  • Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics

  • Highly illustrated

  • Excellent introductory text, can be used for an advanced undergraduate/graduate course text

... Read more

Customer Reviews (1)

5-0 out of 5 stars Excellent book.
I have the older version from 89 I believe. I have seen the newer version and it did not seem to have changed very much.

This is a graduate level text for studies in nonlinear dynamics and chaos. It is meant for practising engineers and physicists really. It does not go into the mathematical perspective of nonlinear dynamics. It treats the theory from a flow rather than mapping based perspective. It also treats the subject matter with much more respect and depth than the Strogatz book of the same name. Strogatz's book is meant more for the undergraduate courses in NLD while this one helps physicists/engineers with traditional vibrations background bridge the gap to NLD and Chaos theory. All in all an excellent introduction to nonlinear dynamics. ... Read more

20. Chaos
by Kathleen T. Alligood, Tim D. Sauer, James A. Yorke
Paperback: 620 Pages (1996-11-07)
list price: US$64.95 -- used & new: US$34.85
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Asin: 0387946772
Average Customer Review: 5.0 out of 5 stars
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CHAOS: An Introduction to Dynamical Systems was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Spanning the wide reach of nonlinear dynamics throughout mathematics, natural and physical science, CHAOS develops and explains the most intriguing and fundamental elements of the topic and examines their broad implications. Among the major topics included are: discrete dynamical systems, chaos, fractals, nonlinear differential equations, and bifurcations. The text also features Lab Visits, short reports that illustrate relevant concepts from the physical, chemical, and biological sciences, drawn from the scientific literature. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulation, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise. ... Read more

Customer Reviews (6)

5-0 out of 5 stars Great Book
This book is both simple enough to understand, and sophisticated enough to provide further understanding.If you are an second or third year undergraduate planning on graduate work, this book is a great way to catch up on advanced mathematics.

5-0 out of 5 stars A/S/Y strike a perfect balance between theory and applications!
It was about the mid 1990's, still assimilating the big hype caused by the eventual and much-publicized proof by Andrew Wiles of Fermat's Last Theorem, when my curiosity (bolstered more by having seen a movie such as The Jurassic Park!) finally led me to taking a first college course on Chaos and Fractals at a California State school. At that time, the funny, surcastic, and somewhat sloppy foreign professor (who happened to be a country-mate of mine, for better or worse), had chosen the brand-new text "Fractals Everywhere" by Michael F. Barnsely for teaching our mid-size class consisting mainly of senior and first-year graduate students in math and sciences. I recall the discussion starting out by covering the basics about the metric spaces and sequences, and I having a head-start over many others coming fresh on the heels of a heavy-duty general topology course just in the previous semester (so for example I could show off to others on the first instruction day what it meant for two metrics to be equivalent). Still, I admit the semester went by without many of us really absorbing the nuts and bolts of the subject, for example why exactly topological transitivity was needed for chaos in an Iterated Function System, and why exactly some known fractals had the given fractional dimensions (eventhough we could compute them). However the students were generally happy to have scratched the surface of this vast, engaging subject, and for the time being it seemed about enough exposure for most of us. Consequently for me, during the several ensuing years in the late 90's the subject leapt mostly into the background, but nearly a decade later since I first took the college course, somehow it came back to the foreground in the company of several other applied subjects such as control, game theory, and information/coding theory.

Now looking back, I find Barnsley's text a very good choice having gone through at the time, but the title by Alligood, Sauer, and Yorke (as a recommendation by a college professor at a different school who had taught his students from it) seemed like a more well-balanced introduction to the area of dynamical systems. In fact I also recall at the time there was a discussion as to whether yet another text by Robert Devaney would have made for a better first course. The aforementioned professor duely noted that Devaney only dealt with the discrete dynamical systems, while A/S/Y treated both the discrete and continuous, hence making the choice of the latter a more suitable one. In any event, the rundown of the topics discussed in the 13 chapters of A/S/Y include: one and two dimensional maps, fixed points, iterations, sinks, sources, saddles, Lyapunov exponents, chaotic orbits, conjugacy, fractals and their dimension, chaotic attractors, measure, Lotka-Volterra models, Poincare-Bendixson theorem, Lorentz and Roessler attractors, stable manifolds and crises, homoclinic and heteroclinic points, bifurcations, and cascades. There are answers and solutions to the selected exercises, as well as extensive references at the back, making up an ideal setting for self-study. The level and style of exposition is targeted towards an advanced undergraduate student who is into applied math or engineering fields. Therefore the authors emphasize concepts and applications instead of getting bogged down in too much mathematical rigor or heavy use of the abstract machinery (which is of course needed for a thorough treatment of the subject at an advanced level; there are in fact several newer titles which all occupy this niche). Notationally and stylistically also, A/S/Y is very accessible and attractive. All in all, an excellent first excursion/introduction to one of the most fascinating areas of applied math, whether for classroom use, or for self-study.

[Review updated and reposted on 08/08/08]

5-0 out of 5 stars Exciting and Lucid Introduction to Chaos Theory
This book is a must-own for anyone interested in nonlinear dynamics and chaos -- I also highly recommend the "Nonlinear Dynamics and Chaos" text by Strogatz.

I especially like the numerous diagrams that clarify everything so well in this book. In addition, the writing includes just the right amount of informal discussion to truly explain the material without retreating into jargon.

A favorite moment in the book is a "challenge" exercise that explains the famous "Period Three Implies Chaos" result: the reader is gently guided through 10 steps resulting in a proof of Sharkovskii's Theorem, a more general result that includes the Period 3 thing as a special case.

Buy it! Simply phenomenal.

5-0 out of 5 stars The definitive guide to dynamical systems!
When I purchased this book three years ago, I had only a rudimentary understanding of dynamical systems. Thankfully, all that was needed to get me started was some intermediate calculus and some basic college-level linear algebra. Since I had been doing both from the time I was a sophmore in high school, I had no trouble getting comfortable with it. The authors present dynamical systems in an easy-to-read style with tests that appear at the end of each chapter after you've had time to catch on.

If you're seriously thinking about getting started in dynamical systems, get this book!

5-0 out of 5 stars great introduction to dynamical systems
I was enrolled in a course at GMU in which the draft version of this text was used.The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math.The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be.Many of the systems can be modeled on a spreadsheet.If you have any interest in Chaos, this book will only strengthen it. ... Read more

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