Product Description
From the inventor/founder of fractal geometry, the award-winning book that turns modern financial theory on its head

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change.

In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again. ... Read more

Customer Reviews (70)

An opportunity for continued thinking
Benoit Mandelbrot's The (Mis) Behavior of Markets is a splendid read and very informative. As many reviewers have noted, Mandelbrot invented fractal geometry. He has also been on the cutting edge (some would say fringe, but he's thinking and questioning) in multiple disciplines, as his curiosity seem to know no bounds. Mandelbrot does a good job of describing the inadequacies of the efficient market hypothesis and CAPM and other sacrosanct theories in finance, and he offers for our consideration an alternative view. His view is based on his assertion of reality; namely that the world of finance is turbulent (as indeed, the world is turbulent), and linear tools relying on reliability and rational man will never tell the full story.

Mandelbrot, to his credit, warns the reader early on that his is not an investment guide. He simply offers his ideas, and admits that some don't offer as much insight currently as he wishes. He is, however, optimistic that his philosophies and his alternative (edge-type) thinking will prevail in some form.

Truly wish I read this before b-school, as he explains why I scratched my head through a good portion because the theories didn't look "right." As a couple of other reviewers have noted, the first part of the book is best, and sort of stumbles to find itself in the second half. All that said, this is a valuable contribution and highly recommended.

An unconventional view of financial markets
Benoit Mandelbrot presents a very sophisticated approach to describing the statistics of financial markets.The assumption of gaussian statistics is often the starting point for modeling many phenomena.Sophisticated modelers soon realize that gaussian statistics are inadequate in many cases; and so, it is not surprising that gaussian statistics fail in modeling financial markets.I can only hope that the organizations that analyze risk for retirement investments and the plans that these organizations recommend do not use gaussian statistics in predicting possible retirement financial scenarios.

Excellent Book
A must-read if you enjoyed Taleb's Black Swan and want more information on the ideas behind Taleb's postulations.

The Awesomeness of Fractals
(Note: first, I recommend that readers read Gaetan Lion's excellent review of this book.My review addresses narrower, somewhat technical aspects of the book.I apologize in advance for its great length.)

Second, some backstory to this book.Institutional investors such as insurance companies or brokerages usually do not focus on picking stocks per se; rather, they operate like an actuary, selecting the odds of particular outcomes and insuring against the bad outcomes in the cheapest way. For a large number of investors, the returns come from "cheaply-held risk," meaning that risky (but potentially higher-performing) assets are insured against massive losses in the least expensive way prudent.Naturally, a cheap way to hold risky assets is to not insure against risk, but of course this is extremely dangerous.


For a smaller number of investors, the returns come from providing the insurance: writing put options, exotic swaps, and so on. Limited liability partnerships that did this sort of thing used to be known as "hedge funds," since they were businesses that sold hedges against risk to other investors. More recently, portfolio insurance (in the forms of exotic derivatives) has become a major source of income for the entire FIRE sector. Even if one nets out the immense losses of 2008, it's been a very lucrative business worldwide.More about that in a minute.

As with other forms of insurance, the paramount consideration is pricing risk, which depends on the size and frequency of market fluctuations.In theory, these fluctuations not only ought to be random, but the frequency of each variation (ranked by size and direction) ought to map out a Normal (Gaussian) curve, as other random phenomena do.Instead, it maps out other curves.Since there MANY other curves that could potentially do the job--and softwares for applying them, too--this is not really a serious hurdle.But the problem doesn't really end there.


If anomalies like the 6 May 2010 1000-pt. drop in the Dow were randomly distributed THROUGH TIME, then adapting risk evaluation methods like the Black-Scholes formula (used to compute the value of derivatives) would be easy. Once we've replaced a Normal distribution with something that fits the data, we would still wrongly expect 6-May-2010 shocks to occur very far apart.But while volatility overall is not at unprecedented levels, individual anomalies are larger and more frequent than ever; and even if we focus on much more commonplace events, we find that they have very un-even distribution through time. In fact, such shifts come in consecutive (or almost-consecutive) bursts; this is known as "autocorrelation," and it makes a hash of any effort to actually price risk.


Prudence says that capital managers should keep value at risk below 20% of the value of the portfolio, which should be easy with a reasonable amount of hedging.But if one acknowledges the possibility both of very large numbers of anomalies, AND their autocorrelation (incidence close together in time), then hedging adequately becomes prohibitively expensive, eliminating gains from trading.


Mandelbrot argues that the patterns of price changes are fractal in nature; the (log) price history for the Dow, for example, looks rather the same if you show a 330-day chart or a 330-minute chart.Revealingly, he demonstrates how to use fractals to simulate a fictional trading chart that mimics the statistical behavior of the real stock.However, after explaining this backstory (and including the marginally relevant story of H.E. Hurst's study of the Nile), the authors have little to add.This is not the fault of fractals per se; indeed, several studies of multifractal models of asset returns (MMAR) compared to GARCH(1,1) suggest that fractals are indeed a stronger tool for capturing the true risk of asset returns.*


Part of the problem may be the difficulty of explaining the mathematics/nature nexus clearly. Mandelbrot is not merely a brilliant mathematician, he's a gifted writer; his 1997 paper introducing MMAR is remarkably easy to read, considering its historical significance.But for even broader diffusion, a prominent financial editor co-wrote the book, and probably decided the upper limit on how much could be explained to non-statisticians.


However, a more serious issue is the lack of rationale for the revised theory. What I mean by this is, we can always tweak the mathematical model to produce results that approximate reality very closely.As explained above, even a random (simulated) process is valuable to a trader, if the random process captures the statistical features of the real process--in this case, a time series of asset prices.But if the mathematical model is nothing more than yet another shrink-to-fit snapshot of history, it's nothing more than data mining writ large.It's as if I generated a Fourier series that precisely matched the movement of the Dow over many years; without an underlying narrative, it's nothing but an ingenious way to draw another chart of PAST price movements. The pattern and timing of anomalies could continue to change over time in a wholly unpredictable way, in the absence of an overriding explanatory narrative.
_______________________________________
* GARCH(1,1): generalized autoregressive conditional heteroskedasticity. The (1, 1) refers to the number of lags of the conditional variance and the number of lags of the squared innovations.An example of such a study would be Thomas Lux, "Multi-Fractal Processes as Models for Financial Returns" (1999).

Standard deviation, CAPM, Modern Portfolio Theory turned on their heads
If you are questioning the use of standard deviation, CAPM, and Modern Portfolio Theory as effective tools for money management supporting asset allocation portfolios at some of the largest and oldest institutions on Wall Street then this book will confirm for you the major flaws supporting these methologies and portfolios. ... Read more

Product Description

The Fractal Geometry ofNature is a mathematics text. But buried in the deltas and lambdasand integrals, even a layperson can pick out and appreciateMandelbrot's point: that somewhere in mathematics, there is anexplanation for nature. It is not a coincidence that fractal math isso good at generating images of cliffs and shorelines and capillarybeds. ... Read more

Customer Reviews (20)

A great insight into the world of fractals
This is a great book for someone looking to discover what all the hullabaloo is about fractals.It provides a wonderful insight into the mind of one of the great mathematical geniuses of our time, Benoit Mandelbrot.I think some people will find his writing style a bit too stodgy, almost arithmetical, but I find it interesting.I especially appreciate how marks off when he's going to be tangential with special brackets.Mandelbrot doesn't delve into too many rigorous mathematical proofs of the various topics he discusses.He broaches each subject in such a way that should be accessible to people from a wide array of sciences and disciplines.I don't recommend this book if you're trying to figure out how to create simple fractal programs.But I enthusiastically recommend it if you want to learn more about fractals, discover a new way to think about and understand nature, or are simply looking for a good bit of erudition.

A fractal is by definition
A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.

I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.

The book its self could easily be used as a text book for school.

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

An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)

How We Mandel
This book is the latest version of a book the famous Benoit Mandelbrot wrote back in the mid-1970s, in which he coined the term "fractal". The subsequent version was released around 1980 and had, among other pictures, a black blotchy image on a white background which he called "the µ-map". Then some joker started calling it "The Mandelbrot Set" and he had to change the book again.

It is true that this is not the best-written book on fractal geometry. However, for a time it was the ONLY book on fractal geometry, and as such has incredible historic value. Imagine in ancient Greece where people had to borrow one of Euclid's latest scrolls to read about things found in no other work.

Personally, this book has taught me only a few things. I had already learned about fractals from articles in 1980s issues of Scientific American, and computer programs in Compute! magazine.

Many black-and-white images suffuse this tome, though there are some color plates which are by no means as complex as today's fractallographies, but will serve as an introduction to the genre.

The only Mandelbrot Set image is the blotchy one mentioned earlier. That's because Dr. Mandelbrot, though he discovered the set, wasn't the first to color the complement, and it was Heinz-Otto Peitgen's 1984 book "The Beauty of Fractals" that has the first color Mandelbrot pictures.

I wholeheartedly recommend this book for a glimpse into history, and the uninitiated may learn something as well; though I wouldn't demand that much of it.

A fractal is by definition
A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.

I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.

The book its self could easily be used as a text book for school.

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

An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)

item as promised
it took a long time to get to me but it was delivered as descibed, great condition... good seller ... Read more

Product Description

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

Customer Reviews (4)

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

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

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

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

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

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

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

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

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

Customer Reviews (1)

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

Product Description
Certain noises, many aspects of turbulence, and almost all aspects of finance exhibit a level of temporal and spatial variability whose "wildness" impressed itself vividly upon the author, Benoit Mandelbrot, in the early 1960's. He soon realized that those phenomena cannot be described by simply adapting the statistical techniques of earlier physics, or even extending those techniques slightly. It appeared that the study of finance and turbulence could not move forward without the recognition that those phenomena represented a new second stage of indeterminism. Altogether new mathematical tools were needed. The papers in this Selecta volume reflect that realization and the work that Dr. Mandelbrot did toward the development of those new tools. ... Read more

Customer Reviews (2)

Clay
M. is a great man in (large) part because of what he has written, including these papers. And yes they are challenging. I find them nearly self-contained though.

No One Can Duplicate The Cover
I went and asked K. G. Monks for help. Even with his direction I only got a bad approximation.
The rest of the book is less readable than that. It is a collection of Dr. Mandelbrot's
old articles. I interviewed Dr. Mandelbrot several years ago before a lecture of his
at U. C. Riverside. He is not a very friendly or communicative man. His
articles in general are very hard to read and without adequate history and definitions.
It is , thus, incredible that his original book was such a success. Looking at
his work, I would call him a "noise" specialist and not a fractalist at all.
This book is really a book about very hard parts of noise theory.
In my mind Dr. Mandelbrot is very wrong in many of his conclusions ,
but he has some very nice results here. Don't
waste your money if you don't have a graduate degree in mathematics
with a specialization in noise, chaosand dynamics. Most of his recent
articles have been on multifractals applied to stockmarket theory.
He is one of the great men of our age
and these articles are his feet of clay. ... Read more

Customer Reviews (1)

A case of bad editing?
My impression from reading this book is that the articles were so clipped down that in most cases it would be impossible from the text to duplicate many of the diagrams.
Since interest in fractals has centered around the graphics
in the popular mind, I blame the major editor for truncated articles by many of these great authors so that the articles are more like summaries
than true articles.
In the past when faced with such articles, I have had to search the references in order to figure out the substance of the article.
Books like this can do more harm to science than good. ... Read more

Product Description
The first book to discuss fractals solely from the point of view of computer graphics, this work includes an introduction to the basic axioms of fractals and their applications in the natural sciences, a survey of random fractals together with many pseudocodes for selected algorithms, an introduction into fantastic fractals such as the Mandelbrot set and the Julia sets, together with a detailed discussion of algorithms and fractal modeling of real world objects. 142 illustrations in 277 parts. 39 color plates. ... Read more

Customer Reviews (4)

Fractals -- Applied Mathmatics and Computer Programming
From page 25" Fractals (a word coined by Mandelbrot in 1975) have blossomed tremendously in the past few years (written in 1988) and have helped reconnect pure mathematics research with both the natural sciences and computing."

This book has both Mathmatical equations and Computer Programs along with explanations and results (many graphs, plots, and color plate images).

If you have an interest in Fractals, Recursion, Computer programming, Image creation, this is a great book and filled with examples.

Great book on fractals and imaging
This old book is a timeless gem. It goes into the details of the mathematics of fractals and also shows well-commented C code for producing fractal imagery along with good color illustrations.
Chapter 1, "Fractals in Nature", uses computer generated images to build a visual intuition for fractal as opposed to Euclidian shapes. There is also a mathematical characterization with Brownian motion as the prototype.
In chapter 2, "Random Fractal Algorithms", randomness is introduced into the algorithms discussed in chapter one as a way of simulating natural phenomena. Ideas are extended to higher dimensions. C programs that produce mountain ranges using these ideas are presented, along with the resulting imagery.
Chapter 3, "Fractal Patterns Arising in Chaotic Dynamical Systems", turns to the topic of dynamical systems and is less mathematical than the first two chapters. There is some mathematics and some illustrations in 2D and black and white that should be familiar to any student of dynamical systems.
Chapter 4, "Fantastic Deterministic Fractals", demonstrates how genuine mathematical research experiments open a door to a new reservoir of fantastic shapes and images. Programs are shown that extend the ideas of chapter 3 into truly beautiful fractals. Ideas here stay mainly in 2D.
The final chapter, "Fractal Modelling of Real World Images", draws from the material of the previous chapters to present C programs that produce clouds, vegetation, smoke, and mountain ranges, all by altering a few of the parameters in the sample code presented by the authors.
This book is much better than more recent titles that bury their algorithms in complex high level languages or "toy books" on the subject that provide dumbed-down applications and in which the simplest possible explanation of fractals is given with no insight. I highly recommend this book to anyone interested in understanding fractal mathematics and in using that mathematics to produce stunning visual effects.

One of the best (if no the best) in the feild
You cant go past this book,

This book reads at any level, Great introduction to the field as well as an indespencible reference. Shows easy to implement code examples, and has lots of pictures showing what can beacheived.

This has been a main reference for a theisis I am currentlyworking on. The question is, why is it out of print. If you can find itit's worth it's wheight in gold.

A must
In my opinion, the best work ever written in the category not-for-beginner-but-available-to-non-specialist (such as Beauty of Fractals, by the same authors). An easy answer to question "How can Igenerate a fractal image with my PC?", from brownian motion to Juliasets. A must for reader interested in fractals (a bit out-of-fashion butstill very interesting field). ... Read more

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Customer Reviews (4)

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

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

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

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

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

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

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

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

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

Product Description
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded.[1] That is, a complex number, c, is in the Mandelbrot set if, when starting with z0=0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,?, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is the square root of -1) gives the sequence 0, i, (?1 + i), ?i, (?1 + i), ?i?, which is bounded and so i belongs to the Mandelbrot set. When computed and graphed on the complex plane the Mandelbrot Set is seen to have an elaborate boundary which does not simplify at any given magnification. ... Read more

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Chapters: Hyman G. Rickover, Benoît Mandelbrot, Casimir Funk, Czesław Miłosz, Isaac Bashevis Singer, Zbigniew Brzezinski, Alfred Tarski, Stanisława Walasiewicz, Max Shachtman, Leonid Hurwicz, George Adamski, Arthur Rubinstein, Rose Pastor Stokes, Albert Sabin, Bronisław Malinowski, Stanisław Mikołajczyk, Karl Maramorosch, Alicia Appleman-Jurman, Samuel Yellin, Moe Drabowsky, Samuel Karlin, Poldek Pfefferberg, Adam Makowicz, Sholem Asch, David Lieber, Wlad Godzich, Anna-Teresa Tymieniecka, Tadeusz Sendzimir, Manfred Schwartz, Jack J. Grynberg, Abraham Low, Sol Rosenberg, Gaspar Tochman, Jeanne Chall, Lee Shubert, Marian P. Opala, Eugene Lazowski, Władysław T. Benda, Edward Werner, Sam S. Shubert, Greg Kuperberg, Ryszard Horowitz, Bert Cochran, Nicholas Minue, Ignacy Szymański, V. J. Jerome, Lyda Roberti, Andrew Schally, Stefan Szefer, Felix Zandman, Shmuel Berenbaum, Dagmara Dominczyk, David Seymour, Jacob J. Shubert, Zygmunt Haupt, Eugene Salamin, Morris Mandel, Morris Michael Edelstein, Ruth Minsky Sender, Adam Wolanin, Frank Walus, Marian Kamil Dziewanowski, Morris Winchevsky, Leonard Schmidtner, Marika Dominczyk, Jacob Wolfowitz, Zypora Spaisman, Julius Finn, Nicholas Andrew Rey, Janusz K. Zawodny, Alexander M. Schenker, Stephen Mizwa, Tadeusz Swietochowski, Witold Woyda, Seymour Rexite, Yetta Zwerling, Dagmara Wozniak, Krzysztof Matyjaszewski, Harry Broudy, Arthur A. Koscinski, Tadeusz Iwaniec, Sylwester Braun, Otto M. Nikodym, Ron Dunin, Zecharia Dershowitz. Source: Wikipedia. Pages: 393. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Zbigniew Kazimierz Brzezinski (Polish: , pronounced ; born March 28, 1928, Warsaw, Poland) is an American political scientist, geostrategist, and statesman who served as United States National Security Advisor to President Jimmy Carter from 1977 to 1981....More: http://booksllc.net/?id=58418 ... Read more

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Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

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This digital document, covering the life and work of Benoit B. Mandelbrot, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 3378 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author

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Chapters: Stephen Wolfram, Henri Poincaré, Aleksandr Lyapunov, Benoît Mandelbrot, Edward Norton Lorenz, Steven Strogatz, Vladimir Damgov, Otto Rössler, Boris Chirikov, Brosl Hasslacher, Denis Blackmore, Mitchell Feigenbaum, James Murdoch Austin, J. Doyne Farmer, Norman Packard, Floris Takens, Harry Swinney, James A. Yorke, David Ruelle, Michael Barnsley, Michel Hénon, Theodor Schwenk. Source: Wikipedia. Pages: 110. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Jules Henri Poincaré (29 April 1854 17 July 1912) (French pronunciation: ) was a French mathematician, theoretical physicist, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is considered to be one of the founders of the field of topology. Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853-1928) in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. The Poincaré group used in physics and mathematics was named after him. Poinc...More: http://booksllc.net/?id=48740 ... Read more