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Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.Book Description
Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses. The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds. ... Read more

Customer Reviews (13)

changed the way I look at the world
Visually, I see nature in a much richer way.As an artist, I find fractals to be inexhaustable inspiration.There is no better text to explain Mandlebrot's theories in a detailed but understandable way than the seminal work itself.Sometimes I got lost in the math, but most of it I could follow.I found helpful the notes in the text indicating which parts were mathematical asides for the technically-minded readers, where other readers could skip ahead without losing any understanding.the illustrations are evocative and timeless diagrams of real phenomena. If I were a more spiritual person, I am sure this book would be proof of the existence of god.

A seminal work
Very few books have so many quotes as this one. I am not sure if there is much left to be said, but I know this. For those professionals who still think that fractals are "spurious solutions coming from the discretization of differential equations", should take a closer look to this book. Not only won't harm, but also will show many interesting features about the nature of fractals and the "fractality" of nature, besides the fact that many of them come from *difference* equations, which are not necessarily related to the discretization of a differential equation. This book is based on serious work from many well-reputed mathematicians before Mandelbrot, e.g., Haussdorff, Lyapunov and some others. Although the book does talk about the mathematics behind fractals (wouldn't be so much a book of mathematics if it didn't, but also a philosophical one) and the necessity of coining some new mathematical terms, it also contains so much about history of mathematics, the path that leads towards fractals. As I said, the book is many times quoted, but (without trying to point a firing, accusing finger), there is a difference in quoting a book because it is famous, and another actually reading it, and having enlightenment for our own sake. Certainly I think is a "must-have-it" for most mathematicians,for many physicists, philosophers of science and engineers, but also it wouldn't be a bad guest in the library of any layman, provided the layman overcomes for some minutes the initial "classical" fear to mathematics. I would say this layman won't regret it at all. Mandelbrot does explain most of the concepts practically "ab initio", from the very scratch, including etymology and history as I previously said. One little thing against this book though: it doesn't have so many color plates as some other books on the subject, but it does have all the needed graphics to grasp the concepts.

Nice coffee table book? Not much else.
The BOOK by the MAN who coined the name fractal and brought them
to the general public. (Actually an enhanced version of an
earlier book with a slightly different title, same publisher.)

This book has historical value I suppose. But there are now
prettier picture books if you want those or you can easily create
your own. And if you are interested in the maths then you should
definitely look elsewhere (Devaney perhaps?). I think there is a
nice collection of papers by early 20th century pioneers
available too.

Now I wonder is Mandelbrot really the mathematician he is reputed
to be in popular imagination? It seems to me there is little here
that was not thought of before in the early 20th century by
Hausdorff, Poincare, Julia, Lebesgue, Bachelier and others. And
the whole fractal idea seems to have a life of its own in popular
imagination that does not to be justified according to the (much
smaller) importance in physics and other sciences.

Essential classic book for everyone's library
Mandelbrot presents unique and infinitely deep look at nature. The emerging theory of interaction shows that his notion of fractal turned to be more fruitful than anyone could guess. Savov's theory of interaction rigorously proves that nature is one self-reproducing and therefore self-similar fractal like interaction.Its oscillating sources remain always finite and synchronize to eject smaller similar ones.

A dated but still fascinating book
This was the book that first caught my attention. It was the cover diagram: a figure the like of which I had never seen. One thing led to another until I finally wrote my own application of fractals, Fractals in Music.

Mandelbrot is an odd character, but a superb thinker. His book does not offer a lot of science, but rather a compelling view of how this fascinating and growing topic developed. I recommend it highly. ... Read more

Book 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 (49)

don't waste your money and time
the author claims that the book will not make you rich but would make you understand the market behaviour better and thus avoid loss, he's right on the first part and wrong on the second part, he may be a genious but if he does not improve his presentation 100 times, this book will achieve one thing only - waste your time and money

a Rich, Accessible compendium of thought
I am a risk manager. The challenges that Mandelbrot has undertaken both politically, socially and intellectually are breathtaking and highly relevant. I am routinely found plodding through dense math texts, trying to remember my greek alphabet and often hoplessly lost in teh terminology. Mandelbrot does a great service to us all when he keeps the language understandable for the laity and eschews the complex formulas. You can tell that he does not need to sound overly smart because he is overly smart.

This book toes together so much history and so many concepts in such an elegant style that it is very hard to oversell the work. I have a hard time imagining a field in which this knowledge is not applicable in some way. And anyone who has even a baseline sense of curiosity will find the interweaving of the many great stories compelling.

I would imagine that some math majors will find that the information is somewhat basic, but only if they are exposed to a lox on non linear problems in a complexity theory or econophysics field. For everyone else, this is a masterpiece, an entertaining, accessible masterpiece.

Oh, and for any of you who like Nassim Taleb's work, this is absolutely essential reading. I also suggest diving into network and sync theories which fill in the gaps left by Mandelbrot. Much good work has been done since he wrote this. "Linked" and "sync" are especially good and accessible.

Great book!
I'm doing research for a lecture about non-normal distributions, difficulties in prediction, etc.My colleague recommended The Black Swan, which he loved.I was plodding through it with difficulty when I found this book.Both are written by mathematical types, and both deal with the economics as the subject matter.But this book is by the founder of fractal geometry, and is much more lively, informative, well-documented and fun to read than the Black Swan, IMHO.

Good on explanation, light on math, heavy on boasting
(Mis)Behavior of Markets is a wonderful book for people looking to understand why modern financial modelling does not adequately explain real market prices and their fluctuations. The authors are quite good at pointing out the shortcomings of current models that can be easily verified by the reader with web access. They also give a decent overview of how an alternate mathematical view shows promise in improving our understand of market volatility. I took away from it that markets are far more chaotic than we currently appreciate (their view) and short-term investors will suffer the costs of this (my view).

There are two points where the book falls short. While it makes generous use of graphs to explain mathematical relationships, it could stand a fair bit more formalism in explaining the math. This isn't supposed to be an academic treatise, to be sure, but the informality made it hard for a skeptic to follow every logical step in the reasoning.

The book may be light on math but it sure isn't light on self-esteem. The author (I'm assuming these parts are chiefly written by Mandelbrot) feels the need to end most of his paragraphs with a reminder of how his contemporaries have underappreciated his groundbreaking research. I'm sure he's smart dude but I kind of assumed that whe

For the financial theorist in you
Mandelbrot is, of course, a genius.In this book Mandelbot attacks orthodox financial theory and substitutes a fractal view of how markets everywhere behave.It's all interesting and Mandelbrot writes in a very accessible style.The conclusions he draws are non-controversial (markets are turbulent, markets are far riskier than we think, etc).An alternative to evaluating risk and reward is offered and might be of interest to theoretical finance people and perhaps some people who trade as a hobby or for a living and like to ponder ways to avoid severe financial loss or ruin.Having known a few traders in complex financial derivatives who did experience ruin, the topic is of great interest to me.As a long term investor who relies mainly on index stock and bond funds and real estate for my investments, I'm happy to see Dr. Mandelbrot's wild graphs in a book and not on my financial statements (fingers crossed!). ... Read more

Book Description

It has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world.

Book Description
Benoit Mandelbrot 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.y 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

Book Description
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

Book Description
This volume offers an excellent selection of cutting-edgearticles about fractal geometry, covering the great breadth ofmathematics and related areas touched by this subject. Includedare rich survey articles and fine expository papers. Thehigh-quality contributions to the volume by well-knownresearchers---including two articles by Mandelbrot---provide asolid cross-section of recent research representing the richnessand variety of contemporary advances in and around fractalgeometry.

In demonstrating the vitality and diversity of the field, thisbook will motivate further investigation into the many openproblems and inspire future research directions. It is suitablefor graduate students and researchers interested in fractalgeometry and its applications.

This is a two-part volume. Part 1 covers analysis, number theory,and dynamical systems; Part 2, multifractals, probability andstatistical mechanics, and applications. ... Read more

Book Description

This is the first book in the Selecta, the collected works of Benoit Mandelbrot. This volume incorporates his original contributions to finance and is a major contribution to the understanding of how speculative prices vary in time. The chapters consist of much new material prepared for this volume, as well as reprints of his classic papers. Much of this work helps to lay a foundation for evaluating risks in trading strategies.

Customer Reviews (3)

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

Book Description
This digital document is an article from American Journal of Applied Sciences, published by Thomson Gale on November 1, 2007. The length of the article is 5461 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

From the author: Keywords: Fractals Cryptography, Digital Signature Scheme, Mandelbrot Fractal Set, and Julia Fractal Set

Citation Details
Title: A new digital signature scheme based on Mandelbrot and Julia fractal sets.
Author: Mohammad Ahmad Alia
Publication: American Journal of Applied Sciences (Magazine/Journal)
Date: November 1, 2007
Publisher: Thomson Gale
Volume: 4Issue: 11Page: 850(9)

Distributed by Thomson Gale ... Read more