Book 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

Book 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

Customer Reviews (3)

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

Book Description
The role of chaos in science and mathematics is examined in detail by the essays that comprise this work. Distinguished scholars specializing in mathematics, physics, and chemistry discuss the following subjects: Fractals, by Benoit Mandelbrot; The Causality Principle, Deterministic Laws and Chaos, by Heinz-Otto Peitgen; The Transition to Chaos, by Mitchell Feigenbaum; Time, Dynamics and Chaos: Integrating Poincare's "Non-Integrable Systems", by Ilya Prigogine; What Is Chaos, by Steve Smale; Chaos and Cosmos: A Theological Approach, by John Polkinghorne; and Chaos and Beyond, by James Gleick. Introduction by John Holte. This volume is number 26 in the Nobel Conference Series. Co-published with the Nobel Conference. ... Read more

Customer Reviews (1)

excellent description of system mathematics
easily read in layman's terms to understand the basic principles of chaos mathematics. ... Read more

Book Description
This digital document is an article from U.S. Kids, published by Children's Better Health Institute on June 1, 2000. The length of the article is 435 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.

Citation Details
Title: FRACTALS, ANYONE?
Author: Francesca Pinoni
Publication: U.S. Kids (Magazine/Journal)
Date: June 1, 2000
Publisher: Children's Better Health Institute
Volume: 13Issue: 4Page: 14

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Book Description
This digital document is an article from International Journal of Humanities and Peace, published by International Journal of Humanities and Peace on January 1, 2003. The length of the article is 5532 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.

Citation Details
Title: Bharata Natyam: classical Indian dance: a Hindu fractal.
Author: Sofia Diaz
Publication: International Journal of Humanities and Peace (Refereed)
Date: January 1, 2003
Publisher: International Journal of Humanities and Peace
Volume: 19Issue: 1Page: 83(6)

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Book Description
This digital document is an article from Skeptic (Altadena, CA), published by Skeptics Society & Skeptic Magazine on January 1, 2001. The length of the article is 883 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.

Citation Details
Title: CHAOS FORUM.
Publication: Skeptic (Altadena, CA) (Refereed)
Date: January 1, 2001
Publisher: Skeptics Society & Skeptic Magazine
Volume: 8Issue: 4Page: 26

Distributed by Thomson Gale ... Read more