Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise

by Manfred Schroeder (Author)

20 customer reviews

ISBN-13: 978-0716723578

ISBN-10: 0716723573

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Product Details

Paperback: 429 pages
Publisher: W. H. Freeman (July 15, 1992)
Language: English
ISBN-10: 0716723573
ISBN-13: 978-0716723578
Product Dimensions: 6.7 x 1.2 x 9.2 inches
Shipping Weight: 1.1 pounds
Average Customer Review: 4.3 out of 5 stars See all reviews (20 customer reviews)
Amazon Best Sellers Rank: #2,579,857 in Books (See Top 100 in Books)
- #263 in Books > Science & Math > Physics > Chaos Theory
- #267 in Books > Science & Math > Mathematics > Pure Mathematics > Fractals
- #1510 in Books > Textbooks > Science & Mathematics > Mathematics > Geometry

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Customer Reviews

4.4 out of 5 stars

5 star		65%
4 star		15%
3 star		10%
2 star		10%
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Most Helpful Customer Reviews

58 of 60 people found the following review helpful

Readable and mathematically rigorous

By Michael J. Edelman TOP 100 REVIEWERVINE VOICE on June 19, 2000

Format: Paperback

What an excellent find! I'd been reading Per Bok's "How Nature Works" and realized I need a better grounding in the basics of fractal mathematics; this book turned out to be just the ticket.
Schroeder starst out with some simple, intuitive examples of curves and regions that do not scale to integral proportions, and from thse he develops and introduces the notion of the Hausdorf dimension of a curve. From there he introduces new concepts graphically- like Koch snowflakes and the Serpienski gasket- by first constructing them and then doing the analysis, introducing new concepts as needed to advance the illustration.
Often Schroeder starts with very non-geometric illustrations; his section on power laws begins with a discussion of language and word frequency, and from there he introduces Zipf's law, and then generalizes to characteristics of power law distributions in general- but not before treating the reading to a fascinating discourse on cognates and false cognates between languages- which he manages to weave into a discussion of self-similarity. Brilliant!
"Fractals, Chaos, Power Laws" could easily be used for a University-level introduction to fractal math, for graduate students or advanced undergrads- yet it's still readable enough to be a find introduction and entertainment to the reader with only a basic background in algebra and perhaps some calculus. The casual reader might not follow all the mathmatical arguments, but he or she could still glean much from this book. Highly recommended for the mathematically inclined looking for education or entertainment.

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38 of 39 people found the following review helpful

A comprehensive introduction to chaos in two levels

By josech on March 16, 2002

Format: Paperback Verified Purchase

This book can be read in two different ways:
The first one is intended for the uninitiated who wants to get an introduction to chaos and fractals; the way Schroeder guides you into the chaotic phenomenae that occur everywhere around us is clear, elegant and funny. He plays with chaos and makes the reader part of this game.
The second way to read this book includes a warning for scholars: This is not a textbook! The mathematical background used to explain this game is strong. Shcroeder lets the committed reader to work with the maths by himself, so you must have paper, pencil, and computer near to you in order to enjoy the book's whole potential, in this case Shcroeder has all the experience and knowledge on the matter to guide you through "this infinte paradise" in a very firm way.
The only thing I'd wish from this book was a new hardcover edition, I've read it so many times that my copy is getting very spoiled.
If you are still interested after reading this book, but you want a little help with your maths then I'd recommend "Chaos Theory Tamed" by Garnett P. Williams. It will do the trick. However if you just want to fall in love with chaos without complications, then you should read "Chaos: The Making of a New Science" by James Gleick.

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20 of 21 people found the following review helpful

Great stuff, not for the uninitiated

By A Customer on December 30, 2000

Format: Paperback

If you've had some background in this kind of mathematics, or are otherwise familiar with concepts like limits and Lebesgue measure, you should thoroughly enjoy this well-written and good-humored introduction to fractals, chaos, and related topics. Do not, however, undertake to read this book as an easy introduction to those topics, because Schroeder uses a number of terms without bothering to define them, and covers a lot of ground in each chapter, from the perspective of a non-mathematician/physicist, at least.
For a shorter, gentler introduction to this material, I recommend R.L. Devaney's "Chaos, Fractals, and Dynamics: Computer Experiments...," which contains BASIC code to allow you to play with these systems on your computer. If that piques your interest enough, you can then turn to Schroeder's book for a broader and fuller treatment of these ideas.

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21 of 25 people found the following review helpful

Collection of specific cases

By Thomas on February 16, 2010

Format: Paperback Verified Purchase

This book explores many cases of self similar structures that give rise to fractals .
It is not mathematically oriented and the few mathematical arguments are easy .
It is full of examples of anecdotical character demonstrating power laws and self similarity (concert halls , music , image treatment etc) .
There are also some nice pictures .
However it is not by any account a book concerning the chaos theory .
As a physicist I have been disappointed .
It is too long to be a book on fractal esthetics and it is too short and too anecdotical to be a book about non linear dynamics .
The only description I can find would be : entertaining mathematical games on the concept of iteration and self similarity .

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9 of 10 people found the following review helpful

For the uninitiated!.--Fun too!

By Palle E T Jorgensen VINE VOICE on February 28, 2003

Format: Paperback Verified Purchase

For the uninitiated! --The author combines insight with story telling. He has a story to tell, and does it well! Not only does he know the theory inside out, he has the ability to get accross the central points so it (almost) seems easy, in any case entertaining, using pictures (including cartoons), humor, and equations when they are needed. He further make clear the many fascinating links between chaos theory, algorithms, technology, and areas of pure math, such as number theory. Highly recommended!

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8 of 9 people found the following review helpful

Best book on chaos

By Steve Uhlig on January 27, 2001

Format: Paperback

This book is a complete guide of all possible situations in science where you may encounter chaos. It provides for every situation an intuitive as well as very formal view of every problem and the corresponding solution. The main drawback concerns its relative inaccessibility for non-scientific people, it requires a quite important scientific background to understand the formal part. Anyway, even for the lay-man, it can be interesting to read, in order to understand the widespread of chaos and non-linearity in real-life situations, not just the purely scientific-related ones.
However, the treatment is terrific, with excellent description and explanations of the how's and why's, at an intuitive level as well as a very rigorous one ! I don't think i've ever read a book of such a high quality...
This book is worth its price, and without a doubt deserves the time you'll need to go through it.

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Most Recent Customer Reviews

good overview lacks details.

Good overview about several aspects of fractals, but it does not go into details.

Published 5 months ago by Airton Deppman

Five Stars

Book arrived perfectly.

Published 6 months ago by Lappoon Rupert Tang

An appetizer, where is the main course?

This book is kind of a tease. You get just enough mathematics to get you interested, but never all you need to get a real understanding. Read more

Published 11 months ago by Thomas J. Trebisky

recommended

This is a fine review of the subject with a nice balance between qualitative and quantitative aspects of fractals. Read more

Published 14 months ago by s. berger

Five Stars

Tough math read on fractals and chaos.

Published 16 months ago by C George Brockus

Good, but a pain.

I got what I'd wanted, but it isn't written the way that I expected. I don't mind the math, but it's the general organization that's problematic.

Published on May 11, 2013 by cygnus.x1

Misleading title, disjointed exposition

I did glean a few interesting bits from this, so for that it gets two stars, but my comments are mostly negative. Read more

Published on March 16, 2013 by a reader

For math and physics geniuses !!!

Book was too mathematically challenging for me (a mere college graduate). One needs to have a PhD in physics and/or math to understand it! Read more

Published on January 30, 2013 by nancymat

Excellent introduction to fractals and power laws

This book is an extraordinarily well written and presented introduction to fractals and power laws. It has a far deeper mathematical level and requires more time and effort to... Read more

Published on August 23, 2010 by Secluded Path

A Chaotic Heaven

What a head-trip! While the Pearly Gates of Paradise may be more than a few minutes away, you are almost certain to enjoy the journey with this book in hand. Read more

Published on February 10, 2008 by Mathew Titus