Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Paperback)

by Manfred Schroeder (Author)

Editorial Reviews

From Publishers Weekly
Readers of James Gleick's 1989 bestseller, Chaos, The Making of a New Science, will find the revolution predicted there in full swing in this advanced look at "self-similarity, ' ' one of chaos theory's most appealing applications. Self-similarity in computer graphics yields the awesome fractal mountain patterns that have made chaos a visible theory for many nonmathematicians. Readers with good command of calculus and some physics will appreciate how far chaos theory has penetrated theoretical physics, biology and the practice of research as described in puns, illustrations and puzzles by this 20th-century Lewis Carroll. Without those skills, however, readers may stand like Alice before a small door that opens on strange new wonders of the physical world, the extended horizons of number theory and advanced math recreation. Schroeder is a professor of physics at Goettingen University in Germany.
Copyright 1991 Reed Business Information, Inc. --This text refers to an out of print or unavailable edition of this title.

Product Description

“As notable as the book’s broad sweep is the author’s good-natured, humorous presentation.”—Physics Today

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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: 9 x 6 x 1.1 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.8 out of 5 stars See all reviews (10 customer reviews)
• Amazon.com Sales Rank: #505,474 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

5.0 out of 5 stars Readable and mathematically rigorous, June 19, 2000

By	Michael J Edelman (Huntington Woods, MI USA) - See all my reviews (TOP 100 REVIEWER)    (REAL NAME)

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.

17 of 17 people found the following review helpful:

5.0 out of 5 stars A comprehensive introduction to chaos in two levels, March 16, 2002

By	"josech" (Mexico City) - See all my reviews

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.

5 of 5 people found the following review helpful:

5.0 out of 5 stars Best book on chaos, January 27, 2001

By	Steve Uhlig (Delft, The Netherlands) - See all my reviews (REAL NAME)

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.