Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise [Paperback]

Manfred Schroeder (Author)

Book Description

ISBN-10: 0716723573 | ISBN-13: 978-0716723578 | Publication Date: July 15, 1992

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

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.

About the Author

Manfred Schroeder is a pioneer in the artistic potential of computer graphics, a world-renowned expert in concert hall acoustics, and holder of over 45 patents. He divides his time between Berkeley Heights, California and Goetingen, Germany.

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: 4.7 out of 5 stars  See all reviews (12 customer reviews)
• Amazon Best Sellers Rank: #743,354 in Books (See Top 100 in Books)
  • #76 in Books > Professional & Technical > Professional Science > Physics > Chaos Theory

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Customer Reviews

Most Helpful Customer Reviews

49 of 49 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
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This review is from: Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (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.

31 of 31 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 review is from: Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Paperback)

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.

13 of 13 people found the following review helpful:

4.0 out of 5 stars Great stuff, not for the uninitiated, December 30, 2000

By A Customer

This review is from: Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (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.