Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chaos, fractals, and other areas of current research and popular interest. Self-similarity is related to svmmetry and is an attribute of many physical laws: particle physics and those governing Newton's laws 0 , gravitation. Symmetry, found throughout the biological universe, is also a basic property of the mathematical universe. In this book the author explores the ideas of scaling, self-similarity, chaos and fractals as they appear throughout the universe of pure and applied mathematics. Because of his formidable research experience, stretching from the acoustical modelling of concert halls to pure number theory, Schroeder is able to take the reader on an intellectual excursion through this vast forest of topics.
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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.
Copyright 1991 Reed Business Information, Inc.
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.
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Customer Reviews
Most helpful customer reviews
2 of 2 people found the following review helpful
Format:Paperback
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!
2 of 2 people found the following review helpful
By josech
Format: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.
1 of 1 people found the following review helpful
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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4.4 out of 5 stars
Most recent customer reviews
3.0 out of 5 stars
Jam-pack of disconnected facts published 20 years ago.
The explanation in this book could be better. The author certainly knows a lot, but he can never update this book to make it more whole. Read more
Published 17 months ago by Nile
5.0 out of 5 stars
Best book on chaos
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... Read more
Published on Jan 27 2001 by Steve Uhlig
4.0 out of 5 stars
Great stuff, not for the uninitiated
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... Read more
Published on Dec 31 2000
5.0 out of 5 stars
Very interesting both for beginners and for experts
One of the best introductory books I've ever read about the subject. A good example of multidisciplinarity and a bridge between theoretical and practical studies. Read more
Published on Jun 22 2000 by Massimiliano Celaschi
5.0 out of 5 stars
excellent! probably the best book on fractals
The best introductory book on fractals and chaos. It has a breath-taking wealth of topics, complete with the intuition behind them, the formulas, the drawings and pictures. Read more
Published on July 22 1999 by Christos Faloutsos (christos@cs.cmu.edu)
4.0 out of 5 stars
A Mathematical wonder: not for the faint of heart!
The book opens up ideas of wonderful depth, but isn't easy reading for those who hate equations. I would put this book in the top ten must read area for fractal people! Read more
Published on Mar 19 1998
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