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Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Dover Books on Physics) Paperback – 1 Jan 2009

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Product details

  • Paperback: 448 pages
  • Publisher: Dover Publications Inc. (1 Jan 2009)
  • Language: English
  • ISBN-10: 0486472043
  • ISBN-13: 978-0486472041
  • Product Dimensions: 23.1 x 15.5 x 2.5 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 444,075 in Books (See Top 100 in Books)

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Product Description

About the Author

A pioneer in the artistic potential of computer graphics, Manfred Schroeder is a world-renowned expert in acoustics. He served as a distinguished member of the research staff of AT & T Bell Laboratories for 33 years and is Professor Emeritus at the University of Goettigen, Germany. Manfred Schroeder: Making Order Out of Chaos Manfred Schroeder (1926–2009) was a German physicist who divided his professional time between Bell Labs and The University of Gottingen. He was a world-renowned authority on acoustics and held numerous patents in many fields. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, reprinted by Dover in 2009, is a feast for the reader with a grasp of algebra and some calculus. He or she will find much to enjoy and think about between the covers of this unique book. Critical Acclaim for Fractals, Chaos, Power Laws: "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." — Publisher’s Weekly "As notable as the book's broad sweep is the author's good-natured, humorous presentation. The willing reader can sit back and enjoy an all-encompassing, irrepressibly enthusiastic tour, ranging from psycho-physics to quasicrystals, from gambling strategies to Bach concertos, from the construction of Cantor Sets to the design of concert halls" — Physics Today "Such a richness of topics and amazing splendor of illustrations." — Mathematics Magazine

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9 of 10 people found the following review helpful By A Customer on 22 July 1999
Format: Paperback
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. A 'must read' for anyone who wants a serious introduction to these fascinating topics.
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1 of 1 people found the following review helpful By zion375 on 31 Jan 2011
Format: Paperback
A math teacher recommended me this book long ago and I agree this is a good recommendation! Good book for those who want to take an insight in fractal and chaos concepts.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 18 reviews
57 of 59 people found the following review helpful
Readable and mathematically rigorous 19 Jun 2000
By Michael J. Edelman - Published on Amazon.com
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.
37 of 38 people found the following review helpful
A comprehensive introduction to chaos in two levels 16 Mar 2002
By josech - Published on Amazon.com
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.
20 of 21 people found the following review helpful
Great stuff, not for the uninitiated 31 Dec 2000
By A Customer - Published on Amazon.com
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.
20 of 24 people found the following review helpful
Collection of specific cases 16 Feb 2010
By Thomas - Published on Amazon.com
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 .
9 of 10 people found the following review helpful
For the uninitiated!.--Fun too! 28 Feb 2003
By Palle E T Jorgensen - Published on Amazon.com
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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