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Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Dover Books on Physics) [Paperback]

Manfred Schroeder , Physics
4.4 out of 5 stars  See all reviews (15 customer reviews)

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Book Description

August 21, 2009 0486472043 978-0486472041
"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
 "An inviting exposition for a literate but not highly scientific audience." — American Mathematical Monthly
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. Author Manfred Schroeder — hailed by Publishers Weekly as a modern Lewis Carroll — conveys memorable insights in the form of puns and puzzles that relate abstract mathematics to everyday experience.
Excellent entertainment for readers with a grasp of algebra and some calculus, this book forms a fine university-level introduction to fractal math. Eight pages of color images clarify the text, along with numerous black-and-white illustrations.

Frequently Bought Together

Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Dover Books on Physics) + The Fractal Geometry of Nature + Introducing Fractals: A Graphic Guide
Price for all three: $60.37

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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

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


Product Details

  • Series: Dover Books on Physics
  • Paperback: 448 pages
  • Publisher: Dover Publications (August 21, 2009)
  • Language: English
  • ISBN-10: 0486472043
  • ISBN-13: 978-0486472041
  • Product Dimensions: 9.1 x 6.1 x 1 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #304,509 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
57 of 59 people found the following review helpful
5.0 out of 5 stars Readable and mathematically rigorous 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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37 of 38 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
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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18 of 19 people found the following review helpful
4.0 out of 5 stars Great stuff, not for the uninitiated December 30, 2000
By A Customer
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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20 of 24 people found the following review helpful
3.0 out of 5 stars Collection of specific cases February 16, 2010
By Thomas
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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8 of 9 people found the following review helpful
5.0 out of 5 stars For the uninitiated!.--Fun too! 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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7 of 8 people found the following review helpful
5.0 out of 5 stars Best book on chaos 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
3.0 out of 5 stars 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 14 months ago by cygnus.x1
2.0 out of 5 stars 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 16 months ago by a reader
5.0 out of 5 stars 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 17 months ago by nancymat
5.0 out of 5 stars 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
5.0 out of 5 stars 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
5.0 out of 5 stars Great Math Book
This is a one of the best semi-technical mathematics books I ever read. What I mean by "semi-technical" is, you need somewhat of a math interest and education to appreciate it, and... Read more
Published on May 29, 2007 by book fan
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 June 22, 2000 by Massimiliano Celaschi
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