- Hardcover: 864 pages
- Publisher: Springer; 2nd edition (February 3, 2004)
- Language: English
- ISBN-10: 0387202293
- ISBN-13: 978-0387202297
- Product Dimensions: 7.5 x 1.9 x 9.4 inches
- Shipping Weight: 3.9 pounds (View shipping rates and policies)
- Average Customer Review: 16 customer reviews
- Amazon Best Sellers Rank: #484,409 in Books (See Top 100 in Books)
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Chaos and Fractals: New Frontiers of Science 2nd Edition
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Fascinating and authoritative, Chaos and Fractals: New Frontiers of Science is a truly remarkable book that documents recent discoveries in chaos theory with plenty of mathematical detail, but without alienating the general reader. In all, this text offers an extremely rich and engaging tour of this quite revolutionary branch of mathematical research.
The most appealing aspect about Chaos and Fractals has to be its hundreds of images and graphics (with dozens in full-color) used to illustrate key concepts. Even the math-averse reader should be able to follow the basic presentation of chaos and fractals here. Since fractals often mimic natural shapes such as mountains, plants, and other biological forms, they lend themselves especially well to visual representation.
Early chapters here document the mathematical oddities (or "monsters") such as the Sierpinski Gasket and the Koch Curve, which laid the groundwork for later discoveries in fractals. The book does a fine job of placing recent discoveries about chaos into a tradition of earlier mathematical research. Its description of the work of mathematicians like Pascal, Kepler, Poincaré, Sierpinski, Koch, and Mandelbrot makes for a fine read, a detective story that ends with the discovery of order in chaos. (For programmers, the authors provide short algorithms and BASIC code, which lets you try out plotting various fractals on your own.)
This is not, however, only a book of pretty pictures. For the reader who needs the mathematics behind chaos theory, the authors in no way dumb down the details. (But because the richer mathematical material is set off from the main text, the general reader can still make headway without getting lost.)
There have been advances in the field since this book's publication in 1992, but Chaos and Fractals remains an authoritative general reference on chaos theory and fractals. A must for math students (and math enthusiasts), Chaos and Fractals also deserves a place on the bookshelf of any general reader or programmer who wants to understand how today's mathematicians and scientists make sense of our world using chaos theory. --Richard Dragan
Topics covered: Overview of fractals and chaos theory, feedback and multiple reduction copy machines (MRCMs), the Cantor Set, the Sierpinski Gasket and Carpet, the Pascal Triangle, the Koch Curve, Julia Sets, similarity, measuring fractal curves, fractal dimensions, transformations and contraction mapping, image compression, chaos games, fractals and nature, L-systems, cellular automata basics, attractors and strange attractors, Henon's Attractor, Rössler and Lorenz Attractors, randomness in fractals, the Brownian motion, fractal landscapes, sensitivity and periodic points, complex arithmetic basics, the Mandelbrot Set, and multifractal measures. --This text refers to the Paperback edition.
“It is relatively discursive and easy to read, with each chapter telling a coherent story, and it highlights the key concepts and ideas, examining a few models in detail and using worked numerical examples as well as visualisations and illustrations … . makes an excellent entry to the broader mathematics of fractals and chaos, especially for students who are curious about the details as well as the core concepts but don’t want to get bogged down in formal mathematics.” (Danny Yee, Danny Yee’s Book reviews, February, 2016)
"It is one of the best introductions to chaos and fractals around. … Unlike some other books on fractals, it can be read by non-specialists … . The book is beautifully produced and well illustrated so it is a pleasure to read." (Hugh Williams, The Mathematical Gazette, Vol. 90 (5l9), 2006)
"The first edition of this vast introduction to chaos and fractals appeared in 1992. This new edition is virtually identical to the original except for some material … . the book is … a wonderful tour of a fascinating area of mathematics, and now the reader can take this tour while carrying around a slimmer (but still hefty) volume. … The authors have a friendly conversational style … . This is a great book … ." (Raymond N. Greenwell, MathDL, May, 2005)
"Chaos and Fractals: New Frontiers of Science is an amazing introduction to the ideas of fractal geometry and chaotic dynamics … . The authors have done a tremendous job in explaining quite difficult concepts in an elegant and simple way … . I enjoyed this book tremendously – the authors have put in a tremendous amount of work in making a vast and interesting subject accessible … . I wholeheartedly recommend this book to anyone with even a passing interest in the subject matter." (Dr. S. Virmani, Contemporary Physics, Vol. 46 (6), 2005)
"There appeared many books in the 1980’s and early 1990’s that … required only a limited mathematical background to understand. They made the fractals, chaos and the Mandelbrot and Julia sets quite popular … . The … book that is under review here is one of these popular books. … The book will remain what it has been so far: an outstanding book that contains all you ever wanted to know about fractals and chaos accessible to all levels of mathematically skilled." (Bulletin of the Belgian Mathematical Society, Vol. 12 (3), 2005)
"The book is written for everyone who wants to learn details of chaos theory and fractal geometry, also for readers who have not much knowledge of technical mathematics. In the fourteen chapters the central ideas and concepts of chaos and fractals are developed … ." (F. Haslinger, Monatshefte für Mathematik, Vol. 144 (4), 2005)
"This is the second … edition of what has been a bestseller since its first publication in 1992. … All the laudatory comments heard twelve years ago about this fascinating book remain entirely valid. No one has succeeded in better presenting … . the presentation has not aged at all – the comprehensiveness of the underlying mathematics and the illustrative power of the figures has never been surpassed. Twelve years after its first edition this book remains a must buy." (André Hautot, Physicalia, Vol. 57 (3), 2005)
"Numerous books have appeared in recent years that either explore the beauty of fractal art, describe techniques for its creation, or investigate some aspect of the related field of chaotic behavior. The present work attempts to accomplish all three goals in one huge volume...the authors should be applauded for their ambitions undertaking." Mathematical Reviews
"This book … contains all one ever wanted to know about fractals, and more. Written by–next to Mandelbrot–the greatest popularizer of the concept of fractal geometry … It contains a wealth of information on nearly every angle of the topic... I enjoyed reading the book for its lucid approach, its attempt at completeness, and especially, for the large number of illustrative figures and pictures." Zentralblatt Mathematik
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So I was so pleased to see a copy of the updated edition at a bookstore. In particular, I was eager to see if they'd updated those "do it yourself" exercises for use with EXCEL. However, as I read through it I was disappointed to notice two changes from the previous edition: first, all of the programming examples had been eliminated; second, the print quality of the color plates was noticeably poorer. And I didn't see much new material added - in fact one of the reviews above observes that the text itself is virtually unchanged. Considering the steep price of this tome, these were significant points to consider. Used copies of the old edition cost under 20 bucks, and IMHO are a better deal (I ended up buying one). So if you're ready to buy, just do yourself (and your wallet) a favor and compare the two editions first.
initial wave of popularity of fractals and chaos theory.
Although the fadishness of chaos and fractals has died
down, a number of solid applications for this theory have
appeared in areas like computer graphics, finance,
modeling computer network traffic and data compression.
I have purchased a number of books on fractals and chaos and
how these concepts can be applied in a number of areas. I
have yet to see a better introduction to the topic. This is
a core reference and I keep coming back to it again and again.
In the spectrum of popular science books, this is definitely
on the technical end. You do not need an advanced background
in mathematics as you do for some books on chaos and fractals,
but the authors do not shy away from equations. However, the
ideas are clearly presented. I have used this book as a
reference for developing software for fractal brownian motion
and Hurst exponent estimation.
"Chaos and Fractals" covers a great deal of material. On a few
occasions I found that the algorithms or explaination were
difficult to follow. In some cases, like the generation of
Gaussian random numbers, I found better, simpler algorithms.
When this book was written, fractals and chaos were fairly new.
It is difficult to avoid comparing this book to an even thicker
book, "A New Kind of Science" by Stephen Wolfram. Although
cellular automata, the core topic of "A New Kind of Science"
are not exactly new, Wolfram claims new and profound
perspectives. Many, including this reviewer, feel that Wolfram's
claims are overblown and egotistical (he has a bad habbit of
claiming credit for innovation, even as he cites other work).
The authors of "Chaos and Fractals" do not make exalted
claims for this work. Yet without any fanfare, this book
really does deliver profound ideas. This is simply a
fantastic book. I recommend it for anyone in the applied
sciences (e.g., computer science, quantitative finance,
geology, etc...). Even for the mathematically sophisticated it
will provide an valuable overview, which is difficult to obtain
"The Colors of Infinity," based on the video documentary by Arthur C. Clarke is a good introduction to fractals. An enjoyable DVD is included of the original TV program, especially if you learn better by watching and listening. The accompanying animated fractals are fascinating, but frustratingly poor resolution. For a more philosophical approach to fractals, I highly recommend "Heaven's Fractal Net" by William Jackson.
Chaos and fractals are subjects that sound modern, interesting and eye-catching in the most of the cases. However, the applications and implications of chaos in the real world constitute the great achievement of human knowledge that the concept represents.
The lecture of this book doesn't require an extensive knowledge of math (but it would be helpful), it requires many will and passion for rediscovering your conception of the universe instead.
Before reading this book I'd recommend "Chaos: the Making of a New Science" by James Gleick and for those who are looking for a more compact but challenging material "Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise" by Manfred Schroeder will be just fine.
Most recent customer reviews
1. Have an understanding of math.
2. I am manic.
3. Supplementary and research may be necessary.
Great book with complex topics.Read more
[...] This will help you to decide if you need the printed book.
No other publication comes close to such complete coverage of the subject.
It is highly readable even for a novice like myself.Read more