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Heinz-Otto Peitgen
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Chaos and Fractals: New Frontiers of Science 2nd Edition

by Heinz-Otto Peitgen (Author), Hartmut Jürgens (Author), Dietmar Saupe (Author)
4.7 4.7 out of 5 stars 34 ratings
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Almost 12 years have passed by since we wrote Chaos and Fractals. At the time we were hoping that our approach of writing a book which would be both accessible without mathematical sophistication and portray these exiting new fields in an authentic manner would find an audience. Now we know it did. We know from many reviews and personal letters that the book is used in a wide range of ways: researchers use it to acquaint themselves, teachers use it in college and university courses, students use it for background reading, and there is also a substantial audience of lay people who just want to know what chaos and fractals are about. Every book that is somewhat technical in nature is likely to have a number of misprints and errors in its first edition. Some of these were caught and brought to our attention by our readers. One of them, Hermann Flaschka, deserves to be thanked in particular for his suggestions and improvements. This second edition has several changes. We have taken out thetwo appendices from the firstedition. At the time of the first edition Yuval Fishers contribution, which we published as an appendix was probably the first complete expository account on fractal image compression. Meanwhile, Yuvals book Fractal Image Compression: Theory and Application appeared and is now the publication to refer to.
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  1. ISBN-10
    0387202293
  2. ISBN-13
    978-0387202297
  3. Edition
    2nd
  4. Publisher
    Springer
  5. Publication date
    February 3, 2004
  6. Language
    English
  7. Dimensions
    7.75 x 2 x 9.25 inches
  8. Print length
    877 pages
  9. See all details
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    Chaos and Fractals: New Frontiers of Science
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Editorial Reviews

Review

“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 atall – 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

Product details

  • Publisher ‏ : ‎ Springer; 2nd edition (February 3, 2004)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 877 pages
  • ISBN-10 ‏ : ‎ 0387202293
  • ISBN-13 ‏ : ‎ 978-0387202297
  • Item Weight ‏ : ‎ 3.85 pounds
  • Dimensions ‏ : ‎ 7.75 x 2 x 9.25 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 34 ratings

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  1. Heinz-Otto Peitgen

    Heinz-Otto Peitgen

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  2. Hartmut Jurgens

    Hartmut Jurgens

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  3. Dietmar Saupe

    Dietmar Saupe

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Customer reviews

4.7 out of 5 stars
34 global ratings

Customers say

Customers find the color plates beautiful, sharp, and eye-catching. They also describe the book as enjoyable, interesting, and an entertainer. Readers mention it's excellent for intermediate knowledge of chaos and a perfect reference for beginners. They say the content is full and easy to understand.

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Color accuracyEnjoymentKnowledge levelReadable
4 customers mention "Color accuracy"4 positive0 negative

Customers find the color plates beautiful and sharp. They also say the accompanying animated fractals are fascinating.

"...the two (having not seen the new one) but I can say the color images are very sharp in the older book...." Read more

"...Chaos and fractals are subjects that sound modern, interesting and eye-catching in the most of the cases...." Read more

"...The numerous color plates were also very beautiful...." Read more

"...Fractal Geometry of Nature are a solid foundation, accessible and well illustrated, for the understanding of the subject. A must have!" Read more

4 customers mention "Enjoyment"4 positive0 negative

Customers find the book very enjoyable, interesting, and eye-catching. They appreciate the general explanations and excitement of the authors. Readers also mention the book is a great entertainer for anyone who wants to spend many hours reading.

"...I found the general explanations, the excitement of the authors, the broader significance of fractals all to be well-worth..." Read more

"This book is a great entertainer for anyone who wants to spend many evenings "playing with chaos"...." Read more

"...a firm understanding in analysis, geometry, and algebra this is very enjoyable." Read more

"Great book..." Read more

4 customers mention "Knowledge level"4 positive0 negative

Customers find the book excellent for intermediate knowledge of chaos. They say it's a perfect reference book for beginners and helpful.

"...I found this book most helpful, but NOT easy for the general reader, beyond the first few, introductory pages...." Read more

"...3. Supplementary and research may be necessary.Great book with complex topics...." Read more

"The content is full and easy to understand. It is perfect reference book for the beginner, as I am...." Read more

"Excellent for intermediate knowledge of chaos..." Read more

3 customers mention "Readable"3 positive0 negative

Customers find the book highly readable and easy to understand. They also appreciate the clear code.

"...It is highly readable even for a novice like myself.It has been a great joy to me.Many thanks to the authors for doing such a great job." Read more

"...OK, they use the old BASIC language, but still the code is clear enough that you can follow it and see what's really going on with these..." Read more

"The content is full and easy to understand. It is perfect reference book for the beginner, as I am...." Read more

Top reviews from the United States

Paul Asbury Seaman
5.0 out of 5 stars It's all true: Best single source on fractals-but get the 1st ed.
Reviewed in the United States on June 18, 2008
Verified Purchase
Thanks to S.J. Will for the tip: Get the FIRST edition (used), as I did and save more than half the price, even of a used copy of this newer edition. Can't compare the two (having not seen the new one) but I can say the color images are very sharp in the older book. As far as content, I too have looked at and bought several books trying to understand fractals. (I am not math-literate, beyond high school algebra.) I found this book most helpful, but NOT easy for the general reader, beyond the first few, introductory pages. As other reviewers have noted, most of it is WAYYYY over the head of anyone who's not a college math major, but skipping through the examples and exercises (some of which are very rewarding if you can stay with it), I found the general explanations, the excitement of the authors, the broader significance of fractals all to be well-worth the price. -- And hey: at over 900 pages ( ! ) and with FORTY color plates, this book is an astounding bargain. Strongly recommended, even for novices.

"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.
5 people found this helpful
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Matthew Radloff
5.0 out of 5 stars A complete book.
Reviewed in the United States on January 31, 2024
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A very good choice for the price.
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Bardo
4.0 out of 5 stars This book is a dream come true.
Reviewed in the United States on September 2, 2008
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This book is a dream come true.
No other publication comes close to such complete coverage of the subject.
It is highly readable even for a novice like myself.
It has been a great joy to me.
Many thanks to the authors for doing such a great job.
One person found this helpful
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josech
5.0 out of 5 stars Excellent for intermediate knowledge of chaos
Reviewed in the United States on February 5, 2002
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This book is a great entertainer for anyone who wants to spend many evenings "playing with chaos". The code in the book is a little dated (BASIC), but you won't have problems to use it as a good reference. The book will guide you through the understanding of the exciting realm of chaos and its hidden monsters.
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.
20 people found this helpful
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Derek
5.0 out of 5 stars Great book with complex topics
Reviewed in the United States on July 25, 2015
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Okay....
1. Have an understanding of math.
2. I am manic.
3. Supplementary and research may be necessary.

Great book with complex topics.

with a firm understanding in analysis, geometry, and algebra this is very enjoyable.
One person found this helpful
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S. J. Will
3.0 out of 5 stars Compare the editions
Reviewed in the United States on April 11, 2008
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I found the 1992 edition of this book at my local public library, and was (like all the other reviewers here) very impressed at the quality. The book deals with a highly technical subject, but does it in a way that you can follow even if you don't have advanced math training. The numerous color plates were also very beautiful. And to top it all off, there were "do it yourself" exercises at the end of the chapters, showing you how to program your computer to run these figures! OK, they use the old BASIC language, but still the code is clear enough that you can follow it and see what's really going on with these equations.

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.
23 people found this helpful
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Kenneth R. Bolser
5.0 out of 5 stars This book has been and is a valuable part of ...
Reviewed in the United States on August 1, 2015
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This book has been and is a valuable part of anyone's chaos theory/fractal geometry library. This book alongside The Fractal Geometry of Nature are a solid foundation, accessible and well illustrated, for the understanding of the subject. A must have!
One person found this helpful
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Ekaterina
5.0 out of 5 stars Great book
Reviewed in the United States on March 21, 2013
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The content is full and easy to understand. It is perfect reference book for the beginner, as I am. I would willingly recommend it to everybody who is interested in the subject.
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Top reviews from other countries

Samuel
5.0 out of 5 stars Very detailed
Reviewed in Belgium on July 15, 2024
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Very detailed information about chaos and fractals. Readable even if you're not an advanced mathematician.
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Hrishikesh Chatterjee
5.0 out of 5 stars Excellent book. But beware of fake copies in circulation.
Reviewed in India on September 30, 2018
Verified Purchase
As many reviewers said, the book is an excellent work. But beware of the fake books at high price in circulation. I ordered this book two times from amazon sellers but each time received fake books. The original book has 40 color illustrations out of 606 and is printed on acid free paper. In the fake copies all pictures are black and white and the paper is just ordinary.
2 people found this helpful
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Johnnie
3.0 out of 5 stars A good conversational description of the subject.
Reviewed in the United Kingdom on November 27, 2018
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This book is a combination of a detailed summary combined with a light mathematical text. I wouldnt say this is a mathematical text book where you can seriously study the topic as there are no problems to solve.

It reads well if you are looking for the conversational side of the subject.

If you are planning on really studying the topic i suggest Faulker's text.
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RAJENDRA PANT
4.0 out of 5 stars This book is very nice
Reviewed in India on March 9, 2014
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This book is very nice. Each and every thing is explained in simple word. This book is very nice. Each and every thing is explained in simple word.
One person found this helpful
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Michal Grochol
4.0 out of 5 stars Close to science
Reviewed in Germany on May 16, 2023
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This is a good book on the boundary between popular science and pure mathematics. It gives many examples and discusses many interesting topics with nice figures. It is quite accessible and thus worth reading.
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