Chaos and Fractals: New Frontiers of Science / Edition 2

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For almost 15 years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse. Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience. The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair Automata, L- systems, Percolation and Strange Attractors. Each chapter is closed by a "Program of the Chapter" which provides computer code for a central experiment. Two appendices complement the book. The first, by Yuval Fisher, discusses the details and ideas of fractal images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals.

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Editorial Reviews

From the Publisher

From the reviews:

"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

From the reviews of the second edition:

"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)

"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)

"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)

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Product Details

  • ISBN-13: 9780387202297
  • Publisher: Springer New York
  • Publication date: 2/3/2004
  • Edition description: 2nd ed. 2004
  • Edition number: 2
  • Pages: 864
  • Product dimensions: 7.48 (w) x 9.42 (h) x 1.88 (d)

Table of Contents

Causality Principle, Deterministic Laws and Chaos.- The Backbone of Fractals: Feedback and the Iterator.- Classical Fractals and Self-Similarity.- Lim and Self-Similarity.- Length, Area and Dimension: Measuring Complexity and Scaling Properties.- Encoding Images by Simple Transformations.- The Chaos Game: How Randomness Creates Deterministic Shapes.- Recursive Structures: Growing Fractals and Plants.- Pascal’s Triangle: Cellular Automata and Attractors.- Irregular Shapes: Randomness in Fractal Constructions.- Deterministic Chaos: Sensitivity, Mixing, and Periodic Points.- Order and Chaos: Period-Doubling and Its Chaotic Mirror.- Strange Attractors: The Locus of Chaos.- Julia Sets: Fractal Basin Boundaries.- The Mandelbrot Set: Ordering the Julia Sets.

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