Chaos and Fractals: New Frontiers of Science

ISBN-13: 9781468493962 / Angielski / Miękka / 2012 / 864 str.

Heinz-Otto Peitgen; Hartmut Jurgens; Dietmar Saupe

Opis

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, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focussed computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.

Recenzje

"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

Spis treści

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.