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The Beauty of Fractals
''The Beauty of Fractals'' is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success.
The book includes a total of 184 illustrations, including 88 full-colour pictures of Julia sets. Although the format suggests a coffee table book, the discussion of the background of the presented images addresses some sophisticated mathematics which would not be found in popular science books. In 1987 the book won an Award for distinguished technical communication.
== Summary ==
The books starts with a general introduction to Complex Dynamics, Chaos and fractals. In particular the Feigenbaum scenario and the relation to Julia sets and the Mandelbrot set is discussed. The following special sections provide in depth detail for the shown images: Verhulst Dynamics, Julia Sets and Their Computergraphical Generation, Sullivan's Classification of Critical Points, The Mandelbrot Set, External Angles and Hubbard Trees, Newton's Method for Complex Polynomials: Cayley's Problem, Newtons's Method for Real Equations, A Discrete Volterra-Lotka System, Yang-Lee Zeros, Renormalization (Magnetism and Complex Boundaries).
The book also includes invited Contributions by Benoît Mandelbrot, Adrien Douady, Gert Eilenberger and Herbert W. Franke, which provide additional formality and some historically interesting detail. Benoit Mandelbrot gives a very personal account of his discovery of fractals in general and the fractal named after him in particular. Adrien Douady explains the solved and unsolved problems relating to the almost amusingly complex Mandelbrot set.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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