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.
Read more about this topic: The Beauty Of Fractals
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