Titlebook: Chaos and Fractals; New Frontiers of Sci Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Textbook 19921st edition Springer-Verlag New York

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Irregular Shapes: Randomness in Fractal Constructions, that a maximum amount of oxygen can be assimilated. Although the self-similarity in these objects is not strict, we can identify the building blocks of the structure — the branches at different levels.

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The Mandelbrot Set: Ordering the Julia Sets,of pictures which can develop on a computer screen. Sometimes many hours are required for their generation; but this is the price you have to pay for the adventure of finding something new and fantastic where nobody has looked before.

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Classical Fractals and Self-Similarity,is a bit overemphasized. Indeed, many of the early fractals arose in the attempt to fully explore the mathematical content and limits of fundamental notions (e.g. ‘continuous’ or ‘curve’). The Cantor set, the Sierpinski carpet and the Menger sponge stand out in particular because of their deep roots

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Limits and Self-Similarity,approach. From this point of view, it is ironic that some of the constructions which Cantor, Hilbert, Sierpinski and others created to perfect their extremely abstract foundations simultaneously hold the clues to understanding the patterns of nature in a visual sense. The Cantor set, Hilbert curve,

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Encoding Images by Simple Transformations,theory, and this chapter is devoted to it. It goes back to Mandelbrot’s book, ., and a beautiful paper by the Australian mathematician Hutchinson.. Barnsley and Berger have extended these ideas and advocated the point of view that they are very promising for the encoding of images.. In fact, this wi