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Julia Sets and the Mandelbrot Set

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The Beauty of Fractals

Abstract

Quadratic Julia sets, and the Mandelbrot set, arise in a mathematical situation which is extremely simple, namely from sequences of complex numbers defined inductively by the relation

$$z_n + = z_n^2 + c,$$

where c is a complex constant. I must say that, in 1980, whenever I told my friends that I was just starting with J.H. Hubbard a study of polynomials of degree 2 in one complex variable (and more specifically those of the form z↦z2+c). they would all stare at me and ask: Do you expect to find anything new? It is, however, this simple family of polynomials which is responsible for producing these objects which are so complicated — not chaotic, but on the contrary, rigorously organized according to sophisticated combinatorial laws.

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© 1986 Springer-Verlag Berlin Heidelberg

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Douady, A. (1986). Julia Sets and the Mandelbrot Set. In: The Beauty of Fractals. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61717-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-61717-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-61719-5

  • Online ISBN: 978-3-642-61717-1

  • eBook Packages: Springer Book Archive

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