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Julia Sets and the Mandelbrot Set

In: The Beauty of Fractals

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  • Adrien Douady

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.

Suggested Citation

  • Adrien Douady, 1986. "Julia Sets and the Mandelbrot Set," Springer Books, in: The Beauty of Fractals, pages 161-174, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-61717-1_13
    DOI: 10.1007/978-3-642-61717-1_13
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