Julia Sets and the Mandelbrot Set

Adrien Douady

A chapter in The Beauty of Fractals, 1986, pp 161-174 from Springer

Abstract: 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.

Keywords: Branch Point; Escape Time; External Argument; Remarkable Point; Small Copy (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-3-642-61717-1_13

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