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Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
2
votes
Is there a way to find regions of depth in the Mandelbrot set other than simply poking around?
Chaos and Fractals: New Frontiers of Science, by
Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe
Chapter 14
24
votes
Accepted
Parametrization of the boundary of the Mandelbrot set
Lasse's answer expanded: Let $\psi$ be the map of the exterior of the unit disk onto the exterior of the Mandelbrot set, with Laurent series
$$
\psi(w) = w + \sum_{n=0}^\infty b_n w^{-n} =
w - \frac{1 …