The Decoration Theorem for Mandelbrot and Multibrot Sets
The Decoration Theorem for Mandelbrot and Multibrot Sets
We prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a “little Mandelbrot set” is removed from the Mandelbrot set, then most of the resulting connected components have small diameters. By universality of the Mandelbrot set similar results hold for quadratic-like families.