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The Mandelbrot set, the Farey tree, and the Fibonacci sequence. (English) Zbl 1076.37512
Summary: In this paper we discuss several folk theorems involving the Mandelbrot set. Each of these theorems concerns the size of the bulbs or decorations attached to the Mandelbrot set. One may recognize the $p/q$ bulbs from the geometry of their antennas. Moreover, the size of these bulbs is determined by the Farey tree. These results are proved using the theory of external rays of Douady and Hubbard, so we also give an explanation of their results.
MSC:
 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations 28A80 Fractals