The Mandelbrot Set and Julia Sets

Combinatorics in the Mandelbrot Set - Discs on Discs and Cardioids

For the discs attached around any n-cycle component, the principal series and Farey sequence rules apply, but multiplied by the cycle number n of the component.

For example, the discs attached to a 3-cycle disc follow the principal series, but multiplied by 3:

we see a 6 (= 3⋅2) -cycle disc, and on each side a sequence of 9 (= 3⋅3), 12 (= 3⋅4), ... discs

the Farey sequence fills in the rest of the discs.

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