Multiple renormalization. Shaggy midgets

In the vicinity of the M3 midget the map fco3 is renormalizable, therefore for c = A, B, C you see "Cauliflower" J(0.35) midgets at z = 0.
Moreover for c = A the map fAo23 is renormalizable too, therefore we see the tiny black circle of the J(0) midget in the left picture and cardioid of the M23 midget on the parameter plane. Note, that filaments are similar. They have   zn = Λ3 zn+12 scaling and 2k-fold symmetry. Small filaments shrink 2 times every new generation.

At last the point B lies in one more M23 midget and the J(C) set below is pure Cantor dust.

You can find your own examples by the "Renormalization" trips applet.

Note, that global dendrite-like structure of J(A) is determined by the fc map (compare e.g. J(-1.54369) set).

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updated 31 May 2003