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 2 k-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).
Previous: Renormalization on complex plane
Next: Renormalization of inverse maps
updated 14 Sep 2013