The Mandelbrot set renormalization
It is evident, that one can apply discussed above "linear" theory to
the midgets on complex plane. You see below the period-3 Mandelbrot midget
located at c3 = -1.7542 . It is
βΛ32 = 52.5334 times smaller then
the main M-set. J(0), Rabbit,
Cauliflower (and all the rest Julia) midgets shrink
Λ3 = -9.29887 times and are
"placed " in the usual typical points (c3, r, c) of the
M3 midget.
The M4 midget scaling
For the biggest period-4 M-midget
Λ4 = -10.55 - 5.448i,
β = 0.7889 - 0.2754i and
m = β Λ42
= 96.14 + 68.23i. So this copy is reduced |m| = 117.88 times
and rotated by Arg(m) = 35.36o.
Contents
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updated 14 Sep 2013
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