# 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 *c*_{3} = -1.7542 . It is
*βΛ*_{3}^{2} = 52.5334 times smaller then
the main M-set. *J(0)*, Rabbit,
Cauliflower (and all the rest Julia) midgets shrink
*Λ*_{3} = -9.29887 times and are
"placed " in the usual typical points *(c*_{3}, r, c) of the
*M*_{3} midget.
## The *M*_{4} midget scaling

For the biggest period-*4* M-midget
*Λ*_{4} = -10.55 - 5.448i,
β = 0.7889 - 0.2754i and
*m = β Λ*_{4}^{2}
= 96.14 + 68.23i. So this copy is reduced *|m| = 117.88* times
and rotated by *Arg(m) = 35.36*^{o}.

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*updated* 14 Sep 2013