basic renormalization example

Hi,

I have a basic question about renormalization within the logistic map.
I want to understand a practical quantitative example whereby I start
with a vertical slice, or parameter value, say 3.525, and then zoom in
to a subdomain, or mini 'child' bifurcation diagram, lets say in the
top of the period 3 window.  From there, how do I find the
'associated' slice (parameter) in this subdomain diagram that it is
directly
related, or self similar to, the parameter in the 'parent' diagram ?
Can anyone walk me through the equation *step by step* to determine
this parameter
value ?  I believe this is renormalization, but need to have a
mathematician show me by example. Best email is klaus_berg95 at yahoo
(trying to avoid spam)
 
Thanks !
 
Klaus