M-set and Farey sequence


From Farey sequence to M-set:
Sources ( delphi programs):
Images:
  1. Ford circles


  2. "Mandelbrot" circles ( = circles on circle)

    Compare this image with that on Robert L. Devaney's page about Rotation Numbers and Internal angles of the Mandelbrot bulbs . Do you see the similarity?
    radius of secondary components ~= (S/2)* sin(Pi * p / q) / (q*q)
    Where S is a diameter (= 2 * radius) of main circle

  3. Theoretical Mandelbrot set ( = circles on cardioid) - (in future )
    radius ~= S * sin(Pi * p / q) / (q*q) for children of cardioid
    where p/q is the internal angle of the child
    and S is the size of the parent, measured (roughly) from its cusp to the bond point with its 1/2 child.
    It is topological model of Mandelbrot set

Bibliography:

Main page


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Author: Adam Majewski adammaj1-at-o2-dot-pl

http://republika.pl/fraktal/


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