parameter rays of root points
of components of family F(1/2)
internal angle of main cardioid = 1/2
Periods of the form: 2 n where n is natural number:
infinity ... , 32, 16, 8, 4, 2 , 1
Pair of external angles = (1/3, 2/3) landing on the point c1= - 3/4 = - 0.75, which is root point of period 2 component
with center c=-1 and radius = 1/4 ... and ...
Pair of external angles = (6/15 = 2/5, 9/15) landing on the point c2= -5/4 = -1.25 , which is root point of period 4 component
with center c=-1.3107 and radius = ... and ...
Pair of external angles = (7/17=105/255,150/255) landing on the point c3 = -1.3680989394 ..., which is root point of period 8 component
cn = the point of attachment of the 2n-cycle and 2n-1-cycle components in the period-doubling cascade = root point of 2n period component:
period 2 : c1 = -0.75
period 4 : c2 = -1.25
period 8 : c3 = -1.3680989394 ...
period 16 : c4 = -1.3940461566 ...
period 32 : c5 = -1.3996312389 ...
period 64 : c6 = -1.4008287424 ...
period 128 : c7 = -1.4010852713 ...
period 256 : c8 = -1.401140214699 ...
period 512 : c9 = -1.401151982029 ...
period 1024 : c10 = -1.401154502237 ...
...
Feigenbaum-Myrberg point = -1.4011551890 ... with pair of external rays (5/12 , 7/12)=(
upper external angles of roots are:
angle(c1)=0.(01)...2=1/3
angle(c2)=0.(0110)...2=6/15
angle(c3)=0.(01101001)...2=7/17
angle(c4)=0.(0110100110010110)...2=106/257
...
Morse-Thue Number
Finch, Steven R. :Mathematical constants / Steven R. Finch. Published/Created: New York : Cambridge University Press, 2003.
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