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Summary

Wake description from program mandel by Wolf Jung ^[3]

The 13/34-wake of the main cardioid is
bounded by the parameter rays with the angles
4985538889/17179869183  or  p0100101001001010010100100101001001  and
4985538890/17179869183  or  p0100101001001010010100100101001010 .

Description from c program by Claude Heiland-Allen :

size 2000 1000
view 53 -3.9779999999999999e-01 6.0011999999999999e-01 3.2219999999999999e-02
text 53 -3.3460905637386334e-01 6.1188130370078908e-01 35
text 53 -3.4395855571008077e-01 6.2268185910744822e-01 32
text 53 -3.4793225333528743e-01 6.3024435047427696e-01 24
text 53 -3.7108040918324769e-01 6.0681605883234302e-01 40
text 53 -3.742346321012836e-01 6.1083553327767892e-01 32
text 53 -4.1773852818981538e-01 5.7370954029709309e-01 31
text 53 -4.0316183833437114e-01 5.9057925786163157e-01 39
text 53 -4.3038457464894059e-01 5.7377316006462575e-01 36
text 53 -3.7647222500415917e-01 6.195630622765923e-01 24
text 53 -3.770035472428892e-01 5.9455169662530905e-01 29
text 53 -3.874535540084551e-01 5.9433580156203969e-01 42
text 53 -3.8616041628013742e-01 5.9140448639552934e-01 21
text 53 -4.2799979986113362e-01 5.7020940230437278e-01 18
text 53 -4.11007350363918e-01 5.9193673437522698e-01 26
text 53 -3.5910239011244915e-01 6.1735345339882686e-01 8
text 53 -3.9295862805848958e-01 5.8654640828551075e-01 34
text 53 -4.0710408308509832e-01 5.8485284286810224e-01 13
text 53 -3.8520845931151926e-01 5.8938731818075474e-01 8/21
text 53 -4.0438954414938139e-01 5.7973854764491106e-01 5/13
text 53 -3.5355339059327368e-01 6.0355339059327373e-01 3/8
text 53 -3.9257154847615527e-01 5.8578136589703722e-01 13/34
ray_in 1000 .(0100101001001010010100100101001010)
ray_in 1000 .(0100101001001010010100100101001001)

Find :

• internal angle 13/13 of main cardioid
• landing point of above ray = bifurcation point = root point of component with period 34
• pair of external rays landin on the root point

Root point :

 c = -0.392571548476155  +0.585781365897037 i  

Angles of the wake external rays different formats :^[4]

${\displaystyle 4985538889/17179869183={\frac {4985538889_{10}}{17179869183_{10}}}=p0100101001001010010100100101001001=.(0100101001001010010100100101001001)=0.(0100101001001010010100100101001001)=0.{\overline {0100101001001010010100100101001001}}_{2}={\frac {100101001001010010100100101001001_{2}}{1111111111111111111111111111111111_{2}}}}$

${\displaystyle 4985538890/17179869183=p0100101001001010010100100101001010=.(0100101001001010010100100101001010)=0.(0100101001001010010100100101001010)}$

References

1. ↑ c program by Claude Heiland-Allen
2. ↑ Claude Heiland-Allen - blog
3. ↑ program mandel by Wolf Jung
4. ↑ knowledgedoor calculators: convert_a_ratio_of_integers