File:Part of parameter plane with Mandelbrot set and bifurcation point 13 over 34 of the main cardioid.png
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Summary[edit]
DescriptionPart of parameter plane with Mandelbrot set and bifurcation point 13 over 34 of the main cardioid.png |
English: Part of parameter plane with Mandelbrot set and bifurcation point 13 over 34 of the main cardioid |
Date | |
Source | Made with c program[1] by Claude Heiland-Allen[2] |
Author | Adam majewski |
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Summary[edit]
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]
References[edit]
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