Summary

Summary

This is numerical aproximation of rectangle part of parameter plane of complex quadratic map

Parameter plane is described using center and radius method^[2] :

center = -3.912868105763494e-01 5.8750703531203696e-01
radius = 2.2435841847477573e-03

One can see 2 external rays :

0.(01001010010010100101001001010010010100101001001010010100100101001001010010100100101001001)
0.(01001010010010100101001001010010010100101001001010010100100101001001010010100100101001010)

that land on the root point :

 c_root = 

of period 89 hyperbolic comonent of the Mandelbrot set, which is located at internal angle :

t = 34/89

on the boundary of main cardioid.

Here is the parameter for book program by Claude Heiland-Allen^[3]

size 1500 1500
view 53 -3.912868105763494e-01 5.8750703531203696e-01 2.2435841847477573e-03
text 53 -3.8850679170464886e-01 5.8778690906453801e-01 29/76
text 53 -3.9295862805848958e-01 5.8654640828551075e-01 34
text 53 -3.9083735476121173e-01 5.8664152432163741e-01 34/89
text 53 -3.8976432105791259e-01 5.8717038285268242e-01 21/55
text 53 -3.9257154847615527e-01 5.8578136589703722e-01 13/34
text 53 -3.8520845931151926e-01 5.8938731818075474e-01 8/21
text 53 -4.3871964861536816e-01 5.6031499408360719e-01 9/23
text 53 -4.2643426597622142e-01 5.6759574309632177e-01 7/18
text 53 -4.0438954414938139e-01 5.7973854764491106e-01 5/13
text 53 -4.8176274578121048e-01 5.3165675522002509e-01 2/5
text 53 -3.5355339059327368e-01 6.0355339059327373e-01 3/8
ray_in 2200 .(01001010010010100101001001010010010100101001001010010100100101001001010010100100101001001)
ray_in 2200 .(01001010010010100101001001010010010100101001001010010100100101001001010010100100101001010)
text 53 -3.9354903235723721e-01 5.8765202602839439e-01 68
text 53 -3.8990710427221476e-01 5.8746623453007119e-01 55

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References

1. ↑ book program by Claude Heiland-Allen
2. ↑ wikibooks : radius and plane
3. ↑ book program by Claude Heiland-Allen