Sequence Fractals Part I #11

238.jpg

z^2+c+s_i
si = 1, -1, 1, -1, …
Center:-3.630601+0.i , Zoom = 400000

Grab the electron microscope and crank up the zoom into the center of Sequence Fractals Part I #10. There is the mini brot that hosts a three-cycle.

Here is a list of the thirty c values that host three-cycles.


3.00:  -3.630601,  0.000000
3.01:  -3.613512,  0.000000
3.02:  -3.595016,  0.000000
3.03:  -3.568618,  0.000000
3.04:  -3.272072,  0.000000
3.05:  -3.136341,  0.000000
3.06:  -3.053155,  0.209961
3.07:  -3.053155, -0.209961
3.08:  -3.012519,  0.060576
3.09:  -3.012519, -0.060576
3.10:  -2.768406,  0.000000
3.11:  -2.308309,  0.000000
3.12:  -2.216607,  0.033713
3.13:  -2.216607, -0.033713
3.14:  -2.147552,  0.000000
3.15:  -0.324744,  0.181271
3.16:  -0.324744, -0.181271
3.17:  -0.320181,  0.000000
3.18:  -0.024650,  0.495512
3.19:  -0.024650, -0.495512
3.20:  -0.006748,  0.135925
3.21:  -0.006748, -0.135925
3.22:  -0.004470,  0.435048
3.23:  -0.004470, -0.435048
3.24:   0.072243,  0.489918
3.25:   0.072243, -0.489918
3.26:   0.104301,  0.479303
3.27:   0.104301, -0.479303
3.28:   0.146654,  0.152514
3.29:   0.146654, -0.152514

Several are on the real axis, they can be found by looking at the other axis-specks in Sequence Fractals Part I #1, they all look similar to today’s picture. 3.22 and 3.23 are found in Sequence Fractals Part I #8. In the Mandelbrot set, the largest real-axis mini, and the top and bottom bulbs host three-cycles. 3.05, 3.08, 3.09, are attached to c=-3, and 3.17 3.20. 3.21 to c=0 in the same way.

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