Sequence Fractals Part I #26

z²+c+s_i
s_i = -1, 1, -1, 1, …
Center:C3.00 -0.028857, 0.822581, Zoom = 100

C3.00 can be found in the upper left corner of the C2.00 picture Sequence Fractals Part I #22

Three cycles can be found by solving f(f(f(0,c),c),c) = 0. The degree 32 polynomial equation gives 32 roots, then take away the two fixed points, leaving 30 three cycles

  30 three cycles
C3.00:  -0.028857,  0.822581
C3.01:  -0.028857, -0.822581
C3.02:   0.000323,  0.777540
C3.03:   0.000323, -0.777540
C3.04:   0.123345,  0.786543
C3.05:   0.123345, -0.786543
C3.06:   0.123768,  0.684849
C3.07:   0.123768, -0.684849
C3.08:   0.256240,  1.261825
C3.09:   0.256240, -1.261825
C3.10:   0.456809,  1.544145
C3.11:   0.456809, -1.544145
C3.12:   0.475692,  1.211907
C3.13:   0.475692, -1.211907
C3.14:   0.543537,  1.408400
C3.15:   0.543537, -1.408400
C3.16:   0.729946,  1.274941
C3.17:   0.729946, -1.274941
C3.18:   0.731182,  1.053796
C3.19:   0.731182, -1.053796
C3.20:   0.774380,  1.836743
C3.21:   0.774380, -1.836743
C3.22:   0.802629,  1.829248
C3.23:   0.802629, -1.829248
C3.24:   0.827269,  1.802481
C3.25:   0.827269, -1.802481
C3.26:   0.828125,  1.397028
C3.27:   0.828125, -1.397028
C3.28:   0.855612,  1.812967
C3.29:   0.855612, -1.812967