Sequence Fractals Part I #29

z²+c+s_i
s_i = -1, 1, -1, 1, …
C3.02: 0.000323, 0.777540, Zoom = 5000

C3.02 with 50x zoom, 2x color

I am not going to show all three-cycle hosts. They all look similar. They are found in an interesting pattern. Three are connected to C1.00 in the usual Mandelbrot way, top and bottom bulbs, and largest mini off the period 2 bulb. Each of lower cycle hosts, C1.00, C2.00, and C2.04 are surrounded by four satellite three cycles.

 15 +i half plane 3 cycles
C1.00:   0.500000,  1.322876  - connected   Sequence Fractals Part I #21
 C3.12:   0.475692,  1.211907 
 C3.14:   0.543537,  1.408400
 C3.16:   0.729946,  1.274941
C1.00:   0.500000,  1.322876  - satellites  Sequence Fractals Part I #21
 C3.08:   0.256240,  1.261825
 C3.10:   0.456809,  1.544145 
 C3.18:   0.731182,  1.053796 
 C3.26:   0.828125,  1.397028 
C2.00:   0.053427,  0.781326  - satellites  Sequence Fractals Part I #22
 C3.00:  -0.028857,  0.822581 
 C3.02:   0.000323,  0.777540
 C3.04:   0.123345,  0.786543 
 C3.06:   0.123768,  0.684849
C2.04:   0.813477,  1.815442  - satellites  Sequence Fractals Part I #24
 C3.20:   0.774380,  1.836743
 C3.22:   0.802629,  1.829248 
 C3.24:   0.827269,  1.802481 
 C3.28:   0.855612,  1.812967