Sequence Fractals Part II #24

$ z^2+c+s_i$
s_i = a,-a,…; a = -0.715
Center: -0.16,0; Zoom = 2.5

Bump the a value by another 0.001. Center is midway between two M1,1 points. Holy Chaos Batman! Is that a Bat-brot?

Named Points for a=(-0.715000, 0.000000)
  2 fixed points
C1.00:   0.215000,  1.086278
C1.01:   0.215000, -1.086278
  6 two cycles
C2.00:  -0.303783,  0.450626
C2.01:  -0.303783, -0.450626
C2.02:   0.411487,  1.038380
C2.03:   0.411487, -1.038380
C2.04:   0.537296,  1.634112
C2.05:   0.537296, -1.634112
  4 1/1 preperiodic points
M1,1.00:  -0.205637,  0.000000
M1,1.01:  -0.119427,  0.000000
M1,1.02:   0.592533,  1.626936
M1,1.03:   0.592533, -1.626936

M1,1.00 and M1,1.01 are again the left and right tips along the centerline. The view from the other critical point is very similar to the a = -0.716 case, Sequence Fractals Part II #22. (So I am not going to waste a post on it.) M1,1.00 is very close to the center of the period 2 bulb. M1,1.01 has crossed over into the main cardioid. That accounts for the thin slice missing just left of M1,1.01.

It would be interesting to look at the picture for the a values where M1,1.00 (this critical point) = C2.0x (2-bulb center, other critical point), and when M1,1.01 (this) = 2-bulb, main cardioid bifurcation (join) point. Also from a few posts ago, the a value where M1,1.00 = M1,1.01 would be interesting. I need to add some software to calculate these collisions, but I am also trying to keep up a post-a-day pace. This is just one more thing in a long list of things I would do differently if things were different. I will save the whining for later.