Sequence Fractals Part II #11

273.jpg

z^2+c+s_i
si = a,-a,…; a = -0.718
Center: M1,1.00; Zoom = 120

M1,1.00 again with another small increase in the parameter a to -0.718.

Named Points:
  2 fixed points
C1.00:   0.218000,  1.089036
C1.01:   0.218000, -1.089036
  6 two cycles
C2.00:  -0.299701,  0.454817
C2.01:  -0.299701, -0.454817
C2.02:   0.413502,  1.041271
C2.03:   0.413502, -1.041271
C2.04:   0.540199,  1.636137
C2.05:   0.540199, -1.636137
  4 1/1 preperiodic points
M1,1.00:  -0.159284,  0.055500
M1,1.01:  -0.159284, -0.055500
M1,1.02:   0.595284,  1.628989
M1,1.03:   0.595284, -1.628989

Whoa! What happened? The Misiurewicz point itself still escapes, but many of the nearby points are captured (white). Up until now, the M points all have baby Mandelbrot sets nearby which capture orbits. But they are small, and usually invisible without high magnification. Here, the white space is huge and looks nothing like the Mandelbot set.

The informal answer is that we are seeing interference from the other critical points.

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