Sequence Fractals Part II #2

264.jpg

z^2+c+s_i
si = a,-a,…; a = -0.75
Center: C1.00; Zoom = 0.25

Here is a look at one of the fixed points. Compare with Sequence Fractals Part I #21 for the a=-1 case.

Some named points
  2 fixed points
C1.00:   0.250000,  1.118034
C1.01:   0.250000, -1.118034
  6 two cycles
C2.00:  -0.256743,  0.498200
C2.01:  -0.256743, -0.498200
C2.02:   0.435577,  1.071747
C2.03:   0.435577, -1.071747
C2.04:   0.571165,  1.657567
C2.05:   0.571165, -1.657567
  4 1/1 preperiodic points
M1,1.00:  -0.124684,  0.236497
M1,1.01:  -0.124684, -0.236497
M1,1.02:   0.624684,  1.650711
M1,1.03:   0.624684, -1.650711

Cn.xx are cycles (periodic) of period n. C1 are fixed points. Mm,n.xx are Misiurewicz (preperiodic) points with pre-period m and period n. Actually this is parameter space (pixel=c) and periodicity happens in dynamic space (pixel=z). So to be technically correct I should say the critical point, 0, is (pre)periodic for the parameter Cn or Mm,n. On the other hand, the anti-technical definition is interesting stuff happens here. The points in the same group are numbered left-to-right (increasing real part) then top to bottom (decreasing imaginary part).

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