Sequence Fractals Part I #21

$ z^2+c+s_i$
s_i = -1, 1, -1, 1, …
Center: C1.00: 0.500000, 1.322876, Zoom = 0.8

The helper functions will be redefined for the new sequence. (Notice the sign flip in key places.)
f₀(z,c) = z²+c-1
f₁(z,c) = z²+c+1
f_c(z) = f(z,c) =f₁(f₀(z,c),c) = (z²+c-1)²+c+1.
Derivative: f_c'(z) = 4z(z²+c-1)

z₀ = 0 is a critical point and will again be the default starting point. The other two critical points will be ignored without guilt. They just bring us back to the sequence starting 1,-1…, about which we already know more than we ever wanted to know.

Fixed points are found when f(0,c) = 0. so c = $ \frac{1\pm\sqrt{-7}}{2}$ = 0.5 ± 1.322876i.

  2 fixed points
C1.00:   0.500000,  1.322876
C1.01:   0.500000, -1.322876

I will start naming named points with a leading letter to avoid confusion with decimal numbers.