Sequence Fractals Part I #18

$ z^2+c+s_i$
s_i = 1, -1, 1, -1, …
Center:--3.051388+0.210786i , Zoom = 10000

For orientation, this center of this picture is up and to the right of Sequence Fractals Part I #12. Using the same notation, as Sequence Fractals Part I #16, $ z_3=z_1\ and\ z_2\neq z_0$ so for this c, the critical point orbit is preperiodic with pre-period 1 and period 2.

In general if z_n+k=z_k and n,k are the smallest values for which this is true, then the orbit is preperiodic with pre-period k, period n, and denoted M_k,n. Such points should be called Misiurewicz points. See https://en.wikipedia.org/wiki/Misiurewicz_point

The wiki article says that it is not a Misiurewicz point unless you are looking at a polynomial conjugate to z^d+c for d >=2. If you are not familiar with the term 'conjugate', it is a particular, precise mathematical concept for a type of "similar to". The key property is that there is only one critical point. Our polynomial has three critical points. (We have been ignoring the other two.) I have been careful to avoid calling something a Mandelbrot set that is not a Mandelbrot set. So I will also avoid calling these Misiurewicz points. However I will stick with the M_ notation.