Sequence Fractals Part IV #5


si = -1.27i, 1, (repeating)
Center:1.0+0.0i , Zoom = 0.5

I have to confess that I am undecided on where to go next. The ‘*si‘ and ‘+si‘ cases are different. These deserve the full treatment as the +si case in Part I and Part II. That includes looking at the Julia sets. Finding Cycles and Misiurewicz points. Exploring how the C and M points move around as the sequence changes. Look at pictures of the other critical points. (These all start at 0 which is always a critical point, the other critical points depend on c and move around. That means extra programming for me.)

On the other hand, both of these classes, ‘*si‘ and ‘+si‘ are part of the universe of slices of the connectivity locus of quartic polynomials. In some sense these two classes are two parts of some much larger whole. I want to avoid “been there, done that”.

To be clear, there are an infinite number of genuinely unique ways to parameterize the space of quartic polynomials. And in each of them, there are an infinite number of genuinely unique 2D cross sections, or slices. And any one of those infinite times infinite number of slices can be selected to explore with pan and zoom.

Contrast this the quadratic case. There are only a small number (afaik) of useful parameterizations, z2+c being ubiquitous. There, the whole universe exists in a single 2 dimensional slice of the parameter space, which we explore with pan and zoom.

To be continued.

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