Sequence Fractals Part I #4


si = 1, -1, 1, -1, …
Center:-3.604665+0i , Zoom = 1024

Here is a zoom into the dark spot on the left side of Sequence Fractals Part I #3.

Recall from Sequence Fractals Part I #1 the two-step iteration formula, f(z,c) = (z^2+c+1)^2+c-1. Call the center of this image cthis = -3.604665+0i. Then f(f(0,cthis),cthis) = 0. I may (will definitely) get sloppy at times and say that cthis is a 2-cycle. But these are parameter space (c) pictures. z is the variable that is iterated and it is the z orbit has properties like convergence, divergence and being a two cycle. Not the parameter c. I should say that the z0=0 orbit with the parameter value c = cthis, is a two cycle. Or maybe that c hosts a two-cycle.

But that is too much of a mouthful, so I will from time to time use the technically incorrect expression. And as long as I am being technical, this is a two-cycle of the two-step function. So it is a four-cycle of the original sequence fractal definition.

And as long as I am dwelling in the minutiae… I have been trying to use the same palette for this set of pictures. The previous palette version of this picture was too dark in the area around the mini. I doubled the color entropy (colors change twice as rapidly) to expose more detail.

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