Sequence Fractals Part V #17

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z^{2^{s_i}}+c
s0=1.0, si+1=(0.6+0.8i)*si
Center: 0+0i; Zoom = 0.004

The start of this series Sequence Fractals Part V #1 was actually the third starting point I considered. Here is the second candidate. The stacked exponents seemed like a natural place to add an exponent to the traditional z2+c. After queuing up a few, I decided that z^{s_i}+c was a simpler place to start.

While no longer the starting point, these are still part of the story. The most noticeable traits are shared by the different placement of the exponent. In fact given the sequence si, we could create a new sequence ri = 2^{s_i}, and then use the previous formula, z^{r_i}+c. Like I said, I did not think about these things when I started.

One of the favorite sequences, where si jumps around the unit circle is back. There is a large area of interest. This image is zoomed way out. The horizontal range is -250,250.

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