Sequence Fractals Part V #28


s1=1, si+1=(0.9+0.1i)*si (repeat after 22 steps).
Center:-0.2-0.2i; Zoom = 0.25

Now let’s switch to non-real exponents. Back in Sequence Fractals Part V #19, I said that if either the real or imaginary part of w is irrational, then zw has infinitely many values. Actually zw has infinitely many values if the angle is irrational (as in today’s formula). I suspect this is also true anytime the imaginary part of w is non-zero. (But I am too lazy to verify that right now.) So today’s equation is one of those where at each step we pick out one of an infinite number of choices for the exponentiation.

I do not wake up each morning, create a picture, write these words and make a blog post. That is only an illusion I create by scheduling the posts to come out at midnight each day. The next few pictures where created very early during the sequence fractal series. This one was created back in May. I am writing these words just a few days (about a week) before publishing the post.

I spent the last few months on the polynomial (positive integer exponent) variations. I put together a rough draft for this non-integer exponent set during that time. Of course I threw out the rough draft and have just been winging it.

Why do I bother to mention this? At the time I created these I was still trying to figure out and demonstrate some mathematical truth in the formula. So my mindset today is substantially different now than it was when I made the picture.

Still, it is part of the story, they take a long time to render, and I do not want to waste it.

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