To get an even better look.
I circled about where the singularities are, but they cause a lightning bolt fractal in about the sea.
Actually the sea of green (purple), means the function \(\beta\) is very large, and therefore iterated \(\log_{\eta_-}\) just takes us to the fixed point faster.
What's remarkable is the branch cut is parallel to \(\mathbb{R}\). And that there's no mixing in the green/purple sea. This means \(\Im(z) \to \pm \infty\) should behave just as we like when we grow the candy strip. It looks like a weird kind of Kneser.
ALSO, try to remember this is all the \(2 \pi i\) periodic solution. You can make \(Ti\) periodic solutions; let \(T\to\infty\) and it looks just like the Abel solution.
I circled about where the singularities are, but they cause a lightning bolt fractal in about the sea.
Actually the sea of green (purple), means the function \(\beta\) is very large, and therefore iterated \(\log_{\eta_-}\) just takes us to the fixed point faster.
What's remarkable is the branch cut is parallel to \(\mathbb{R}\). And that there's no mixing in the green/purple sea. This means \(\Im(z) \to \pm \infty\) should behave just as we like when we grow the candy strip. It looks like a weird kind of Kneser.
ALSO, try to remember this is all the \(2 \pi i\) periodic solution. You can make \(Ti\) periodic solutions; let \(T\to\infty\) and it looks just like the Abel solution.
