sexp for base (1/e)^e ~= 0.0660?

[sheldonison]

....
The superfunction generated from the "lower" fixed point looks like this:

(scale is from -10 to +10 on both axes).

So I'd guess that it should look like that in the lower half-plane.

Not sure what to do about the upper half-plane, though.

Ok, here's a shot at the upper half of the complex plane, based on what I computed yesterday, generated from an 11 "multi-term" approximation, \( \exp(11 \pi i z) \). It is pretty clear that one could probably stitch these two functions together, this upper function, and the lower function you generated from the L=-0.196+1.691i fixed point; by choosing the logarithmic branch to be to the left of the first singularity, seen near -1.99+0.23i. From the left of the singularity, there is a common path between the two functions. The scale here is 2x the scale of your plot, from -5 to +5 on the real axis, and from 0 to 2 on the imaginary axis.
- Sheldon
   
EDIT: Here is the upper fixed point function from -4 to +2, at 0.15i which is just under the logarithmic singularity branch, where the singularity at approx -1.99+0.23i. If the logarithm branch is chosen correctly, there is a very clear path to the left, going to the secondary fixed point, of -0.196+1.691i.
- Sheldon