Is bugs or features for fatou.gp super-logarithm?

[sheldonison]

Thank you.
by the why, how can I get the photo like this?  https://math.eretrandre.org/tetrationfor...p?aid=1311
i need some code.

Its a combination of an excel spreadsheet; uniquecharts.xls download and the circchart function I recently added to fatou_experiment 
  fatou_experiment.gp (Size: 74.91 KB / Downloads: 934) (also other cleanup and updates).  I think I'm ready to update the main fatou.gp link.  Also, I understand the singularities in the theta mapping for bases like B=0.1, and why so many sample points are needed for theta mapping (more later).  Also, I understand why there is a difficult programming problem where the slog(B=0.1) converges beautifully within a circle connecting the fixed points, but even with the theta mapping, there are points outside the circle where the computation of the Schroder function leads to the slog being misbehaved even though the slog is accurate everywhere else.  Obviously, this effects the sexp as well, since it is the inverse.   More later, time is very limited right now.
B=0.1+I*E-30; matrix_ir(B,300,300,14/15,24/25);
plot of slog between fixed points; l=0.399012978260252; l2=-0.301845266020991+1.98089260122376*I;
The two misbehaving slivers are when the algorithm for determining which branch of the logarithm of Psi is broken; but this is a very difficult programming problem and my solution works except for these Tetration bases on the real axis near the origin.
\( \frac{\ln(\Psi)}{\ln(\lambda)}+\theta\left(\frac{\ln(\Psi)}{\ln(\lambda)}\right) \)