eta as branchpoint of tetrational

[sheldonison]

Now I was able to generate the graph! Yessss!!!!
....
The scale is -40 to +40 (WOW!) on both axes. Zero is in the center.

Wow. It is soooo close to the attracting regular iteration on the real line... I could see why the regular seems so good now as an extension of tetration, and why it seems like it would create an "analytic" tetrational in the base when concatenated with the Kneser iteration at \( b > \eta \). The singularity/branch point of tetration at base \( \eta \) must be incredibly mild. Weeeeeeeeeeerd -- tetration seems once again to be the weirdest complex function I've ever seen.

Looks great! Thanks for making the graph. I'm not sure I understand all of your comments though... regular tetration at a base>eta would be a complex superfunction, with no real valued real axis, right?
- Sheldon