Fractal behavior of tetration

[Kouznetsov]

tetration fractal

Dear Bo:
1. Thank you for the link, beautigul pics. However, those pics do not correspond to tetration or superexponential, althouch, they are related to the reiterated exponential.
As I understand, in our notations, they correspond to the play with base b.
In my case, b=e is fixed.
Formally, my set F is periodic, while the structures you refer are not.
Perhaps, the pics you mention should be cited. How is it better to cite those pics?

2. I have the expression for the set of branchpoints of the modified slog, while the primary cutlines go to the right hand side direction. The formula is:
\( S \subset \{L,L^*\} \)
\( S=S \cup \{ \log(z)+2\pi \mathrm{i} m,~ z\in S,~ m\in \mathbb{N}~:
|\Im(\log(z))+2\pi m| > \Im(L)~ \} \)
The resulting set S is not dense, as the F above, the set S is countable and its measure is zero. How do you like it?