Riemann surface of tetration
#1
Given the logarithm has a helix shaped Riemann surface, the iterated logarithms related to tetration assure that the Riemann surface is quite complex as well as fractal. Has anyone worked with the Riemann surface of tetration? If so, what did you determine?

Edit: removed idea about tetration periods being assicated with Riemann surfaces.
Daniel
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#2
How about just discussing the Riemann surface of iterated logarithms? For example what is the Riemann surface for \(\log{(\log{(z))}}\)?
Daniel
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