riemann surface for tetration and slog?

[Kouznetsov]

   

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I was looking for something like this (a parametric plot of the imaginary part of a function) at wikipedia:
http://en.wikipedia.org/wiki/File:Rieman...ce_log.jpg
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But I was expecting something like a logarithmic branch cut.

Tetratophile, in the case of many branchpoints, the structure is more complicated.
While I can show what happens if you rotate two and three cutlines:
   
You may try to plot the real or imaginary part of the function as a surface in the 3-dimentional space using some Mathematica software. Due to the countable set of intersections, I expect such a surface to look like a foam, http://upload.wikimedia.org/wikipedia/co...lastic.jpg