Lambert W function and the Super Square Root

[andydude]

W = ln (ssrt (e^x))

Yes, indeed.

I once thought that was unique, but now I have come to realize that it is an example of topological conjugacy. If you would like, there are many more equations like yours, encoded in the diagrams on page 48 of the Tetration Ref.. Topological conjugacy is at the very heart of continuous iteration. It underlies Abel functions, Schroeder functions, regular iteration, intuitive iteration, and the interesting correlation between x^^oo, W(x), and ssqrt(x).