complex iteration (complex "height")

[Ivars]

You mean \( \frac{1}{e}[4](-\frac{1}{\Omega})=1 \)? Thats not true. \( b[4]t \) is only real for integer \( t \) (considering \( e^{-e}<b<1 \)).

But .. You have not really considered negative heights, have You?
May be its different then.
\( b[4]t \) is real at t=integers only for t(height ) >0 ;
for t=0 it is real for all b and \( b[4]0=1 \);
what about t<0? May be there the points t (when t<0) where \( b[4]t \) are real (or at least \( b[4]t =1 \)) and t are not negative integers?

Just asking, the idea came from your formula anyway, setting \( (1-\ln{(a)^z)} = 0 \) , so that infinite iterations in both directions cancel out (log and exp). If formula works for bases in that range in general, why not for negative heights?

Ivars