Hmm, my mind is not well to follow today, sorry James.
I remember to have worked with the problem to find the fixpoints by an analysis different from iterating the function.
This was one of my earliest contributions here and I had not much experience in putting things in established mathematical terms and derivation-process. Anyway, perhaps there is an idea in it that you've overlooked so far. In short I looked at the conditions on \(a\) and \(b\) where \(t=a+bî \) and \(\alpha\) and \(\beta\) where \( \log(t)=u=\alpha+\beta î \) to write this as function on \( \beta \) alone and if I remember correctly had a better/faster access to the fixpoints than by the iteration, however didn't use it much. See here: tetration-function (stupid name, I simply had no better ideas...)
Gottfried
I remember to have worked with the problem to find the fixpoints by an analysis different from iterating the function.
This was one of my earliest contributions here and I had not much experience in putting things in established mathematical terms and derivation-process. Anyway, perhaps there is an idea in it that you've overlooked so far. In short I looked at the conditions on \(a\) and \(b\) where \(t=a+bî \) and \(\alpha\) and \(\beta\) where \( \log(t)=u=\alpha+\beta î \) to write this as function on \( \beta \) alone and if I remember correctly had a better/faster access to the fixpoints than by the iteration, however didn't use it much. See here: tetration-function (stupid name, I simply had no better ideas...)
Gottfried
Gottfried Helms, Kassel
