Next I show the last two plots with final(?) computation of the regular iteration.

First we see, that as expected, at integer heights the trajectories match, and the integer iterates of the three roots join at the expected powers of Z

However, the trajectories do not combine after the first match, what were that, what I expected initially. The trajectories cross each other without joining, and the trajectory of z2 seems does two times more windings than that of z1

The two following plots simply show the extreme winding if the height is increased to the next unit interval. I've no more comment there, only that this introduces the question, whether there could be some normalizing of the continuous iteration-process, which allows to trajectories to join. And if that is possible (and meaningful) whether such a "normalization" has some impact for the sexp-iteration.

Gottfried

First we see, that as expected, at integer heights the trajectories match, and the integer iterates of the three roots join at the expected powers of Z

However, the trajectories do not combine after the first match, what were that, what I expected initially. The trajectories cross each other without joining, and the trajectory of z2 seems does two times more windings than that of z1

The two following plots simply show the extreme winding if the height is increased to the next unit interval. I've no more comment there, only that this introduces the question, whether there could be some normalizing of the continuous iteration-process, which allows to trajectories to join. And if that is possible (and meaningful) whether such a "normalization" has some impact for the sexp-iteration.

Gottfried

Gottfried Helms, Kassel