Gottfried,
Have you looked at this thread before?
http://math.eretrandre.org/tetrationforu...php?tid=89
I think, if you look at the pictures, that you will see that there are singularities, fanning out from the fixed point at real 4. To get to the real axis, you will have to navigate a course between the singularities. This is likely the cause of the slow convergence, as well as the need for high precision.
I've never actually tried to reach the real axis, and indeed I assumed it was impossible. But without actually trying, I can't be sure. If you do find a path to the real axis, I'd be curious to know the details.
Have you looked at this thread before?
http://math.eretrandre.org/tetrationforu...php?tid=89
I think, if you look at the pictures, that you will see that there are singularities, fanning out from the fixed point at real 4. To get to the real axis, you will have to navigate a course between the singularities. This is likely the cause of the slow convergence, as well as the need for high precision.
I've never actually tried to reach the real axis, and indeed I assumed it was impossible. But without actually trying, I can't be sure. If you do find a path to the real axis, I'd be curious to know the details.
~ Jay Daniel Fox