02/03/2014, 01:13 PM
Very nice pic Gottfried.
I think the phenomenon is not typical for tetration but for most functions with a limited amount of fixpoints.
What surprises me is that the shapes are so close to perfect circles.
I wonder how it looks like if the real fixpoints approaches its limits.
In other words what happens if the base gets close to eta ?
Do we get figure 8 shapes instead of circles because of the anticipation of the pair of conjugate fixpoints ?
What happens with functions with 2 or more fixpoints ? do they also have these circles around their fixpoints ? In other words, do they locally ( around the fixpoints ) behave the same as the plot given by gottfried here ?
Why not ellipses ??
And what if there is no fixpoint ?
Maybe we need riemann surfaces to understand this better ?
Many questions as usual.
Regards
Tommy1729
I think the phenomenon is not typical for tetration but for most functions with a limited amount of fixpoints.
What surprises me is that the shapes are so close to perfect circles.
I wonder how it looks like if the real fixpoints approaches its limits.
In other words what happens if the base gets close to eta ?
Do we get figure 8 shapes instead of circles because of the anticipation of the pair of conjugate fixpoints ?
What happens with functions with 2 or more fixpoints ? do they also have these circles around their fixpoints ? In other words, do they locally ( around the fixpoints ) behave the same as the plot given by gottfried here ?
Why not ellipses ??
And what if there is no fixpoint ?
Maybe we need riemann surfaces to understand this better ?
Many questions as usual.
Regards
Tommy1729
