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