(02/03/2014, 01:13 PM)tommy1729 Wrote: What surprises me is that the shapes are so close to perfect circles.Concerning the shape:[please see my updated previous post, I've inserted two new pictures] as the base point
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 ??
Note also on the real axis, righthand of the fixpoint, the occurence of some "mirror"- or "Reflexion"-points: just for the two additional iterations to the right(=negative height) from the currrently most right point (
The left part of the curve has then the horizontal lines +-<not-yet-determined-imaginary-value> as limiting asymptote.
Well, I'm really curious too what the shape is with bases nearer to eta...
Gottfried
Gottfried Helms, Kassel