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 [Update] Comparision of 5 methods of interpolation to continuous tetration Gottfried Ultimate Fellow Posts: 854 Threads: 126 Joined: Aug 2007 02/03/2014, 01:59 PM (This post was last modified: 02/03/2014, 04:15 PM by Gottfried.) (02/03/2014, 01:13 PM)tommy1729 Wrote: 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 ??Concerning the shape:[please see my updated previous post, I've inserted two new pictures] as the base point $z_0=1$ goes to the left then the shape becomes first a distorted oval (picture 2) and later a -left-open ellipsoidic looking shape going to negative infinity to the left (picture 3). 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 ( $\text{reflexion}(z_0) = y_0 \approx 1.86300282587$ the "zero-reflexion" $\text{reflexion} (z_{-1}) = y_{-1} \approx 2.37147238675802$ and then "neg infinity-reflexion" $\text{reflexion}(z_{-2})= y_{-2} \approx 3.29126767409758$). The left part of the curve has then the horizontal lines +- as limiting asymptote. Well, I'm really curious too what the shape is with bases nearer to eta... Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/13/2013, 02:20 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by MikeSmith - 10/14/2013, 10:42 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/14/2013, 01:19 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by MikeSmith - 10/14/2013, 08:22 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 12:59 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/14/2013, 10:07 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 12:00 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 01:09 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/15/2013, 07:14 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/15/2013, 11:14 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/16/2013, 12:54 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/16/2013, 04:12 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/16/2013, 05:07 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/22/2013, 12:17 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/22/2013, 01:53 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/27/2013, 11:40 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/28/2013, 04:17 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:11 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:29 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/29/2013, 09:37 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/28/2013, 11:32 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 10/29/2013, 01:11 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/29/2013, 02:52 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 11/01/2013, 02:16 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/01/2014, 12:09 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/04/2014, 12:31 AM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 02/03/2014, 01:13 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 01:44 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 01:59 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by tommy1729 - 02/03/2014, 10:35 PM RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 02/03/2014, 11:07 PM

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