• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 [Update] Comparision of 5 methods of interpolation to continuous tetration sheldonison Long Time Fellow Posts: 633 Threads: 22 Joined: Oct 2008 10/28/2013, 04:17 PM (This post was last modified: 10/28/2013, 05:20 PM by sheldonison.) (10/27/2013, 11:40 PM)Gottfried Wrote: Here ist a picture which shows the mapping of the small positive part of the imaginary axis .... of the powertower with base 4. The whole segment becomes more and more distorted and shrinks when iterated to the complex fixpoint. What is especially interesting me are the "eyes" /the whitespace in the inner spiral - and what about of regions of overlap in there if my initial linesegment where longer, say up to 0.8*I. This direction would be related by complex iteration heights - but I've not yet reliable computations of that heights.http://math.eretrandre.org/tetrationforu...hp?tid=358 is a link to Jay's post on the Chi-Star, which is the distorted part of the limiting behavior of your graph as well. To get the Chi-Star, one has to take the regular Schroeder function, developed from the complex fixed point, of the real axis of the sexp(z) solution. Then the pattern repeats, scaled. And then each of the "eyes" would extend all the way to infinity in a beautiful complicated recursive pattern. Jay's post also shows the relationship with the chi-star and the region which gets Riemann mapped in Kneser's construction, which Tommy asked about. - Sheldon « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Possible continuous extension of tetration to the reals Dasedes 0 1,349 10/10/2016, 04:57 AM Last Post: Dasedes Tribonacci interpolation ? tommy1729 0 1,934 09/08/2014, 10:37 AM Last Post: tommy1729 How many methods have this property ? tommy1729 1 2,493 05/22/2014, 04:56 PM Last Post: sheldonison (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 1,924 05/22/2013, 07:02 AM Last Post: Gottfried [UFO] - a contradiction in assuming continuous tetration? Gottfried 18 20,875 08/29/2010, 08:44 PM Last Post: Gottfried Self tetraroot constructed via Newton series interpolation mike3 2 6,545 07/11/2010, 03:38 AM Last Post: mike3 Borel summation and other continuation/summability methods for continuum sums mike3 2 5,193 12/30/2009, 09:51 PM Last Post: mike3 A false interpolation paradigm (?); a reconsideration Gottfried 4 7,306 09/17/2009, 08:17 AM Last Post: bo198214 exponential polynomial interpolation Gottfried 3 7,028 07/16/2008, 10:32 PM Last Post: andydude A related discussion on interpolation: factorial and gamma-function Gottfried 6 10,366 06/27/2008, 06:38 PM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)