Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[Update] Comparision of 5 methods of interpolation to continuous tetration
Here ist a picture which shows the mapping of the small positive part of the imaginary axis in heights of h=1/20 when computed by the "polynomial method" with the diagonalization of the 64x64 Carlemanmatrix.

The coordinates of the initial linesegment are computed by the 21 coordinates at the imaginary axis between 0 and 0.5 I. To avoid logarithms of zero this is a bit translated by adding 1e-4*I to the coordinates.

Then 20 iterations with height of 1/20 are computed for that whole initial line. This gives the red skewed rectangle in the rough area (0+0I,0+0.5I,1,1+0.5*I)
Then that matrix of coordinates is completely mapped by natural iterations 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.

Attached Files Image(s)
Gottfried Helms, Kassel

Messages In This Thread
RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/27/2013, 11:40 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  My interpolation method [2020] tommy1729 1 688 02/20/2020, 08:40 PM
Last Post: tommy1729
  Possible continuous extension of tetration to the reals Dasedes 0 1,677 10/10/2016, 04:57 AM
Last Post: Dasedes
  Tribonacci interpolation ? tommy1729 0 2,285 09/08/2014, 10:37 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 3,019 05/22/2014, 04:56 PM
Last Post: sheldonison
  (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 2,250 05/22/2013, 07:02 AM
Last Post: Gottfried
  [UFO] - a contradiction in assuming continuous tetration? Gottfried 18 24,644 08/29/2010, 08:44 PM
Last Post: Gottfried
  Self tetraroot constructed via Newton series interpolation mike3 2 7,271 07/11/2010, 03:38 AM
Last Post: mike3
  Borel summation and other continuation/summability methods for continuum sums mike3 2 5,937 12/30/2009, 09:51 PM
Last Post: mike3
  A false interpolation paradigm (?); a reconsideration Gottfried 4 8,380 09/17/2009, 08:17 AM
Last Post: bo198214
  exponential polynomial interpolation Gottfried 3 7,812 07/16/2008, 10:32 PM
Last Post: andydude

Users browsing this thread: 1 Guest(s)