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 complex base tetration program Gottfried Ultimate Fellow Posts: 767 Threads: 119 Joined: Aug 2007 02/07/2016, 05:27 AM (This post was last modified: 02/07/2016, 01:23 PM by Gottfried.) Discussing the (extended) Kneser-method the question of fixpoints is relevant. Here I have produced a picture of the fixpoints of tetration to base(î) , I found 2 simple fixpoint (attracting for exp, attracting for log, both used for the Kneser-method), and three periodic points - making things a bit more complicated. The fixpoints were sought using the Newton-algorithm for the joint threefold exponentiation $f(z)= \log_i(\log_i(\log_i(z)))$ and the iteration $z_{k+1} = f(z_k)$ . This means for example, that for the point in the top-left edge with the blue color having the z-value z_0=-5 - 5i the Newton-algorithm using iteration $z_{k+1} = f(z_k)$ arrives at the fixpoint 3.0 (having the complex value of about -1.14+0.71I in a moderate number of iterations. The blue point at coordinate z_0=-2.5+1I needs less iterations and the a bit lighter blue points near the periodic point 3.0 need even less iterations. Perhaps this post should be moved into a discussion of the Kneser-method or of the general problem of fixpoints. Gottfried Here is the picture: Attached Files Image(s)     Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread complex base tetration program - by sheldonison - 02/29/2012, 10:28 PM RE: complex base tetration program - by Kouznetsov - 02/29/2012, 11:49 PM RE: complex base tetration program - by sheldonison - 03/01/2012, 12:09 AM RE: complex base tetration program - by sheldonison - 03/01/2012, 10:34 AM RE: complex base tetration program - by Kouznetsov - 03/01/2012, 12:04 PM RE: complex base tetration program - by sheldonison - 03/01/2012, 03:47 PM RE: complex base tetration program - by sheldonison - 03/02/2012, 09:20 AM RE: complex base tetration program - by sheldonison - 03/07/2012, 12:08 AM RE: complex base tetration program - by sheldonison - 03/07/2012, 06:08 PM RE: complex base tetration program - by sheldonison - 03/08/2012, 09:51 PM RE: complex base tetration program - by mike3 - 03/10/2012, 06:59 AM RE: complex base tetration program - by sheldonison - 03/10/2012, 08:53 PM RE: complex base tetration program - by mike3 - 03/11/2012, 12:27 AM RE: complex base tetration program - by sheldonison - 03/12/2012, 04:20 AM RE: complex base tetration program - by sheldonison - 03/16/2012, 07:42 PM RE: complex base tetration program - by Gottfried - 02/06/2016, 01:37 AM RE: complex base tetration program - by sheldonison - 02/06/2016, 04:04 PM RE: complex base tetration program - by Gottfried - 02/06/2016, 05:36 PM RE: complex base tetration program - by Gottfried - 02/07/2016, 05:27 AM RE: complex base tetration program - by sheldonison - 02/07/2016, 12:28 PM RE: complex base tetration program - by Gottfried - 02/07/2016, 01:25 PM RE: complex base tetration program - by Gottfried - 10/24/2016, 11:50 PM RE: complex base tetration program - by sheldonison - 10/26/2016, 08:01 AM RE: complex base tetration program - by Gottfried - 10/26/2016, 10:02 AM

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