• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 complex iteration (complex "height") Gottfried Ultimate Fellow Posts: 766 Threads: 119 Joined: Aug 2007 11/14/2007, 09:32 AM (This post was last modified: 11/14/2007, 02:42 PM by Gottfried.) Here I add two plots, which show bases s=2 and base s=sqrt(2), when tetrated to complex heights h. The height-parameter h follows the border of the complex unit-disk, so passes the coordinates (1,0),(0,i),(-1,0),(0,-i ) and is exp(2*Pi*I*x) . Also I have added 4 different scalings of h by the zoom-factor g, where g=1 (h is on the complexunit-circle), g=0.75 (h has radius 0.75), g=0.5 and g=0.25. This is a small picture for s=2:     and this a small picture for s=sqrt(2):     The curves for value g=1.25 (radius of h=1.25) are partly erratic; a better approximation-method should be able to smooth them a bit. Gottfried Attached Files Image(s)         Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread complex iteration (complex "height") - by Gottfried - 11/14/2007, 09:32 AM RE: complex iteration (complex "height") - by bo198214 - 03/21/2008, 05:21 PM RE: complex iteration (complex "height") - by Gottfried - 03/22/2008, 01:01 AM RE: complex iteration (complex "height") - by bo198214 - 03/22/2008, 12:10 PM RE: complex iteration (complex "height") - by Gottfried - 03/22/2008, 03:25 PM RE: complex iteration (complex "height") - by bo198214 - 03/23/2008, 01:28 AM RE: complex iteration (complex "height") - by Gottfried - 03/23/2008, 06:43 AM RE: complex iteration (complex "height") - by bo198214 - 03/23/2008, 08:47 AM RE: complex iteration (complex "height") - by Gottfried - 03/23/2008, 10:16 AM RE: complex iteration (complex "height") - by Ivars - 03/22/2008, 09:15 AM RE: complex iteration (complex "height") - by bo198214 - 03/22/2008, 11:59 AM RE: complex iteration (complex "height") - by Ivars - 03/22/2008, 07:45 PM RE: complex iteration (complex "height") - by bo198214 - 03/22/2008, 07:49 PM RE: complex iteration (complex "height") - by Gottfried - 03/22/2008, 08:23 PM RE: complex iteration (complex "height") - by Ivars - 03/22/2008, 08:56 PM RE: complex iteration (complex "height") - by Gottfried - 03/22/2008, 10:36 PM RE: complex iteration (complex "height") - by Ivars - 03/23/2008, 04:06 PM RE: complex iteration (complex "height") - by Gottfried - 03/22/2008, 03:32 PM RE: complex iteration (complex "height") - by Ivars - 03/26/2008, 06:22 PM RE: complex iteration (complex "height") - by bo198214 - 03/26/2008, 08:54 PM RE: complex iteration (complex "height") - by Ivars - 03/26/2008, 10:05 PM RE: complex iteration (complex "height") - by Ivars - 03/27/2008, 07:41 AM RE: complex iteration (complex "height") - by Ivars - 03/28/2008, 11:55 AM RE: complex iteration (complex "height") - by bo198214 - 03/28/2008, 12:56 PM RE: complex iteration (complex "height") - by Ivars - 03/28/2008, 03:13 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Complex Tetration, to base exp(1/e) Ember Edison 7 3,029 08/14/2019, 09:15 AM Last Post: sheldonison An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 13,623 01/14/2017, 09:09 PM Last Post: Vladimir Reshetnikov Negative, Fractional, and Complex Hyperoperations KingDevyn 2 6,822 05/30/2014, 08:19 AM Last Post: MphLee new results from complex dynamics bo198214 25 37,025 02/25/2013, 01:42 AM Last Post: sheldonison Complex Tetration Balarka Sen 16 23,648 02/21/2013, 02:23 PM Last Post: sheldonison (MSE) periods in (z*exp(z*exp(...))) for complex z Gottfried 0 3,036 04/16/2012, 10:24 AM Last Post: Gottfried Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 3,069 09/04/2011, 05:59 AM Last Post: Gottfried Real and complex behaviour of the base change function (was: The "cheta" function) bo198214 39 56,412 08/13/2011, 06:33 PM Last Post: bo198214 Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 10 17,783 06/09/2011, 05:56 AM Last Post: bo198214 "Kneser"-like mapping also for complex base? mike3 2 6,258 11/07/2010, 01:37 PM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)