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 Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/24/2008, 08:13 AM I checked with the routine in PariTTY most kindly provided by Gottfried to me few trajectories of interesting points on real axis from fractal picture, $e^{-\pi/2}=I^I$. If we look for $h(e^{-\pi/2})$ without I on top, it is just real number 0.4745409995126511230174679441, while iterating with I on top obviosuly leads to oscillating behaviour since first iteration leads to $(I^I)^I=I^{-1}= -I.$ So I am looking for (a^(a^.........(a^I)) where $a= e^{-\pi/2}=0.2078795763507619085469556198$ mybase = exp(-Pi/2) %27 = 0.2078795763507619085469556198 ffrac_init(1.0*I,mybase) ffrac_init(1.0*I,mybase) %28 = 1.000000000000000000000000000*I for(k=1,20,print(ffrac)) for(k=1,20,print(ffrac)) -2.524354897 E-29 - 1.000000000000000000000000000*I -2.524354897 E-29 + 1.000000000000000000000000000*I -7.57306469 E-29 - 1.000000000000000000000000000*I -7.57306469 E-29 + 1.000000000000000000000000000*I -2.019483917 E-28 - 1.000000000000000000000000000*I -2.019483917 E-28 + 1.000000000000000000000000000*I -5.301145284 E-28 - 1.000000000000000000000000000*I -5.301145284 E-28 + 1.000000000000000000000000001*I -1.337908095 E-27 - 1.000000000000000000000000001*I -1.337908095 E-27 + 1.000000000000000000000000002*I -3.332148464 E-27 - 1.000000000000000000000000002*I -3.332148464 E-27 + 1.000000000000000000000000005*I -8.25464051 E-27 - 1.000000000000000000000000005*I -8.25464051 E-27 + 1.000000000000000000000000013*I -2.039678757 E-26 - 1.000000000000000000000000013*I -2.039678757 E-26 + 1.000000000000000000000000032*I -5.036088018 E-26 - 1.000000000000000000000000032*I -5.036088018 E-26 + 1.000000000000000000000000079*I -1.242739915 E-25 - 1.000000000000000000000000079*I -1.242739915 E-25 + 1.000000000000000000000000195*I But perhaps this corresponds to case You mentioned, that iterations with z on top of a does not converge. Ivars « Next Oldest | Next Newest »

 Messages In This Thread Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/19/2008, 09:02 PM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/20/2008, 06:12 AM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 06:43 AM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 04:46 PM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 04:59 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 08:36 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 09:08 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/21/2008, 06:33 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/21/2008, 10:29 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/22/2008, 08:13 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/23/2008, 06:51 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/23/2008, 11:44 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/24/2008, 08:13 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/24/2008, 08:55 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/24/2008, 04:09 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/25/2008, 08:28 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:48 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/25/2008, 06:08 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:12 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 07:43 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/26/2008, 09:01 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 10:30 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 01:11 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:51 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/27/2008, 08:10 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/27/2008, 09:23 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/27/2008, 11:45 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by tommy1729 - 04/11/2014, 10:54 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 04/12/2014, 01:10 AM

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