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Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I)
#5
Few more fractal pictures from z^(z^(z^(z^...........(z^I)

Very interesing neighboroughood of e^pi/2, with 4 armed spirals. This part seems to be infintely fractal, and quite complex. I wonder of course it what we see is structure of I ( since I^(1/I)= e^(pi/2)) as this map gives numbers whose selfroot is z.At least for real base there is no difference with infinite tetration h??? And if we add few more I on top of infinite power tower, it will not change anything?

Fine region around

   

UltraFine region (another 1000 times zoomed) around

   

There also few interesting points where many rays converge to, one of them is x=1.998.. , Y= 1.1972.. Of course, exact values can only be obtained by higher bailout settings.

   

Also, I add 2 regions near 0

   

and -1 , also interesting patterns.
   

Thanks Henryk for helping me to learn about fractal images.I think this may somehow also help to understand what "imagination" does
Ivars
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Messages In This Thread
RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 04:59 PM

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