Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I)

[Ivars]

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 \( z=e^{\pi/2} \)

   

UltraFine region (another 1000 times zoomed) around \( z=e^{\pi/2} \)

   

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