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Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I)
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I wondered what results can be obtained if we calculate 2^I , 2^(2^I) , etc.







etc up to infinity of power tower.

Also, another interesting bases:



Golden mean may be interesting since



where

And in general a and z as basis.

I checked with Pari precision 200:







but so this iteration where it converges leads to numbers whose self roots is base a - for real numbers - as IF there was no I on top.. Like normal tetration

Would You know of anyplace where such results would be published, e.g graphically on complex plane?

Ivars
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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

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