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Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I)
#16
While studying this, I have become little puzzled about the way converges. When iterated from z_0=I with a any precision available in PARI, it shows a tri-cycle behaviour, as do many other imaginary numbers (e.g 2*I, 3*I etc. ), if I have made the calculations right.

I know the analytic expression for convergence of based on Lambert function, but the way approaches fixed point seems not one that could ever stop having sharp angles . If it would be a spiral type behaviour, looping , than it would be easier to accept. Even 2 point oscillating approach would seem strange to accept as tending to limit value and truly stopping oscillations.

?

Ivars
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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

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