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Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I)
#11
Hello, Henryk

In Chaos Pro, is there a way to find coordinates [x,y] of an interesting region/point? So far I could only use zooming the are which was fine for e^pi/2, e^-e, e^(1/e) , e^pi/2 which are rather distinct points with interestingly different behaviour of iteration z_0=I, z=pixel^z in their neighborouhood, ( I have placed the pictures in the thread) but that is very time consuming if points are less obvious and e.g. off real axis. Imaginary axis is almost invisible.

Also, could You look into my question in the thread, why (z^(z(^z(.............z^I) = h(z) (seems to be) where it converges on real axis? And would mapping the trajectory of this convergence give some additional information about the point compared to just computing it step by step on real axis?

My interest would be to perform continuos iteration, of course, to see the full trajectory. I did discrete one for leading to and the behaviour seems chaotic, but there are not enough points ( 10 integer iterations only).


Perhaps any finite z on top of iterations of a^(a^(a^.....z) will lead to h(a) via different trajectories.


Thank You in advance,

Ivars
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Messages In This Thread
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

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