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Tweet tweet tweet

Sadly, one of the reasons for misconceptions with the previous post related to the little thought I gave to the problem followed by some coding errors in exploring the question. As with many errors, this has been instructive for me.

The following graphic aims to illustrate the zone of convergence of the complex plane for the iterated exponential:

itexpcomplmap

The red vertical lines representing the bounds…reassuring given the limits of the numerical recipe I used.

The qualitative behaviour of the iterations for different starting positions are shown in the following animated gif. The green vertical lines are the bounds and the moving vertical line is the starting value. Click on the image if the animation is not playing. The graphic will appear in window.

itexp

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Categories: Mathematica, Mathematics
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