Dmitrii Kouznetsov's Tetration Extension

[Kouznetsov]

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In the left part of fig. 2 its not \( T \) but \( \Im(T) \) as the period is purely imaginary.

Yes. Thanks!

Did you btw play around with other complex fixed points, differently from the one nearest the real axis?
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Not yet. We shold calculate tetrations with various asymptotic behavior.
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For the distribution of fixed points I even created a small "movie"
here.

Good! Could you trace them? A movie would be good for evolution of the map of tetration as ln(b) increases. (Yet, I have only 3 stapshots: b=sqrt(2),b=2,b=e).

But you didnt give me your code yet!

Oops... I was sure I did. Now I see, I forgot. Sorry. Check now, codes for fig.3a and fig.3b should be there.

Attached is the somewhat ameteurish result for base \( sqrt{2} \). The red lines are \( |f|=1,2,4 \).

Why do blue lines pass through integer values at the real axis?
(You may reduce a little bit up-to-last argument in the conto function, and increase a little bit the last argument; contour lines will come closer to singulatity).