File:E1efig09abc1a150.png

Complex maps of tetration $\mathrm{tet}_b$ to base
$b\!=\!1.5$ , left,
$b\!=\!\exp(1/\mathrm e)$ , center, and
$b\!=\!\sqrt{2}$ , right.

$f\!=\! \mathrm{tet}(x\!+\!\mathrm i y)$ is shown in the $x,y$ plane with levels $~p\!=\!\Re(f)\!=\! \mathrm{const}~$ and levels $~q\!=\!\Im(f)\!=\! \mathrm{const}~$. The integer levels are shown with thick lines.

This image is close to the figure 9 in the article ^[1].

The C++ generators of the pictures used in the figure are available and will be uploaded upon request.

Copyleft 2011 by Dmitrii Kouznetsov. You may copy, modify and/or distribute the image for free but the source should be attributed.

References