File:TetrationPolynomial25power.jpg

${\displaystyle f=\ln \left(\sum _{n=0}^{25}c_{n}z^{n}\right)}$

Levels ${\displaystyle \Re (f)=-2,-1,0,1,2,3,4}$ are shown with thick black curves.

Levels ${\displaystyle \Re (f)=-1.8,-1.6,-1.4,-1.2,-0.8,-0.6,-0.4,-0.2}$ are shown with thin red curves.

Levels ${\displaystyle \Re (f)=1.8,1.6,1.4,1.2,0.8,0.6,0.4,0.2}$ are shown with thin thin blue curves.

Levels ${\displaystyle \Im (f)=-2,-1}$ are shown with thick red curves.

Levels ${\displaystyle \Im (f)=1,2}$ are shown with thick blue curves.

Levels ${\displaystyle \Im (f)=\pm \pi ,\pm 3\pi }$ are shown with thick pink curves.

Levels ${\displaystyle \Im (f)=\pm 1.8,\pm 1.6,\pm 1.4,\pm 1.2,\pm 0.8,\pm 0.6,\pm 0.4,\pm 0.2}$ are shown with thin green curves.

Upper left corner: the same for function ${\displaystyle log(f)}$

Botton, left: overlap of the upper two images.

Botton, right: lines of constant modulus and constant phase of holomorphic tetration in the same range.

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