Pentation Fractals

[bo198214]

Or more precisely: If \(c\) is the pixel value as a complex number, then the "tetration" fractal would be obtained by the iteration of \(f_c(z)=c^z\), so the "pentation" fractal would be obtained by the iteration of the function \(f_c(z)={}^zc\) while your fractal is obtained by iteration of which function?

I'm iterating \[^z(\sqrt{2})\].

You mean, you iterate \(f(z)={^z}(\sqrt{2})\) with initial value \(z_0=c\).
But a pentation fractal (in your terminology) would be to iterate \(f(z)={^z}c\) with initial value \(z_0=c\) or even \(z_0=0\) or \(z_0=1\).
Do you agree?