(10/22/2022, 12:59 PM)Daniel Wrote: I'm testing my tetration software by creating a pentation Fantou set. The two following fractals are are generated by Mathematica and the second by FractInt. The tetration equation that is iterated to get to pentation is \[^z(\sqrt{2})\]
Wait, wait, wait - if we call the fractal of \(z^{z^{z^{\dots}}}\) tetration fractal (though that naming seems not right to me already - I would call it "exponentiation fractal" because the repeated operation is exponentiation), then I would assume we call the fractal of \({}^{{}^{{}^{\dots}z}z}z\) the pentation fractal and not the fractal of \({}^{{}^{{}^{z}\sqrt{2}}\sqrt{2}}\dots\), which would follow from your formula.
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?