hey bodies I felt like to share some of plots of iterations with u *just for visual treatment(?no)
plz feel free to share if you have any interesting graphs (gifs are better!)
for \(exp_e(z)\): (due to some branch cuts there are 2 points in the right and some cuts in the left should be excluded)
p1: \(exp_e^t(z), t\in[-1,1]\)
p2: \(exp_e^{e^{it}}(z), t\in[0,2\pi)\)
p3: \(exp_e^{it}(z), t\in[-1,1]\)
also I have to say that does the iteration to an imag height always tortune and rotate the original function in some manner? at least the photos represent to me with such impression
All these iterations generated by Kneser's tetration.
for \(sin(z)\):
p4: for real \(z\in[-\pi,\pi]\), plot \(sin^t(z),t\in[0,1]\)
Generated by fixed point method.
plz feel free to share if you have any interesting graphs (gifs are better!)
for \(exp_e(z)\): (due to some branch cuts there are 2 points in the right and some cuts in the left should be excluded)
p1: \(exp_e^t(z), t\in[-1,1]\)
p2: \(exp_e^{e^{it}}(z), t\in[0,2\pi)\)
p3: \(exp_e^{it}(z), t\in[-1,1]\)
also I have to say that does the iteration to an imag height always tortune and rotate the original function in some manner? at least the photos represent to me with such impression
All these iterations generated by Kneser's tetration.
for \(sin(z)\):
p4: for real \(z\in[-\pi,\pi]\), plot \(sin^t(z),t\in[0,1]\)
Generated by fixed point method.
Regards, Leo 