for iterations of tan(z) (generated from parabolic fixed point z=0)
p1~p4 \(z\in\{z|-2\pi\le\Re(z),\Im(z)\le2\pi\}\)
p1: \(tan^t(z), t\in[-1,1]\)
p2: \(tan^t(z), t\in[0,2]\)
p3: \(tan^{it}(z), t\in[-1,1]\)
p4: \(tan^{e^{i\theta}}(z), \theta\in[0,2\pi]\)
p1~p4 \(z\in\{z|-2\pi\le\Re(z),\Im(z)\le2\pi\}\)
p1: \(tan^t(z), t\in[-1,1]\)
p2: \(tan^t(z), t\in[0,2]\)
p3: \(tan^{it}(z), t\in[-1,1]\)
p4: \(tan^{e^{i\theta}}(z), \theta\in[0,2\pi]\)
Regards, Leo 