share with others#plotted #functional_iterations

[Leo.W]

One hint, Leo, the images look much better if you save it as .png (or sometimes also named .apng).
I don't know what program you use to create the animations, but if there is a way to save it as .png or .apng, give it a go!
(however if it works with .apng you have to rename it to .png before uploading to the forum.)
Otherwise really nice animations.

Thank you
sadly I just found that .apng has way larger file size.... 50MB for an animation as 12MB as gif, our forum allows only about 16MB for one single file
anyway thank you

These plots are the iterations of \(f(z)=e^z-1\) generated at parabolic fixed point z=0
I defined 2 branch cuts artificially \(Re(z)<0\wedge Im(z)=\pm1\) for \(Re(t)>0\), other branch cuts are following the natural branch cut of \(\log(z+1)\). All images show z in \(\{z|-2\pi\le\Re(z),\Im(z)\le2\pi\}\)
p1:\(f^t(z),t\in[-1,1]\)
p2:\(f^t(z),t\in[0,2]\)
p3:\(f^{it}(z),t\in[-1,1]\)
p4:\(f^{e^{i\theta}}(z),\theta\in[0,2\pi)\)