share with others#plotted #functional_iterations

[Leo.W]

It seems I lost my PC's memories about the iteration plots, I had to compute them again

for sin(z) generated from the parabolic fixed point z=0: (the gifs so large!)
p1~p5 \(z\in\{z|-2\pi\le \Re(z),\Im(z)\le 2\pi\}\)
p1: \(sin^t(z), t\in[-1,1]\)
p2: \(sin^{e^{i\theta}}(z), \theta\in[0,2\pi]\)
p3: \(sin^t(z), t\in[-2,0]\)
p4: \(sin^t(z), t\in[0,2]\)
p5: \(sin^{it}(z), t\in[-1,1]\)
(to balance the file size and the accuracy the images are very blurry)

[Leo.W]

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: \(tan^{e^{i\theta}}(z), \theta\in[0,2\pi]\)

[bo198214]

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.

[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:\(f^{e^{i\theta}}(z),\theta\in[0,2\pi)\)

[bo198214]

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

Two things:

1. If the file is too big, then you could try the optimizer https://ezgif.com/optipng
   I actually had to do that myself because the apng-output of sage is not optimized and I also ran into the 16MB limit (but with the optimzed image it worked).
   
2. The 16MB is already maximum that the forum configuration allows. Maybe one can fiddle with some PHP settings, not sure