The Different Fixed Points of Exponentials

[bo198214]

Wow that's a lot of info, thank you for keeping me up to date.
I have only little info in return
For animated images you can also make them by hand with this site:
https://ezgif.com/apng-maker
as long as you have a series of PNGs (but that should be possible with Pari/Gp).
Actually I also used that site for making the previous images, because Sage's built in default animation transforms it into a GIF, and that makes the images look crappy (pixelation, script becomes badly readable, etc). But with the above tool you make an APNG out of PNGs so no information is lost.

[bo198214]

This time I wanted to know how the fixed points behave if the base moves along Shell-Thron boundary. 
And what a wonderful dance is that! Daniel, when you talk of beauty ...

   
The indifferent fixed point moves on the red curve. But here one sees that one can not really assign, which of the two repelling fixed points is the other primary fixed point.
   

[bo198214]

I moved the subsequent posts to this thread.