Iterating at fixed points of b^x

[jaydfox]

Here is a little animated gif that shows how the fixed points in the complex plane change in dependency on the base \( b \).
For \( \eta=e^{1/e} \) the animation shows b going through \( \eta+0.2 \dots \eta-0.1 \).

Random, off-topic question, and feel free to move this, but what do you use for animating gifs? I have yet to find a decent gif animating program that isn't free.