[RBerenguel]

I did some research on this on the side for my dissertation, but never published it. The fact centers approximate the boundary generalises to almost any point in the plane as a consequence of normality of some sequences, and generalises to most families of complex iteration under very mild conditions. I’ve had a preprint that I never felt like finishing for something like 15 years lying around.

[QuadmasterXLII]

If you ever decide to put it out as-is, I'd love to read it!

[RBerenguel]

I should probably brush it up and just upload it to Arxiv. But then I need ok from my advisor, and maybe she’d rather not (since she’d be a coauthor of that..). I’ll try again, thanks for the encouragement.