Very nice explorations! Thank you for sharing.
I’d noticed the square arrangements showing up sometimes with oversized circle packings, but I’ve never really dug down into exactly why it happens.
It’s also interesting to compare this with points distributed through electrostatic type repulsion (see the examples here), where the repulsion strength is some negative power of distance. That produces large regions of triangular arrangements, but doesn’t seem to result in the other polygonal packings you get with the spring-like repulsion used in circle packing (where the strength is linear with distance).
I wonder if these square arrangements could even be used as a way of making quad dominant meshes. Perhaps there’s some way to encourage square packed regions to form even more.
Maybe a sort of multi-layered repulsion with 2 distances…
