markdow

No, I haven't adapted my program to accommodate different masses so I haven't looked much. Just in my head it's easy to see there are a lot of cyclic systems with different masses (with identical radii, and rational mass ratios). I think they would appear "not quite right" as we associate disk area with mass. It should be a pretty easy change to add mass into the dynamics, so eventually I'd like to see what that's like.

Different masses and different radii is also possible, but that severely restricts the possibilites for cyclic systems.

Yes,

works for any n, not just n=3. I still can't do these in my head, even whey the cycles aren't long.

It is always the second disk in a line that gets "swapped", and at the next set of collisions they get swapped back, so the cycle is not much longer with higher n.

Here's n=5, speeded up as these GIFs get too large.

Yes, any number; every ball makes a circuit with a fixed number of steps (4, 8 and 12 steps here), n*4. Any n will result in a cycle eventually. This has 24 steps, where 4, 8 and 12 divide 24 evenly.

I think so with the other one, but not sure. I'll try higher n and get back to you.

It rotates 90 degrees clockwise every quarter period, but that's hard to see at this speed.

Good stuff!