Puzzle #551 - Three of Threes (Slitherlink)

This kind of Slitherlink structure, with evenly spaced out 3s has some interesting properties that I don't fully understand. The consequences when interacting with 1s and 2s are pretty hard to track, but 3s are somewhat approachable. So, I made this puzzle to try to get a feel for the structure better.

puzz.link interface