Let's make some squares aware of their relationship to each other.
This is an age-old, ultra-solved problem, so I decided to hit the "books". I found this cool link, and followed it.
Getting a super traditional smooth-walking-and-wall-hugging behavior down pat can be tricky.
I found that broad-phase algorithm tweak that they offer as an optimization turns out to be essential to capture all the scenarios I'm concerned with.