This comment does a great job of clarifying the picture: https://news.ycombinator.com/item?id=17106193.

It's effectively a visualization of gcd(x,y), and has almost nothing to do with primes. Once you realize that, it's a lot easier to reason about a lot of the patterns, although it is still a pretty interesting visualization.

That's a 7 year old comment; did you just remember it existed?

Thanks for the link!