If I push this up to n=1000 for the underlying sequence, I end up with this, which...sort of stops looking like a spiderweb entirely in favor of a less interesting sharp pinwheel. Which will only get worse for n. I may have to explore a modified rendering approach, maybe with log values.
All of which, along with any actual explanation, feels like a tomorrow thing. But I'm glad I got a little start on this tonight finally.