Some of these point arrangements superficially resemble Chladni figures (https://chalkdustmagazine.com/regulars/on-the-cover/cover-ch...) coming from the vibrations of a square drum.
Orthogonally, I wonder if these arrangements are generalizable to give lower bounds for N = n^2 + 1
None of the images has any squares.
The n=17 case is a famous math meme.
But where is the picture for this lower bound packing?
Responding to a couple comments here: there is no picture or new arrangement of squares because those are _upper_ bounds for the problem. The best known arrangement, i.e. the best known upper bound, has not changed.