I updated the “hivegraph.pl” script to give the “storeys” of the beehive plots y-values that made their slopes linear, and thus hopefully cause patterns to stand out. I wanted to create hive plots with plenty of bees to test it out, and I wasn’t disappointed in the results. The first discrete semiprime I created, 1490521, produced a lovely pattern-y beehive plot:
The second one I chose, 3826351, had a more sparse and random-looking collection of bee points:
The difference in point density (which is the difference in steps needed to find factorization by starting with the adjusted ceiling square and increasing by 2) might explain the difference in apparent pattern.
Much fruitful study ahead. I think shaping these plots like pyramids more than classical beehives is the way to go.