Great, thanks for sharing, I like the generalization very much! why the hexagon shows different type of visual patterns in some sectors more reminiscent of parallel lines, or is it an illusion? And it is so nice you dug up that golden oldie:

Ulam spiral to appear on Sept. 2013 cover of Math Horizons

http://community.wolfram.com/groups/-/m/t/102049

Here is a particularly stunning version from that post's comments by @Jari Kirma

With[{size={1920,1200},numbers=100000,r=4/(3 GoldenRatio)},
    Graphics[{White,Table[Disk[RotationTransform[Pi(3-Sqrt[5])n]
       [{Sqrt[n],0}],r/Max[1,PrimeOmega[n]]],{n,numbers}]},
    PlotRange->(r/3) (# {-1,1}/2&/@size),ImagePadding->None,
       ImageSize->size,Background->Black]]