Very interesting tilings, but — I'm not sure I understand: If the points to be removed depend only on their row numbers and nothing else, then the Voronoi regions should show a constancy in the vertical direction, should they not? —Dan
On Jan 9, 2016, at 9:03 AM, Thane Plambeck <tplambeck@gmail.com> wrote:
Make a 23x23 square array of points, numbered from 1 to 529 row-wise. Remove all the points whose number is congruent to 0, 1, or 2 modulo 5. Then compute the Voronoi cells of that arrangement of points inside a bounding rectangle.
This is the picture you get (use VoronoiMesh[] in Mathematica)
https://www.flickr.com/photos/thane/24191215291/in/dateposted-public/
Here's another one with different values of 23, 0, 1, 2, 5, so to speak (unfortunately I forgot to write them down in my enthusiasm)
https://www.flickr.com/photos/thane/24191270151/in/dateposted-public/
Anyway, this seems to be a simple way to make lots of interesting looking tilings on the cheap.
(1) I can't possibly be the first person to do this...I'd welcome references (2) Can all the wallpaper groups be realized this way?