3 ms·
I haven't read the paper -- was 13 sides proved to be minimal? Or is the next quest to find a tile with fewer sides that tile the plane aperiodically?
by waynecochran 4y ago
I haven't read the paper -- was 13 sides proved to be minimal? Or is the next quest to find a tile with fewer sides that tile the plane aperiodically?
- fsckboy 4y agothe point is that this is the first (so, only known) tile shape that is also aperiodic. Previously aperiodic tiling schemes (like Penrose) required several tiles of different shapes. any additional single tile shape that was aperiodic would be interesting regardless of how many sides it has. I supposed if there turned out to be many of them there would be a grouping based on how many sides.
- fsckboy 4y agoI need to correct myself! What has been discovered is a family of shapes that are all aperiodic in the same pattern. https://cs.uwaterloo.ca/~csk/hat/examples/animation.gif https://cs.uwaterloo.ca/~csk/hat/examples/animation.gif https://cs.uwaterloo.ca/~csk/hat/animation.mp4 https://cs.uwaterloo.ca/~csk/hat/animation.mp4
- galaxyLogic 4y agoWhat would be interesting is a 3D mono-tile to cover 3D space. A SUPER LEGO. Assuming such a block also had like 13 or so sides I think you could keep such "bricks" together without glue and build houses and anything. Then disassemble if needed and build a different house.