3 ms·
So one thing I that this aperiodic monotile had me wondering, does it have any non-trivial non-viable partial tiling? By which I mean you start laying down til
by im3w1l 3y ago
So one thing I that this aperiodic monotile had me wondering, does it have any non-trivial non-viable partial tiling? By which I mean you start laying down tiles right, and it looks like they fit together fine. Your construct has no holes and is "reasonably convex", like nowhere does it curve inwards by a lot. But because of some mysterious long-range self interaction it's actually impossible to complete the tiling process into something encompassing the whole plane.
- Karliss 3y agoDepends on your definition of non-trivial and reasonably convex. After playing with the tiles a little bit it seems to me that placing 4 (maybe even 3) hats on top of each other is one such configuration. You can place 1-2 more tiles on each side, but you quickly endup with state where the dead end is obvious.