All Questions

Call a finite collection of tiles that can tile the plane if we have to use each tile at least once tiling. Is there a collection of at least 3 tiles that is not tiling, but such that after removing ...

This may be a very basic question, but I have not found an answer to it so far in my search. The question is whether there is an "algorithmic" way to check unique-composition/recognizability ...

Is the following problem known to be un/decidable? Problem: Given a finite configuration of Penrose tiles in the plane, determine if there is an extension of the configuration tiling the whole plane.

Consider an aperiodic tiling. By definition, there is a $C$ such that, for any box of side $C$, the part of the tiling contained in the box can be continued to the whole plane only in a non-periodic ...

The aperiodic monotile problem asks whether there exists a single tile that every tiling of the plane made with it results non-periodic. What is known about this problem? If this tile exists, how can ...