0
votes
1answer
138 views

Can aperiodic tilings be non-hierarchical? and confusion over domino problem

Anyone experienced with the undecidability of aperiodic tiling? It's related to the halting problem which Turing proved was undecidable in the 30's and basically superimposes tiles onto other tiles ...
2
votes
1answer
121 views

Recognizing parallelogram tilings from their vertex set

Suppose I have a tiling of the plane with parallelograms where the sides of the parallelograms come from a specified finite set of vectors. If I only have access to the vertices of this tiling I may ...
5
votes
1answer
230 views

Decidability of periodic tilings of the plane

I'm interested in tilings of the plane by squares, with labels on the edges. It's well known that (1) the question "can one tile the plane with the following finite set of tiles?" is undecidable, and ...
13
votes
4answers
1k views

Decidability of tiling R^2

Does there exist a closed curve, with finite area and finite circumference, of which it is undecidable (in an axiomatic system where it is constructable) whether it can tile the plane? I know the ...