All Questions
Tagged with decidability tiling
8 questions
7
votes
1
answer
248
views
Decidability of completing Penrose tilings
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.
- 509
1
vote
2
answers
103
views
A variation of domino tiling problem with fusions
I know several specific variations of the domino tiling problem has been determined to be decidable or undecidable, such as the seed domino problem. I have a variation which I have not been able to ...
- 633
1
vote
1
answer
213
views
Possible weaker version of the Domino/Wang tiling problem
This may be a dumb question, but I was wondering whether the question of 'periodically tiling the plane from a finite set of tiles' is the same as the domino tiling problem or a weaker version. I ...
- 633
4
votes
0
answers
171
views
Undecidability for hyperbolic Wang-tilings - pentagons, heptagons, octagons, oh my!
Berger proved that the problem of determining if a finite set of Wang tiles can tile the plane is undecidable. Robinson reproved Berger's result and raised the question of considering the ...
- 5,349
-1
votes
1
answer
261
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 ...
- 1
2
votes
1
answer
146
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 ...
- 85.5k
10
votes
2
answers
1k
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 (...
- 2,519
17
votes
3
answers
2k
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 ...
- 453