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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 ...
user101010's user avatar
  • 5,349
5 votes
1 answer
405 views

Computational approach deciding whether a set of Wang Tile could tile the space up to some size

As an applied person, I'm facing one practical problem deciding whether a set of Wang tile could tile the plane periodically or aperiodically. Although both problems seem undecidable, but I'm on a ...
user40780's user avatar
  • 867
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 ...
fastforward's user avatar