Discrete & Computational Geometry
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On Aperiodic Sets of Wang Tiles
Foundations of Computer Science: Potential - Theory - Cognition, to Wilfried Brauer on the occasion of his sixtieth birthday
Two-by-Two Substitution Systems and the Undecidability of the Domino Problem
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Fixed Point and Aperiodic Tilings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
| Hi-index | 0.00 |
Wang tiles are unit size squares with colored edges. By using a fixed-point theorem à la Kleene for tilings we give novel proofs of classical results of tilings problems' undecidability by way of diagonalization on tilings (made possible by this theorem). Then, we present a general technique to construct aperiodic tile sets, i.e. , tile sets that generate only aperiodic tilings of the plane. Our last construction generalizes the notion of self-simulation and makes possible the construction of tile sets that self-simulate via self-similar tilings, showing how complex the self-simulation can be.