Name
Abstract | ||
|---|---|---|
We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasi-periodic tiling. We prove that the tilings by a tileset that admits only quasi-periodic tilings have a recursively (and uniformly) bounded quasi-periodicity function. This corrects an error from [6, theorem 9] which stated the contrary. Instead we construct a tileset for which any quasi-periodic tiling has a quasi-periodicity function that cannot be recursively bounded. We provide such a construction for 1-dimensional effective subshifts and obtain as a corollary the result for tilings of the plane via recent links between these objects [1, 10]. |
Year | Venue | Keywords |
|---|---|---|
2010 | JAC | cellular automata,dynamic system,1 dimensional |
DocType | Volume | Citations |
Journal | abs/1012.1222 | 3 |
PageRank | References | Authors |
0.64 | 6 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexis Ballier | 1 | 25 | 4.01 |
| Emmanuel Jeandel | 2 | 123 | 20.06 |