Abstract
A pseudo-self-similar tiling is a hierarchical tiling of Euclidean space which obeys a nonexact substitution rule: the substitution tor a tile is not geometrically similar to itself. An example is the Penrose tiling drawn with rhombi. We prove that a nonperiodic repetitive tiling of the plane is pseudo-selt-similar if and only if it has a finite number of derived Voronoi tilings up to similarity. To establish this characterization, we settle (in the planar case) a conjecture of E. A. Robinson by providing an algorithm which converts any pseudo-self-similar tiling of ℝ2 into a self-similar tiling of ℝ2 in such a way that the translation dynamics associated to the two tilings are topologically conjugate.
Original language | English |
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Pages (from-to) | 289-306 |
Number of pages | 18 |
Journal | Discrete and Computational Geometry |
Volume | 26 |
Issue number | 3 |
DOIs | |
State | Published - Oct 2001 |
Externally published | Yes |