## 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 ℝ^{2} into a self-similar tiling of ℝ^{2} 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 |