Rapid Convergence to Frequency for Substitution Tilings of the Plane |
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| Authors: | José Aliste-Prieto Daniel Coronel Jean-Marc Gambaudo |
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| Affiliation: | 1.Centro de Modelamiento Matemático,Universidad de Chile,Santiago,Chile;2.Facultad de Matemáticas,Pontificia Universidad Católica de Chile,Santiago,Chile;3.Laboratoire J.-A. Dieudonné,Université de Nice - Sophia Antipolis, CNRS,Nice Cedex 02,France |
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| Abstract: | ![]()
This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve. |
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