Physics – Mathematical Physics
Scientific paper
2007-10-20
Philosophical Magazine 88 (2008) 2017-2023
Physics
Mathematical Physics
Paper submitted to Phil. Mag. (for Proceedings of Quasicrystals: The Silver Jubilee, Tel Aviv, 14-19 October, 2007)
Scientific paper
10.1080/14786430802035691
The Penrose tiling is directly related to the atomic structure of certain decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It is known that the numbers 1, $-\tau $, $(-\tau)^2$, $(-\tau)^3$, ..., where $\tau =(1+\sqrt{5})/2$, are scaling factors of the Penrose tiling. We show that the set of scaling factors is much larger, and for most of them the number of the corresponding inflation centers is infinite.
Cotfas Nicolae
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