Point processes for decagonal quasiperiodic tilings

Details Point processes for decagonal quasiperiodic tilings Point processes for decagonal quasiperiodic tilings

2009-05-30

arxiv.org/abs/0906.0087v1

Acta Cryst. A 65 (2009) 342-351

Physics

Mathematical Physics

20 pages + 9 figures, submitted to Acta Cryst. A

Scientific paper

A general construction principle of inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of an expansion and a division of the tiles, where the expanded tiles can be divided arbitrarily as far as the set of prototiles is maintained. A certain kind of point decoration processes turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quarternary and the other ternary. Properties of the ternary tilings with rhombic, pentagonal, and hexagonal prototiles are investigated in detail.

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