Construction of 2D quasi-periodic Rauzy tiling by similarity transformation

Journal Article · Fri May 15 00:00:00 EDT 2009 · Crystallography Reports

DOI:https://doi.org/10.1134/S1063774509030018· OSTI ID:22050842

Zhuravlev, V G

A new approach to constructing self-similar fractal tilings is proposed based on the construction of semigroups generated by a finite set of similarity transformations. The Rauzy tiling-a 2D analog of 1D Fibonacci tiling generated by the golden mean-is used as an example to illustrate this approach. It is shown that the Rauzy torus development and the elementary fractal boundary of Rauzy tiling can be constructed in the form of a set of centers of similarity semigroups generated by two and three similarity transformations, respectively. A centrosymmetric tiling, locally dual to the Rauzy tiling, is constructed for the first time and its parameterization is developed.

• OSTI ID: 22050842
• Journal Information: Crystallography Reports, Vol. 54, Issue 3; Other Information: Copyright (c) 2009 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7745
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FRACTALS
PERIODICITY
SYMMETRY
TRANSFORMATIONS