ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
Using 2 × 2 and 3 × 3 matrices, Rao & Suryanarayan [Physica (Utrecht) (1994), B193, 139–146] and Clark & Suryanarayan [Acta Cryst. (1991), A47, 498–502] have obtained quasiperiodic tilings of the plane with n-fold rotational symmetry, n = 2, 3, 4, 5, 6, 8 with two unit prototiles. In this paper, a generalized method for generating quasiperiodic lattices for n-fold non-crystallographic axes is given by employing Chebychev and associated Chebychev matrices of order n, and some of their properties are derived. The method is based on the self-similarity principle. The properties of the matrices are applied to create self-similar tiles by solving an eigenvalue problem that shows how many of each type of tile to use and sheds light on how to configure the boundaries of the next generation's tiles. The tilings generated contain the above-mentioned filings as special cases. Thus, this approach introduces the basic techniques from linear algebra to the study of filings.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767395001711
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