Aperiodic Tilings by Right Triangles

N. Vereshchagin

doi:10.1007/978-3-319-09704-6

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Aperiodic Tilings by Right Triangles

P. 29–41.

Vereshchagin N.

Let ψ denote the square root of the golden ratio, ψ = ( 5 − 1)/2.
A golden triangle is any right triangle with legs of lengths a, b where
a/b = ψ. We consider tilings of the plane by two golden triangles: that
with legs 1, ψ and that with legs ψ, ψ 2 . Under some natural constrains
all such tilings are aperiodic.

Language: English

DOI

Keywords: Self-Similar Tilings

In book

Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Turku, Finland, August 5-8, 2014. Proceedings

Vol. 8614. , Berlin: Springer, 2014.

Ammann tilings: a classification and an application

Durand B., Shen A., Vereshchagin N., / Series math "arxiv.org". 2012. No. 2896.

We describe all Ammann tilings of a plane, a half-plane and a quadrant. In our description, every tiling is associated to an infinite sequence of two letters. We provide simple criteria of (a) whether a tiling associated with a sequence tiles the entire plane, a half-plane or a quadrant and (b) whether tiling associated with ...

Added: December 11, 2013

Limit Theorems for Self-Similar Tilings

Bufetov A. I., Solomyak B., Communications in Mathematical Physics 2013 Vol. 319 No. 3 P. 761–789

We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit ...

Added: February 11, 2013