Fibonacci direct product variation tilings

Author:

Baake Michael1ORCID,Gähler Franz1ORCID,Mazáč Jan1ORCID

Affiliation:

1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

Abstract

The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This rule admits various modifications, which lead to 48 different inflation rules, known as the direct product variations. They all result in tilings that are measure-theoretically isomorphic by the Halmos–von Neumann theorem. They can be described as cut and project sets with characteristic windows in a two-dimensional Euclidean internal space. Here, we analyze and classify them further, in particular, with respect to topological conjugacy.

Funder

Deutsche Forschungsgemeinschaft

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference13 articles.

1. Aperiodic Order

2. Three variations on a theme by Fibonacci

3. B. Sing, “Pisot substitutions and beyond,” Ph.D. thesis, Bielefeld University, 2007, available electronically at http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:361-11555.

4. Fractals and Hyperspaces

5. A primer of substitution tilings of the Euclidean plane

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