Semi-detached House

Discovered by


A simple substitution rule with inflation factor 2, using two prototiles only. A glimpse on the image hopefully explains the name. The translation module is a square lattice, which is a hint that the semi-detached house tilings may be a model set with p-adic internal space. This question (model set or not) was raised in [Fre02] and was answered in [FS] .

Substitution Rule

Rule Semi-detached House


Patch Semi-detached House


Frettlöh, D
Nichtperiodische Pflasterungen mit ganzzahligem Inflationsfaktor
Univ. Dortmund 2002,

Frettlöh, D and Sing, B
Computing modular coincidences