The Ammann–Beenker Tilings Revisited

Nicolas Bedaride (1) , Thomas Fernique (2)

1 I2M - Institut de Mathématiques de Marseille
2 LIPN - Laboratoire d'Informatique de Paris-Nord

This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings as the solution of a simple optimization problem.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]; Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Nicolas Bedaride, Thomas Fernique. The Ammann–Beenker Tilings Revisited. Aperiodic, Sep 2012, Cairn, Australia. ⟨10.1007/978-94-007-6431-6_8⟩. ⟨hal-01219105⟩