Kurt Bruckner’s view on the Penrose tiling

Abstract

We demonstrate the potential of Kurt Bruckner’s ‘addition algorithm’, which is based on the substitution rule for the generation of the Robinson triangle tiling, a variant of the Penrose tiling. The artist Kurt Bruckner developed his straightforward approach intuitively for the creation of quasiperiodic ornaments. This versatile method can be used for the construction of achiral, homochiral and racemic quasiperiodic ornaments, as well as for the generation of decorated two-level (two-color) Penrose tilings. Therefore, the underlying tiling is always the same kind of Penrose tiling, which is invariant under the action of specific mirror and black/white mirror operations in contrast to unit tiles that are decorated in specific ways. Compared to the underlying classical substitution method the advantage of Kurt Bruckner’s approach is its simplicity and versatility for the creation of decorated tilings. Using a vector graphics editor, large and arbitrarily complex quasiperiodic ornaments can be easily generated manually.