Statistics of 'worms' in Penrose tilings

Publisher Website
Google Scholar
Abstract
Certain structural aspects of two-dimensional Penrose tilings are studied using de Bruijn's pentagrid picture. The authors discuss the statistics of hexagons, decagons and 'worms' (sequences of adjacent hexagons bounded by two decagons). They show that within the discrete framework considered here, phason modes and structural transformation modes are located along particular 'worms' and they derive the spatial distribution of the latter.