The configurational entropy of two-dimensional random Penrose tilings

Abstract

The configurational entropy of two-dimensional random tilings of Penrose rhombi has been calculated by two methods. Estimating the configurational degeneracy by determining the number of available configurations of each tile during physical model building gave an entropy of 0.495k per tile for a compositionally unconstrained tiling. Geometrical models based on the number of configurations around each vertex without correlations between them, gave higher values.