A novel algorithm for a quasiperiodic plane lattice with fivefold symmetry

Abstract

Conventionally, Penrose tilings with fivefold symmetry are constructed with the aid of two characteristic rhombic tiles and sets of rules based on either matching of markings on the tiles or their subdivision. Both these procedures involve decision making when tiling is to be done extensively. In the present communication, a fool-proof method of producing Penrose tilings using a set of operations that can be repeated ad infinitum is described. The steps in the present procedure are akin to conventional crystallographic operations and can be expressed in simple mathematical terms which bring out some interesting aspects of Penrose tilings.