Hexagonal Picture Languages Generated By Assembling Hexagonal Tiles

Abstract

We propose a new formalism for generating hexagonal picture languages based on assembling of hexagonal tiles and hexagonal dominos that uses rules having two sites namely context site and a replacement site. More briefly a hexagonal picture can be generated from a finite set of initial hexagonal picture by iteratively applying the rules from a given set of rule sequences called a Hexagonal Tiling Rule System (HRTS). We claim that this HRTS system have a greater generative capacity than Hexagonal Tiling System (HTS), even in the case of one letter alphabet. This is possible due to the repeated use of replacement site.