Octagonal picture languages

Abstract

A picture grammar is the generation of pictures through description of words. The picture is represented in matrix form of finite alphabet using various grammars. Picture grammar can be achieved through context free grammar or regular expressions. Here we extend hexagonal picture language to octagonal picture language thereby introducing octagonal Wang system (OWS) and octagonal picture language. Previously hexagonal Wang system coincides with hexagonal tile system. Here we determine the same using octagon that is to check the coincidence of octagonal Wang system and octagonal tile system. We use octagons since they form several interior angles that lead to the base for drawings and architectural planning.