Presenting a Method to Generate Existing and Novel Girihs (Islamic Geometric Patterns) for All Systems and Families Based on 7-Fold Patterns

Abstract

Girih s (Islamic geometric patterns) are an example of graphic designs in architectural spaces. Some wonderful Islamic geometric patterns are produced by 7-fold polygonal sub-grid elements. In this paper, after examining 7-fold patterns, we will present a method based on the symmetry groups theory to construct 7N-point girih s. This method is based on a step-by-step process from constructing the minimal essential information (template motif) needed to generate a particular symmetry type within the fundamental region to replicating the unit girih in a two-dimensional plane based on a suitable net. Finally, we will present a notation system for the method of this paper consisting of generative parameters to construct girih s of the 7-fold system and other Bonner’s systems classified into four families: acute, middle, obtuse, and two-point. • This paper aims to discover the generative parameters to create Islamic geometric patterns for all systems (including the 7-fold system) and families (including the 2-point family). • Our proposed method is based on the symmetry groups theory and is a rail-based method. • In this paper, we have paid attention to the orientation of girihs which was not considered in previous works as a parameter.