Algorithmic Decomposition of Geometric Islamic Patterns: A Case Study with Star Polygon Design in the Tombstones of Ahlat

Abstract

The current practice is to make the mathematical analysis of many Islamic patterns in 2D; however, since such patterns actually have 3D features, the third dimension must also be considered. Indeed, the three-dimensional features of the patterns made by carving on stone are very numerous. In this work, it is proposed to perform a 3D mathematical analysis of patterns of this type by algorithmic decomposition. In the cemetery of Ahlat, which is an existing monument, a tombstone with high three-dimensional features, designed by Asil b. Veys (Uveys), was chosen for algorithmical analysis. The mathematical design rules of the star polygon pattern in the selected monument were determined, as based on the shape grammar theory. The probable rules for the creation of the star polygon pattern in this study were produced simultaneously in the computer environment using a visual programming language and a 3D parametric pattern generator of the pattern was created.