Islamic geometric patterns constitute one of the most significant ornamental features of Islamic architecture and have been the subject of numerous studies concerned with their classification, analysis, and reconstruction. However, most previous research has focused on the abstract geometric structure and generative logic of these patterns, while their modes of visual manifestation and execution in historical works have received comparatively less independent attention. By introducing the concept of “articulation” as distinct from “design,” the present study investigates different modes through which girih patterns are expressed and displayed in Iranian Islamic architecture. The research aims to identify and classify different articulation types, extract the geometric and algorithmic rules governing the visual appearances of girih patterns, and to evaluate the extent to which these rules correspond to historical examples.

The study adopts a logical argumentation method combined with geometric analysis. Research data were collected from library sources, historical monuments, and drawings produced by traditional master craftsmen. Subsequently, the geometric procedures that generate different appearances were modeled algorithmically in Grasshopper, and the results were compared with historical examples. The findings indicate that the visual appearances of girih patterns can be classified into six principal categories: alternating tiles, line thickening, edge offsets, emphasized intersections, interweaving, and Shah-Girih. Algorithmic modeling revealed prerequisite relationships and specific geometric requirements for the underlying design. Moreover, traditional craftsmen were not merely executors of geometric rules. By providing a new framework for analyzing girih patterns, this study contributes to the generation of new patterns in Islamic architecture.