Exploring Muqarnas Generation Through Graph Theory: Node and Surface-Based Approaches

Computational theories and technologies have significantly transformed traditional perspectives on design and creativity. Extraordinary three-dimensional Muqarnas are among the cultural heritages that face extinction. This study provides a comprehensive understanding of muqarnas by examining its historical, philosophical, and conceptual foundations alongside its formal, structural, and algorithmic principles. After reviewing prior approaches to analyzing the geometric and constructional aspects of muqarnas, the paper presents a parametric and generative application of graph-theoretical principles for muqarnas design. The method is applied to generate muqarnas structures through node-based and surface-based approaches, utilizing the two-dimensional plan of the Mihrab of Hakim Mosque in Isfahan. The proposed method enables both the reproduction of existing muqarnas and the generative design of new three-dimensional structures, thereby contributing a computational framework that supports future analytical and reconstructive studies.