Topological approaches to the study of Seljuk architectural ornaments: insights from a mosque, madrasa, and palace in Anatolia

This study examines the topological properties of architectural decorations from the Anatolian Seljuk period, with a focus on the Malatya Grand Mosque (1224), the Kubadabad Palace (1227), and the Konya Karatay Madrasa (1251). By employing knot theory and two-structures, the research delves into the intricate interlaced motifs found in tile work and other decorative elements. The introduction of mathematical invariants, such as crossing numbers, linking numbers, and bracket polynomials, serves to classify and compare these historical patterns. The findings reveal the remarkable sophistication of Seljuk architecture, which infused their work with profound cultural and cosmological symbolism. This research beautifully bridges art history and mathematics, providing a fresh perspective on the structural and symbolic complexity of Seljuk architectural ornamentation. Ultimately, the results highlight the timeless significance of these designs, inspiring both contemporary art and science.