The Geometric and Algorithmic Decomposition of the Main Gate Muqarnas in the Mosques Designed by Architect Sinan in Istanbul

Abstract Beneath the intricate surfaces of muqarnas—key elements of Islamic architecture—lie complex two- and three-dimensional geometric systems. Despite their widespread historical use, these geometric characteristics remain insufficiently examined. This research offers a comparative analysis of thirteen muqarnas from the main gates of Istanbul mosques, all designed by the architect Sinan. Plans and elevations were generated with their constituent cell types, after which each muqarnas was algorithmically encoded and analyzed in three dimensions. The study identifies notable compositional parallels among several main gate muqarnas, evident in both their plans and three-dimensional configurations, despite minor internal variations. Additional similarities appear in star patterns, stratification, and cell typologies, while rare forms such as oyster and nail cells are also documented.