THE MATHEMATICS OF MUQARNAS: COMPUTATIONAL APPROACHES TO COMPLEX GEOMETRIES

Abstract

With the advancement of technology and CAD software, we are now able to design sophisticated geometries and modeling forms for assessments. Instead of the “box form” which was previously considered the most efficient form in our world, complex geometries are now considered for their structural superiority and aesthetics.

Muquarnas have been an architectural element used in traditional Islamic and Persian architecture that has a complex mathematical system consisting of polygonal geometries. They are a type of corbel mostly for decorative purposes and applied to domes, squinches, arches and vaults. Muqarnas are mostly constructed by extruding a 2D plan projection, which follows the logic of Islamic geometric patterns. With the aid of computer generative design and parametric modeling, we can produce advance and modern designs of muqarnas compositions. Muqarnas have the potential to be structural when integrated with form design and creating a new spatial experience based on the scale.

Muqarnas can be a source of inspiration and there are mathematical rules and algorithm governing its construction. Since there is disconnected knowledge being passed down, methods to construct these complex forms are being uncovered again and made sense from the hand drawn methods to digital and parametric modeling techniques. It is the ability to link geometry, tessellation and architecture that may give new insights to the construction of complex forms.