This study sheds light on a holistic understanding of muqarnas with its historical, philosophical and conceptual backgrounds on one hand and formal, structural and algorithmic principles on the other hand. The vault-like Islamic architectural element, muqarnas, is generally considered to be a non-structural decorative element. Various compositional approaches have been proposed to reveal the inner logic of these complex geometric elements. Each of these approaches uses different techniques such as measuring, unit-based decoding or three-dimensional interpretation of two-dimensional patterns. However, the reflections of the inner logic onto different contexts, such as the usage of different initial geometries, materials or performative concerns, were neglected. In this study, we offer a new schema to approach the performative aspects of muqarnas tectonics. This schema contains new sets of elements, properties and relations deriving partly from previous approaches and partly from the technique of folding. Thus, this study first reviews the previous approaches to analyse the geometric and constructional principles of muqarnas. Second, it explains the proposed scheme through a series of algorithmic form-finding experiments. In these experiments, we question whether 'fold', as one of the performative techniques of making three-dimensional forms, contributes to the analysis of muqarnas in both a conceptual and computational sense. We argue that encoding vault-like systems via geometric and algorithmic relations based on the logic of the 'fold' provides informative and intuitive feedback for form-finding, specifically in the earlier phases of design. While focusing on the performative potential of a specific fold operation, we introduced the concept of bifurcation to describe the generative characteristics of folding technique and the way of subdividing the form with respect to redistribution of the forces. Thus, in this decoding process, the bifurcated fold explains not only to demystify the formal logic of muqarnas but also to generate new forms without losing contextual conditions.