Reconnoitring computational potentials of the vault-like forms: Thinking aloud on muqarnas tectonics

Abstract

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.

دراسة تحليلية لتشکيلات المقرنصات في العمارة الإسلامية باستخدام المحاکاة الرقمية

“…[3] Throughout history, the transition from square planning to circuit planning in three-dimensional has been a difficult subject not only for craftsmen but also for philosophers, mathematicians, and designers. [22] This study enhances a comprehensive understanding of muqarnases with their historical, philosophical, and conceptual backgrounds, on the one hand, structural and algorithmic principles, to reveal the internal logic of these complex geometric elements. [22]…”

“…New prospects for muqarnas design have given rise to the widespread use of digital models and manufacturing techniques, which have given rise to new prospects for the design of muqarnas. [22] The formation of three-dimensional muqarnas provides new insights for mathematics to analyze the shape outside aesthetic and ornamentation features in the digital age. The emerging digital design approach and computational thinking explore innovative possibilities of muqarnas in forming spaces and developing tourism.…”

A Study on Measuring Complexity in Muqarnas Patterns

“…It is known that, in traditional muqarnas making, it was a common tendency to begin with 2D pattern generation and afterwards building the 3D form through plane projections. The arrangements of muqarnas elements were mostly symmetrical and the niches were also equal (Alaçam et al 2017).…”

“…In traditional way of making, beginning with a two-dimensional pattern and projecting this pattern into three-dimensional form is crucial. Non-interlocking three-dimensional forms are used to construct the elevated third-dimensional muqarnas based on referenced two-dimensional muqarnas pattern drawing (Alaçam et al 2017). In this sense, a muqarnas organization and its projection onto two-dimensional planar surface carries a high level of spatial (Özdural, 1990), structural (Notkin, 1995;Dold-Samplonius & Harmsen, 2015), geometrical (Notkin, 1995), and topological (Alaçam et al 2017) complexity.…”

A generative design case study for UAV-based assembly and fabrication: parametric analysis and synthesis of Iranian-Islamic Muqarnas

“…Muqarnas were invented in the early 10th century and they have changed a lot over time in terms of design and construction methods in different geographical areas, from east of Asia until Spain and west of Africa (Kazempourfard, 2014). Muqarnas is considered as a complex kind of decorations that initially aim to generate threedimensional facades involving shadow and light and create unparallelled lines, and secondly to develop more surfaces to apply more micro decorations (Alaçam et al, 2017).…”