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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.

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... Muqarnas (used ornaments), indeed, is one of the most sophisticated ornaments, which has been considered a symbol of Islamic architecture [35]. Muqarnas originally belongs to the early 10th century, and they have changed to a great extent over time in terms of their design and construction methods in different geographical areas, from East Asia to Spain and West Africa [36]. It is considered a complex element for decoration that initially aims to create 3D facades involving shadow and light by using unparalleled lines and to develop more surfaces to apply more micro decorations [37]. ...
... (used ornaments), indeed, is one of the most sophisticated ornaments, which has been considered a symbol of Islamic architecture [35]. Muqarnas originally belongs to the early 10th century, and they have changed to a great extent over time in terms of their design and construction methods in different geographical areas, from East Asia to Spain and West Africa [36]. It is considered a complex element for decoration that initially aims to create 3D facades involving shadow and light by using unparalleled lines and to develop more surfaces to apply more micro decorations [37]. ...
... The next step in the discussion is studying the effect of constant and dynamic external shading on useful daylight. To be more precise, the second set of simulation results, such as daylight autonomy analysis, room illumination in three windowless modes (base model), and fixed shading, as well as dynamic and responsive parametric shading to establish a useful daylighting interval between 1800-300 lux based on fundamental studies, [36] has been analyzed for more space in the room ( Figure 10). The next step in the discussion is studying the effect of constant and dynamic external shading on useful daylight. ...
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(1) Background: considering multiple, and somehow conflicting, design objectives can potentially make achieving a high-performance design a complex task to perform. For instance, shading devices can dramatically affect the building performance in various ways, such as energy consumption and daylight. This paper introduces a novel procedure for designing shading devices as an integral part of daylightophil architecture for office buildings by considering daylight and energy performance as objectives to be optimal. (2) Methods: to address the topic, a three-step research method was used. Firstly, three different window shades (fixed and dynamic) were modeled, one of which was inspired by traditional Iranian structures, as the main options for evaluation. Secondly, each option was evaluated for energy performance and daylight-related variables in critical days throughout the year in terms of climatic conditions and daylight situations (equinoxes and solstices including 20 March, 21 June, 22 September, and 21 December). Finally, to achieve a reliable result, apart from the results of the comparison of three options, all possible options for fixed and dynamic shades were analyzed through a multi-objective optimization to compare fixed and dynamic options and to find the optimal condition for dynamic options at different times of the day. (3) Results: through different stages of analysis, the findings suggest that, firstly, dynamic shading devices are more efficient than fixed shading devices in terms of energy efficiency, occupants’ visual comfort, and efficient use of daylight (roughly 10%). Moreover, through analyzing dynamic shading devices in different seasons and different times of the year, the optimal form of this shading device was determined. The results indicate that considering proper shading devices can have a significant improvement on achieving high-performance architecture in office buildings. This implies good potential for daylightophil architecture, but would require further studies to be confirmed as a principle for designing office buildings.
... 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. ...
... 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. On the contrary, it is possible to achieve complexity in a muqarnas application based on simple assumptions and rules. ...
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Muqarnas forms and patterns carry a high level of spatial, structural, geometrical, and topological complexity. Having a high-level complexity and its definition through simple geometrical and mathematical relations makes muqarnas rich source of information content. By using entropy, which is one of the most important components of information theory, the complexities of built environments or building elements in various scales can be measured. Within the scope of this study, three entropy-based methods were used to calculate the complexities of the muqarnas patterns located in the portal of the Buruciye Medrese, which was built in the Seljuk Period in Sivas. In this study, only shape factor was chosen among various factors for calculation and a layer-based representation was used to represent muqarnas patterns. As a result of the study, it was seen that calculated entropy value changed when the muqarnas pattern had different levels of detail. In addition, it was observed that the entropy values of the discrete layers differed from each other.
... The three-dimensional characteristics of Islamic motifs, such as double-layered designs and weaves, have also been investigated (Necipoğlu 1996;Bonner 2003;Rigby 2005). Muqarnas, a distinct architectural element, has been analysed based on the folding principle (Alaçam et al. 2017). Some studies have also developed new designs inspired by these patterns. ...
Article
This study investigates the traditional religious architecture through the examination of Armenian Khachkar motifs at Varagavank Monastery in Van, Turkey. “Khachkar” is pivotal within Armenian religious architecture, denoting a minor architectural style and symbolising “cross-stone.” The study employs a parametric identification method to extract the fundamental unit of Khachkar motifs and develop a model to explore various variations. By utilising a mathematical analysis, the research showcases the practicality of this approach in facilitating diverse transformations within intricate designs. The study offers a comprehensive analysis of the built heritage found in Armenian religious architecture, enhancing the understanding and appreciation of these cultural artefacts. The findings of this study on Khachkars make valuable contributions to architectural research and deepen our comprehension of their significance in Armenian religious art.
... This is because of the use of computer-aided technologies and computational methods to either perform analysis or develop new patterns. Alaçam [22] discussed the emergence of digital design approaches and computational thinking to explore the unvisited potentials of muqarnas. Albert et al. [2] developed a new computational method that could possibly create pattern designs and compare patterns between different cultures. ...
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Recently, scholars have embraced sustainability as a crucial concept deeply ingrained in architectural designs, particularly Islamic geometric patterns (IGP). These patterns hold significance in reflecting Islamic history, identity, and culture. This systematic review explores how scholars have integrated IGPs into modern design, considering the sustainability aspect. The Preferred Reporting Items for Systematic Reviews (PRISMA) reporting checklist was used due to its organized structure as a guide to conduct this review (2012–2022). Data was collected through recognized databases (i.e., Scopus and ProQuest) that house a wide array of journals and publications. Selected journals were categorized based on sustainability pillars—environmental, economic, social, and cultural. In addition, case studies from the region are discussed, as studies didn’t explicitly explore the connection between sustainability and the use of Islamic geometric patterns in modern design. Findings indicate that papers predominantly discuss the positive effects on environmental and economic sustainability through IGP implementation. Conversely, social sustainability received comparatively less attention from scholars. Case studies showed that most building designs in the Middle East use IGP to conserve Islamic history and identity, especially in the United Arab Emirates (UAE). This review sheds light on the potential of geometric patterns as a vehicle for sustainable design and contributes to the broader discourse on sustainable architecture.
... The same authors initially generalized the earlier method, which was limited to rectangular muqarnas compositions, covering the construction of muqarnas domes through the Almoravids period until now [170]. Also, Alacam et al. [171] investigated the performative potential of a specific fold on muqarnases and developed computational strategies for form-finding and analysis of vaulting structures. Maarouf and Zeid [172] formulated a parametric generative process Ranjazmay Azari et al. ...
Article
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Currently, there is a tendency to use Islamic Geometric Patterns (IGPs) as important identities and cultural elements of building design in the Middle East. Despite high demand, lack of information about the potential of IGPs principles have led to formal inspiration in the design of existing buildings. Many research studies have been carried out on the principles of IGPs. However, comprehensive studies relating to new possibilities, such as structure-based, sustainable-based, and aesthetic-based purposes, developed by computer science and related technologies, are relatively rare. This article reviews the state-of-the-art knowledge of IGPs, provides a survey of the main principles, presents the status quo, and identifies gaps in recent research directions. Finally, future prospects are discussed by focussing on different aspects of the principles in accordance with collected evidence obtained during the review process.
... Circular spaces or transitions between rectilinear and circular spaces can be generated with this modular method to provide the easy to construct dry-fit blocks. Additionally, a further generalization of the method has the potential to produce re-configurable vaulting systems (Alaçam et al. 2017). As this methodology was initially developed in the context of the MSc EARTHY Studio at TU Delft (Nourian et al. 2020), these blocks were originally intended to be made of cast earth blocks. ...
Conference Paper
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In contrast to the contemporary aesthetic account, Muqarnas are geometrically complex variations of Squinches used for structural integration of rectilinear geometries and curved geometries. Inspired by the historical functionality of Muqarnas, we present a generalized computational workflow for generating dry-fit stacking modules from two-dimensional patterns in order to construct a dome. Similar to Muqarnas these blocks are modular in nature, complex in geometry, and compression-only in their structural behavior. We demonstrate the design of such structures based on the exemplary Penrose pattern and showcase the variations & potentials of this method in comparison to conventional approaches.
... Between 2005 and 2015, researchers investigated the different representations of muqarnas in computer environment and performative features (structural and acoustic) of muqarnas by using computer aided tools (Harmsen, 2006;Hensel, 2008;Abbasy-Asbagh, 2013). Since 2015, there have been studies aiming to interactively modify and optimize the performative properties of muqarnas with generative approaches (Alaçam and Güzelci, 2016;Alaçam et al. 2017;Alaçam and Güzelci, 2018). Recently, studies have been conducted in which muqarnas are analyzed with objective methods such as entropy and shape grammar (Güzelci and Alaçam, 2019;Agirbas and Yildiz, 2020;Güzelci et al. 2020;). ...
Conference Paper
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The experiments of form and technique in the Early Ottoman Period, turned into the search of perfection in architecture, with entering the Classical Ottoman Period in the 16th century. This period was known as the era of masterpieces in Ottoman Architecture. Portals have always been an essential element of these buildings, in which muqarnas patterns are used as elements of decoration to emphasize the entrance. As the most important architect of that era, Sinan used muqarnas patterns in his buildings remarkably, with many different styles. According to Ayla Ödekan, the geometrical schemes of the period before the 16th century, especially the Bayezid II era, affected the muqarnas organizations of Sinan. In this paper, based on Ödekan’s hypothesis, 2-dimensional muqarnas patterns of portals from Bayezid II and Sinan era, are evaluated through a comparative analysis. To get a better understanding on the differences and similarities of the muqarnas patterns, 3 examples from each period (6 in total) are selected. The sample set covers Edirne Beyazıt Mosque (1487), Adana Yağ Mosque (1501) and İstanbul Beyazıt Mosque (1506) from 15th and early 16th century and İstanbul Süleymaniye Mosque (1557), Edirne Selimiye Mosque (1575), and Manisa Muradiye Mosque (1585) from Sinan era. Both hand drawings made by Fatin Uluengin and drawings made by Shiro Takahashi on the computer were used to compare selected muqarnas. In the method suggested in this paper, muqarnas patterns are considered as a source of information which might lead different ways of readings through a geometrical analysis. Further to redrawing the 2- dimensional plan projections of the selected samples, muqarnas patterns are analyzed. During the analysis process, three features became more prominent as: muqarnas schemas, initial geometry and angular organization. It is considered that the outcomes of this study will provide valuable insights for architects and art historians, and researchers from related fields.
... 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 (1). Muqarnas is considered as a complex kind of decorations that initially, aim to generate three-dimensional facades involving shadow and light and create unparalleled lines, and secondly to develop more surfaces to apply more micro decorations (2). ...
Conference Paper
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This study proposes a DfMA (from design to assembly) based on Unmanned Aerial Vehicle (UAV) and uses Iranian-Islamic Muqarnas as the case study due to their geometric modularity. In Islamic architecture, different geographic regions are known to have used various design and construction methods of Muqarnas. There are four main specifications of the Muqarnas that define to which category they belong; first, its three-dimensional shape, that provides volume. Secondly, the size of its modules is variable. Third, its specific generative algorithm. And finally, the 2-dimensional pattern plan that is used in the design. First, this study presents thus a global analytical study that drives a generative system to construct Muqarnas, through a careful balance of four specifications. In this second step, the paper reports the result of using a parametric tool, Grasshopper and parametric plugins, for creating a generative system of several types of Muqarnas. This synthetic translation aims at expanding our understanding of parametric analysis and synthesis of traditional architecture, advancing our understanding towards using parametric synthesis towards UAV-based fabrication of Muqarnas, by taking advantage of their inherent repetition and recursion.
... Harmsen (2006) and Dold-Samplonius and Harmsen (2005) Muqarnas, which appear formally complex, are in fact formed according to simple rules (Dold-Samplonius 1992; Gherardini and Leali 2016). Özdural (1991) and Alacam et al. (2017) agree that muqarnas are created by sequentially raising the plan drawing from 2D to 3D. Uluengin (2018) and Takahashi (2019) also analysed the muqarnas, starting from the ground projection plan. ...
Article
Many muqarnas contain star polygons in their ground projection plans. Such star polygons usually have equal edge lengths. In this study, the geometric background of irregular star polygons with unequal edge lengths, observed in some ground projection plans of muqarnas, was investigated. The plan of the muqarnas at the main gate of the Atik Valide Mosque was examined according to the theoretical framework of shape grammars. As a result of the case study, it was concluded that ellipse grids were used to form the layout of the ground projection plan of muqarnas. It was shown that stars placed in the areas formed by the intersections of the ellipse grid formed irregular polygons naturally. In addition, a parametric 3D geometry of muqarnas was obtained by considering a geometric decomposition of the analysed ground projection plan of muqarnas.
... Moreover, Cenani and Cagdas (2007) explored new methods for the generation of three-dimensional forms, based on Islamic patterns. Also, Alacam et al. (2017) analysed muqarnas by folding principle. In addition, Kaplan and Salesin (2004) have developed a tool that produces new designs by bringing Islamic patterns into the third dimension (by translating the patterns into the hyperbolic plane), and hence, in their attempt to move the patterns into the third dimension, they were able to go one level further up from this. ...
Article
The current practice is to make the mathematical analysis of many Islamic patterns in 2D; however, since such patterns actually have 3D features, the third dimension must also be considered. Indeed, the three-dimensional features of the patterns made by carving on stone are very numerous. In this work, it is proposed to perform a 3D mathematical analysis of patterns of this type by algorithmic decomposition. In the cemetery of Ahlat, which is an existing monument, a tombstone with high three-dimensional features, designed by Asil b. Veys (Uveys), was chosen for algorithmical analysis. The mathematical design rules of the star polygon pattern in the selected monument were determined, as based on the shape grammar theory. The probable rules for the creation of the star polygon pattern in this study were produced simultaneously in the computer environment using a visual programming language and a 3D parametric pattern generator of the pattern was created.
Chapter
This paper examines the computational relation between the pattern designs and the construction of historical brick wall panels. The general aim is to devise a method to integrate the geometric and constructional aspects of architectural knowledge in the digital modeling of heritage as part of the increasing interest and need for putting technology to use in practices of conservation and cultural sustainability. Parametric shape rules are computation tools and means for exposing and understanding the three-dimensional relations between the parts of an architectural structure as well as its generative system. We have been analyzing a particular series of brick panels from the Anatolian Seljuk period. In this genre, panels are composed of both plain and glazed bricks of different colors and shapes, materializing abstract geometric patterns in the way that they are placed vertically and horizontally. The plural ways in which different parts and wholes can be perceived on one panel are due to not only the constructional relations between individual bricks but also the geometric motifs formed by the groups of bricks. In this study, we expand the breadth and variety of the examples for more in-depth analysis. Existing architecture and construction history literature on the brick structures of the period provide inferences on the types of brick bonds, sizes, shapes, and surface finishing. Studying photographs, photogrammetry-based models, and survey drawings, we identify the parameters of this type of bricklaying based on these inferences and define the smallest number of shape rules either as pattern rules or brick rules, required for recreating the panels. Local deformations and minor divergences observable in the data are disregarded. The sequential application of sets of pattern rules and brick rules simulates the reconstruction of existing and novel panels in the said genre. We have tested and validated the syntactic accuracy of our grammar through an existing shape interpreter. We have also assessed the results of our generative system comparatively with the brick patterns of different panels of the said period and geography. Differently from the existing grammars that make visual styles explicit, the parametric definition and the sequencing of rules in our study facilitate the categorical documentation of the similarities and differences of patterns as part of a physical construction process. The proposed means to document existing structures and their design and construction, in pattern and brick rules, respectively, serves purposes of conservation and restoration and, in turn, the integration of cultural-historical knowledge with contemporary tools provides ground for designers to explore these issues today. Currently limited to flat surfaces, the parameters and rule sets can be expanded in future studies to similar designs observed on surfaces with various curvatures, making an even stronger connection to complex geometries.KeywordsBrick constructionParametricShape grammarsArchitectural heritage
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Recent developments in archeological research extend diverse technological methods for the geometric deciphering and cultural understanding of various historical building components. One of the emerging methods in this field is the development of generative algorithms to develop computational models for the comparative study of variation among different structures belonging to a common era, style, or region. In this study, we present a novel approach for the computational analysis and parametric modeling of muqarnas found among Anatolian Seljuk architecture in Kayseri and Sivas built in the 13th century. Using four different octagonal muqarnas structures, we outline common generative rules showing recursive stacking of geometric layers, fractal patterns and hierarchical branching of the axis of symmetry. A recursive algorithm is developed that can offer a generative study of muqarnas structures using proportions based on the ‘silver ratio.’ The development of the algorithm is presented through rules and variations that can offer a novel perspective for the geometric understanding and categorization of muqarnas in the region.
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As a historical and ornamental building element, muqarnas are widely found among the entrances of madrasas, mosques, and hans in Anatolian Seljuk architecture. In Kayseri (Turkey), muqarnas structures are characterized by symmetrical distribution of patterned geometric layers that presents computational rules for the design and construction of these ornamental structures. The presented research focuses on 12 unique muqarnas structures that are analyzed through a computational methodology combining photogrammetry, three-dimensional modeling, symmetry, and graph theory. The computational analysis shows that Seljukid muqarnas exhibit patterned branching of the symmetry axis between layers radiating from their geometric center. Using the modeled samples, the article analyzes inherent symmetry rules and growth patterns while offering a novel way of studying, modeling, and categorizing muqarnas.
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Le dialogue avec la tradition est toujours un enjeu majeur dans la société iranienne d’aujourd’hui. Différents mouvements architecturaux mêlant l’architecture traditionnelle et l’architecture contemporaine se sont succédé ces dernières décennies en Iran. Par ailleurs, nous assistons au développement de plus en plus rapide du « digital » dans tous les aspects de la discipline architecturale, ce qui a comme conséquence le rapprochement de la conception et de la fabrication. L’émergence des outils numérique en architecture, notamment les outils paramétriques et algorithmiques, facilite et encourage le recours à la géométrie (complexe).L’un des fondements de l’architecture traditionnelle iranienne est la géométrie, dont la présence est fort visible au sein des éléments structurels et décoratifs. C’est donc la réémergence de la géométrie grâce au numérique qui nous a amenés à nous pencher sur la réinterprétation du Muqarnas pour réfléchir à sa transposition dans le contexte contemporain iranien. Le Muqarnas est un élément à caractère spatial et géométriquement complexe de l’architecture iranienne en période islamique, à la fois structure et ornement. Dans cette démarche de génération de nouveaux Muqarnas, nous ferons appel aux outils paramétriques et algorithmiques qui ouvrent de nouvelles perspectives. C'est l'objet premier de ce travail de recherche que de savoir comment et avec quelle approche réinterpréter le Muqarnas à l’aide des outils numériques. En prenant connaissance des études antérieures sur les Muqarnas, nous avons acquis la conviction qu'une étude historique de l’évolution des Muqarnas nous permettrait de structurer notre démarche de réinterprétation avec des outils numériques.Il s'agit ainsi, dans un premier temps, de réinvestir l’histoire des Muqarnas en étudiant leur évolution, en particulier dans sa dimension géométrique. Cette étude nous permettra de déduire des « principes géométriques », essentiels pour la réinterprétation numérique des Muqarnas. Les principes géométriques issus de l’étude historique sont, dans un deuxième temps, intégrés dans plusieurs approches génératives numériques. Chaque approche présente une logique algorithmique et paramétrique de génération des Muqarnas dont on évalue les avantages et les limites.Enfin, une troisième partie est consacrée à la mise en œuvre des modèles numériques issus des différentes approches génératives et à la réalisation de prototypes à différentes échelles
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Purpose This study proposes a DfMA (Design for Manufacture and Assembly) based on unmanned aerial vehicle (UAV) and uses Iranian-Islamic Muqarnas as the main case study due to their geometric modularity. In Islamic architecture, different geographic regions are known to have used various design and construction methods of “Muqarnas”, a type of decorated dome. Design/methodology/approach The paper presents a study on parametric analysis of the Iranian-Islamic Muqarnas and analyses its components, geometric relations and construction methods that should be considered when constructing one. This study aims to use the Muqarnas analysis as a driver to generate a DfMA basis on the UAVs and parametric fabrication. In Islamic architecture, different geographic regions use various design and construction methods of Muqarnas. There are four main parameters of the Muqarnas that define their classification; first, their three-dimensional shape, that provides volume. Second, the size of their modules is variable. Third, their own specific generative process-algorithm, and finally, the two-dimensional pattern plan that is used as a basis in the design. Thus, the authors present a global analytical study that drives a generative system to construct Muqarnas, through a careful balance of the four parameters. Findings This study thus presents a global analytical study that drives a generative system to construct Muqarnas, through a careful balance of four specifications. The paper reports the result of using a parametric tool, Grasshopper and parametric plugins, for creating a generative system of several types of Muqarnas. This synthetic translation aims at expanding our understanding of parametric analysis and synthesis of traditional architecture, advancing our understanding towards using parametric synthesis, with the scope to fabricate and assemble modules towards UAV-based fabrication of Muqarnas. To do so, the authors are taking advantage of their inherent repetition and recursion. Originality/value In the first step, this paper reviews studies on traditional Muqarnas (both Iranian and non-Iranian) and relevant parametric approaches. In the second step, the study aims to create a general generative system for Muqarnas. The creation of a generative system for Muqarnas is driven towards the creation of three-dimensional fabrication of their components so that these are assembled automatically using a swarm of UAVs. This particular drive imposes specific constraints in the parametric system, as the assembly of the final components, the authors posit, can only take place in a pick and place fashion.
Article
This paper presents a comparative case study on the digital modeling workflows of a particular muqarnas system. After the literature review and the definition of the context, several digital modeling workflows were described as element-based, tessellation-based and block-based workflows by using computer-aided design and parametric modeling software. As the case study of this research, these workflows were tested on a muqarnas design located at the Sultanhanı Caravanserai in Central Anatolia. Then, workflows were compared according to three qualities: analytical, generative, and performative. The outcomes of element-based workflow has more analytical solutions for the study, where tessellation-based workflow has more generative potential and block-based workflow is more performative.
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Throughout history, mathematicians from different cultures and places traced other scholars’ work to make a contribution and extend the knowledge of the geometry field. In the Islamic world, artisans combine the theoretical knowledge about geometry and making skills to build more sophisticated and complicated geometric patterns. Today, the underlying principles of geometric patterns are still a research subject of many physicists and mathematicians. Geometric patterns are used both in design and construction phases of muqarnas which is a specialized spatial element in Islamic Architecture. In the scope of this study, after a comprehensive analysis, new muqarnas patterns are generated by using algorithms.
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Muqarnas is one of the original and iconic patterns in Iranian architecture, which has been identified and developed over various periods and constructed in a variety of forms by Iranian architects. Different patterns of muqarnas are observed in various typologies of Iranian architecture, such as tombs, mosques and bazaars. This study aims to answer the question: what are the similarities and differences between muqarnas patterns in Tabriz historic bazaar? To find the differences and similarities, the geometry of muqarnas applied in various parts of Tabriz historic bazaar is analyzed. Despite apparent similarities, muqarnas ornaments seem to have different patterns in accordance with different spaces; resulting in a variety of designs. This study seeks an applied objective and employs a descriptive-analytical method. The information necessary for the study is collected through library research, field surveys (observations) and geometric drawings of muqarnas patterns prepared by AutoCAD and 3Ds Max. Since Tabriz was destroyed by the earthquake in 1779 and most of its buildings, e.g. Tabriz historic bazaar, were constructed during the Qajar dynasty, the study may illustrate the geometric patterns of muqarnas in the Qajar era in Tabriz. The muqarnas ornaments of buildings such as Saheb-al-Amr Mosque, Hojat-al-Islam Mosque, Kacheh CHilar Saray, Haj Safar Ali Mosque-School and the Small Mosque (the Bala mosque) all located in the bazaar are analyzed in terms of formal, static, design and implementation criteria. The findings of this study indicate that the muqarnas ornaments of Tabriz historic bazaar have different types, shapes and positions depending on the land-use of buildings. In religious buildings, muqarnas ornaments were applied in the barrel vaults on altars and the pendentives of domes; but in public spaces, such decorations were constructed in the places overlooking the courtyard and the small iwans (porches) on upper floors. However, the patterns applied in religious buildings were more complex than those of non-religious buildings.
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The history of cross vaults began almost two thousand years ago with a widespread use during the Middle Ages and Renaissance, becoming nowadays one of the most diffused and fascinating structural typologies of the European building cultural heritage. However, conversely to the undeniable excellence achieved by the ancient masons, the structural behaviour of these elements is still at the centre of the scientific debate. In this regard, with the aim of reviewing the knowledge on this subject as a concise and valuable support for researchers involved in conservation of historical buildings, with a focus on design rules and structural analysis, the present study firstly introduces the cross vaults from a historical perspective, by describing the evolution of the main geometrical shapes together with basic practical rules used to size them. Then, the paper deals with the subsequent advancements in structural analysis methods of vaults, until the development of modern limit analysis.
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In the 15th and 16th centuries a peculiar type of Late-Gothic vault lacking symmetry about longitudinal and transversal axes of the plan appears in at least thirty two buildings throughout Europe; the oldest examples could be located in Poland. They are tierceron vaults with diamond shaped liernes, where the main keystone and the whole or part of diagonal ribs are absent. A number of written European sources include instances of this type of vault: the Frankfurt Lodge Book of Master WG (c. 1560-1572), the Wiener Sammlungen collection (spanning from mid-15th century and the beginning of 16th century) and the Musterbuch of Hans Hammer (last decades of the 15th century). The design of this kind of vault is not simple; it does not seem to arise from a mere process of ribs multiplication. Although some types of Late Gothic vault were developed in particular countries, master masons travelled throughout the continent, an a permanent exchange took place amongst the different lodges. In many occasions, conscious copies of models were likely made, perhaps reflected in travel sketchbooks nowadays missing. Lacking other documents, a method to go beyond superficial resemblance and look for deeper connections is to analyze how the geometrical layout for both plan and volume has been addressed, since methods for deriving overall elevation from plan were only exchanged among masons. This paper deals with two examples of this kind of vault that use the same plan layout to span different types of bay: a square one at a corner of the cloister of Basel cathedral (c. 1440-1645), and a rectangular one at the crossing of the church of Bebenhausen Abbey (c. 1467) (fig. 1). This study, supported by a precise data gathering based on crossing-image photogrammetry, is focused on the layout of the rib network. Although both vaults seem to follow the same design, the geometrical construction of plan and elevation is entirely different. The two cases show an advanced use of Gothic design procedures to solve problems easily.
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This paper discusses the design exploration of funicular shell structures based on Thrust Network Analysis (TNA). The presented graphical form finding approach, and its interactive, digital-tool implementation target to foster the understanding of the relation between form and force in compression curved surface structures in an intuitive and playful way. Based on this understanding, the designer can fully take advantage of the presented method and digital tools to adapt the efficient structural system to the specific needs of different architectural applications. The paper focuses on simple examples to visualize the graphical concept of various modification techniques used for this form finding approach. Key operations and modifications have been identified and demonstrate the surprisingly flexible and manifold design space of funicular form. This variety of shapes and spatial articulation of funicular form is further investigated by discussing several built prototypes. This contribution was awarded the 'Best Student Paper' at ACADIA 2013.
Article
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This paper presents a new computational framework based on Thrust Network Analysis (TNA) for the design of funicular structures. Fast and robust solving algorithms enable the interactive exploration of these constrained structural systems. By giving explicit, bidirectional control over the internal force distribution and overall geometry to the designer, free exploration of these statically highly indeterminate systems is made possible. The equilibrium of funicular compression networks is represented by reciprocal diagrams, which visually express the force dependencies between different parts of the structure. By modifying these diagrams in real-time, the designer is able to explore novel and expressive vaulted geometries that are blurring the difference between shapes associated to typical compression-only forms, obtained e.g. with hanging networks, and freeform surface structures. The power of this framework for design is demonstrated by a user-friendly software implementation, which has been used to design and build a freeform, thin-tile masonry vault.
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Performance-oriented design is not without precedent. In the past, architecture responded with great sophistication and beauty to the need to preserve local resources and provide diverse and suitable conditions for human habitation. In the current context of escalating environmental and ecological changes, learning from precedents and developing their potential is becoming increasingly important. However, many architects refuse to look back in fear of returning to an imagined medieval condition, preferring instead to invest in the technologies that lie at the core of the environmental change and spatial and social division, which we may no longer be able to afford. In response to these circumstances, Michael Hensel examines the potential of past approaches to passive environmental modulation as a reworked spatial paradigm for design that interrelates material, spatial and environmental dynamics with dynamic patterns of habitation. Copyright © 2008 John Wiley & Sons, Ltd.
Thesis
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Today digital models for design exploration are not used to their full potential. The research efforts in the past decades have placed geometric design representations firmly at the center of digital design environments. In this thesis it is argued that models for design exploration that bridge different representation aid in the discovery of novel designs. Replacing commonly used analytical, uni-directional models for linking representations, with bidirectional ones, further supports design exploration. The key benefit of bidirectional models is the ability to swap the role of driver and driven in the exploration. The thesis developed around a set of design experiments that tested the integration of bidirectional computational models in domain specific designs. From the experiments three main exploration types emerged. They are: branching explorations for establishing constraints for an undefined design problem; illustrated in the design of a concept car. Circular explorations for the refinement of constraint relationships; illustrated in the design of a chair. Parallel explorations for exercising well-understood constraints; illustrated in a form finding model in architecture. A key contribution of the thesis is the novel use of constraint diagrams developed to construct design explorers for the experiments. The diagrams show the importance of translations between design representations in establishing design drivers from the set of constraints. The incomplete mapping of design features across different representations requires the redescription of the design for each translation. This redescription is a key aspect of exploration and supports design innovation. Finally, this thesis argues that the development of design specific design explorers favors a shift in software design away from monolithic, integrated software environments and towards open software platforms that support user development.
Chapter
The topic of this chapter is the geometry and the construction of vaulted and decorative systems called ‘muqarnas', one of the most typical elements of Islamic architecture. This way of ‘vaulting spaces' or building roof and decorations with a system of regular staircase-elements that break down the surface covering it with simple geometrical figures, so as to make up complex patterns, spreads throughout Arabic countries, leading to the development of several styles, deriving from different generative geometries, and from building techniques and used materials. The reason which accounts for the widespread development of this type of decoration is to be found in the prohibition of the Moslem religion to portray idols or anthropomorphic figures of God, in contrast with the decorative techniques of sculpture and painting characterizing Christian art. The geometrical study which is at the basis of the Islamic art of decorating is arousing new interest and attention as regards the new systems of parametric modeling in computer art, besides opening new perspectives in standardized building techniques with new materials. Full Text Preview Introduction In the new Encyclopaedia of Islam, Doris Behrens-Abouseif (Behrens-Abouseif, 2015) defines muqarnas as: “ a type of decoration typical for Islamic architecture all over the central and eastern parts of the Muslim world; for its counterpart in the Muslim West, see muqarbas”. The term derives from the Greek korwnio, Latin coronis , Fr. corniche , Italian. cornice , (Germ. Karnies ), and it is a popular term, or a mason’s technical term. Wolfhart Heinrichs (Heinrichs, 1997) has some doubts on this accepted etymology. The fact that there is a sin-sad-variation in this word means that the written tradition of its root is not very firm. The Greek word meaning everything that is curved ’, can be used as an adjective meaning ‘ crook-beaked ’, ‘ curved ’ and as a noun referring to anything curved or bent. In the Lisan al-‘Arab , the architectural term muqnrnas is nowhere to be found. Various words are listed under both the sin and the sad form of the root q-r-n-s/s: it is the geographical morphological term qurnas (also qirnas ) which is defined as “s omething like a nose projecting in a mountain. ”. Accepting this, the Arabian verb qarnasa would mean:‘ to furnish a structure with projecting overhanging elements ’ and the past participle muqarnas , consequently, would originally have meant ‘ (a structure) furnished with projecting overhanging elements .’ In the Persian lexicographical tradition the architectural meaning of muqarnas is well documented, as a s tructure which they used to make in the form of the qurnas, the latter being the nose of the mountain . It should be mentioned that in the Persian tradition the architectural term muqarnas often seems to have had a much meaning, covering any kind of cupola with paintings. Although the plausibility of the etymology qurnas - muqarnas cannot be denied, Heinrichs points out that it does have certain weaknesses. However, it also appears to have a number of advantages over its competitors. The term muqarna refers to an often merely decorative element, but at times also a structural one, typical of Islamic architecture and composed of a series of niches embedded within an architectural frame, geometrically connected and forming a three-dimensional composition around a few basic axes of symmetry. This method of building vaults, developed around the middle of the 10th century in north-east Iran and later spread throughout the Arabic world. Figure 1. Leon Auguste Asselineau, 1853: the Hall of the Abencerrages, the Alhambra, Granada – Spain The muqarnas vault is composed of three-dimensional geometrical elements with a multifaceted surface, called blocks , being assembled; juxtaposed in horizontal rows, projecting one on the other, so as to cover apses, domes, hackles, transitions between tambours and domes, minaret projections or wall discontinuities (gates, windows, corner solutions, etc.) mainly for aesthetic reasons, but also for structural purposes, creating, awesome spaces. They look like beehives and sometimes like a cave-like vault with stalactites (only in certain types of muqarnas in the Mamluk and Mozarabic areas, like the Alhambra in Granada. (see Figure 1). The result is a three-dimensional geometric weave of complex multifaceted mesh with an ever-varying pattern strongly affecting the space of vaulted and domed settings, creating in this way extraordinary light/shade effects. At first sight muqarnas look more like sculpture equipment, almost inlay work in surfaces, rather than an architectural motif, although they are the result of a geometric and building process based on the standardization of blocks. Continue Reading
Article
An increasing number of architectural design practices harness the power of parametric design tools. The aim of these tools is to facilitate and control complex building geometries. Parametric design programs such as Grasshopper (GH) for Rhino or Generative Components popularized this approach by providing easy-to-use visual programming environments that integrate with computer-aided design (CAD) packages. A logical next step consists in connecting parametric designs to applications that evaluate non-geometric aspects such as building physics or structural performance. This brings about new opportunities of collaboration between architects and engineers in the early stages of building design. The ease of testing alternatives by tweaking a set of parameters also opens the door for the application of generic optimization algorithms. Karamba is a finite element program geared towards interactive use in the parametric design environment GH. Being a GH plug-in, it seamlessly integrates with the diverse habitat of other third party programs available for GH. These range from building physics applications to genetic optimization engines. In the author's company, Karamba is used in early-stage design, form-finding, and structural optimization. “White Noise”, a mobile exhibition pavilion for the Salzburg Biennale, serves as a case study that shows how Karamba can be used to optimize the structural performance of intricate building geometries.
Article
The purpose of this paper is to propose new three-dimensional translations of the two-dimensional plan of a muqarnas found incised on a plaster slab, discovered in Takht-i Sulayman, Iran, and studied and analysed by Ulrich Harb. Harb proposed a three-dimensional interpretation, but this does not match the general historical context suggested by the contemporary examples of muqarnas forms, nor does it match the logic of the composition suggested by the two-dimensional plan. New three-dimensional decodings of the plan are therefore proposed. The method used by this paper is proposed as a model for later studies concerning the decoding of similar historical patterns.
Article
A trained architect, who works with the Specialist Modelling Group (SMG) at Foster + Partners, Daniel Piker is also the developer of the Kangaroo plug-in for Rhinoceros® and Grasshopper®. He explains how Kangaroo has been devised to simulate aspects of the behaviour of real-world materials and objects in order to modify designs in response to engineering analyses, engendering an intuitive sense of the material world.
Article
This paper analyzes the type of muqarnas (muqamas-corbel) that appeared under some gadrooned domes during the fourteenth and the fifteenth centuries in Egypt and Central Asia.It starts with a study of the gadrooned dome type, its proper terminology, origin, evolution, and sub-types.Then, the paper defines the muqarnas-corbel under gadroons, presents the buildings where it appeared, suggests its formal origins, draws an evolution map, and concludes its regional stylistic attributes.Finally, and based on the above, it decodes two historical muqarnas-corbel drawings into possible three-dimensional forms
Article
Muqarnas, or stalactite vaults, are three--dimensional ornaments, common in the Islamic architecture. They are used in vaults, domes, niches, arches, and as an almost flat decorative frieze. It is the function of a muqarnas to guarantee a smooth transition between straight walls and more curved parts. A muqarnas vault is built from different niche--like elements, arranged in horizontal tiers. One of the main characteristics of muqarnas is its form as a three--dimensional unit that can be represented as a two--dimensional outline. In this study, we focus on the question whether this two--dimensional projection contains all structure information of the three--dimensional muqarnas vault. Explicit definitions are given to create a framework in which we are able to describe the muqarnas structure. Each muqarnas element is described by means of parameters representing its type and measurements together with parameters that describe the position of the element in the muqarnas vault. A graph theoretical approach makes it possible to include the structure information of the three--dimensional muqarnas in the two--dimensional outline. This is done by constructing a directed subgraph from the muqarnas design. The main task is then to find all directed subgraphs corresponding to a muqarnas design for which a three--dimensional muqarnas representation is possible. We can construct three--dimensional computer reconstructions directly from the directed subgraphs. An algorithm is developed for constructing the directed subgraphs and reconstructing the three--dimensional muqarnas. Two software tools are designed to execute this process. The program plantograph finds the directed subgraphs corresponding to a muqarnas structure from a muqarnas design. The program graphtomuq converts a subgraph into a three--dimensional computer reconstruction of the muqarnas. The various subgraphs result in different muqarnas reconstructions with the same plane projection. Some interaction is necessary to select the required reconstruction, for this art historical expertise is essential. The differences between muqarnas with the same plane projection can be local or global. Local means that by exchanging several elements the muqarnas are equal. Muqarnas are globally different if more elements are involved and the shape, or number of tiers, of the muqarnas differ. We can restrict the number of reconstructions if we know the proportions of the vault into which the muqarnas needs to fit. This gives a restriction on the amount of tiers that can be used. This work focuses on the muqarnas vaults fitting into domes or niches from the Seljuk and Ilkhanid periods. Different tests of such muqarnas from Anatolia and Iran are given. Additionally a new interpretation for the oldest known design which is found at Takht-i Sulayman is presented. Muqarnas, oder Stalaktitengewölbe, sind dreidimensionale Ornamente, die in der islamischen Architektur verbreitung finden. Sie werden in Gewölben, Kuppeln, Nischen, auf Bogenkonstruktionen, oder als fast flache dekorative Friesen genutzt. Ein Muqarnas hat die Aufgabe, einen fließenden Übergang von einer geraden Wand zu einem gekrümmten Teil zu gewährleisten. Ein Muqarnasgewölbe wird von verschiedenen nischeartigen Elementen, die in horizontalen Stockwerken angeordnet sind, aufgebaut. Ein Hauptmerkmal der Muqarnas ist, dass die Form eine dreidimensionale Einheit darstellt, welche in einem zweidimensionalen Grundriss repräsentiert werden kann. Wir konzentrieren uns auf die Frage, ob die zweidimensionale Projektion alle Strukturinformationen des dreidimensionalen Gewölbes enthält. Um einen Rahmen zu schaffen, in dem wir die Muqarnasstruktur beschreiben können, führen wir explizite Definitionen ein. Jedes Muqarnaselement wird parametrisiert, um Typ, Abmessungen und Position in dem Gewölbe beschreiben zu können. Ein graphentheoretischer Ansatz ermöglicht es, die Strukturinformationen des dreidimensionalen Muqarnas in einem zweidimensionalen Grundriss zu integrieren. Dies wird durch die Konstruktion gerichteter Teilgraphen aus dem Muqarnasentwurf realisiert. Die Hauptaufgabe ist es, alle gerichteten Teilgraphen eines Muqarnasentwurfs zu finden, für die eine dreidimensionale Muqarnasrepräsentation möglich ist. Die dreidimensionalen Computerrekonstruktionen können dann direkt von den gerichteten Teilgraphen ausgehend aufgebaut werden. Wir haben einen Algorithmus eintwickelt zur Konstruktion der gerichteten Graphen und zur dreidimmensionalen Rekonstruktion des Muqarnasgewölbes. Der Algorithmus wurde in zwei Computerprogrammen implementiert. Das Programm plantograph findet alle gerichteten Teilgraphen, die mit einer Muqarnasstruktur eines gegebenen Muqarnasgrundrisses, korrespondieren. Das Programm graphtomuq übersetzt einen Teilgraph in eine dreidimensionale Computerrekonstruktion. Die verschiedenen Teilgraphen ergeben verschiedene Muqarnasrekonstruktionen mit gleicher Projektion. Eine Interaktion mit dem Anwender ist nötig um die gewünschte Rekonstruktion auszuwählen, wofür Fachwissen in Kunstgeschichte erforderlich ist. Die Unterschiede zwischen Muqarnasgewölben mit gleicher Projektion können lokal oder global sein. Lokal bedeutet, dass die Muqarnas durch Austauschen einzelner Elemente ineinander überführt werden können. Muqarnas sind global unterschiedlich, wenn mehrere Elemente miteinbezogen sind und dadurch die geometrische Form und die Anzahl der Stockwerke variiert. Die Rekonstruktionsmöglichkeiten können eingeschränkt werden, wenn die Abmessungen des Gewölbes, in das ein Muqarnas eingebaut werden soll, bekannt sind. Die Anzahl der Stockwerke ist dadurch beschränkt. Wir konzentrieren uns auf Muqarnasgewölbe, die in Kuppeln oder Nischen eingebaut sind und der seldschukischen oder ilkhanidischen Zeitperiode entstammen. Der Algorithmus wurde an verschiedenen Muqarnasgrundrissen aus Anatolien und dem Iran getestet. Zudem wird eine neue mögliche Intepretation für den ältesten bekannten Muqarnasentwurf, eine in Takht-i Sulayman gefundene Platte, präsentiert.
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