## Muqarnas Design Framework

The design of muqarnas vaults is based on a smooth transition from two-dimensional forms to three-dimensional ones. Such a transition is believed to be a creative and progressive process. The spatial properties of vault-like elements result in various experiments with the development from a rectangular or square shape to a dome-like structure. Thus, muqarnas designs usually include several basic elements that are combined in repetitive layers to produce complicated surfaces.

Muqarnas drawings in-plane projection represent traditional design methods utilized by Islamic architects who applied strict geometric and mathematical rules to create their architectural works. Such drawings give a general understanding of the main principles of muqarnas design. The absence of overlapping elements in muqarnas makes it possible to project three-dimensional structure to the plane surface rather easily. Still, ancient architects used a special system of abbreviations in their drawings which makes them too complicated. It is generally recognized that different shapes are difficult to distinguish in such plane projections. Nevertheless, it is possible to say that muqarnas design is created with the help of a limited number of geometric elements that are simple and uncompounded. The links between the elements are determined by a geometric system of strict conformity. These two basic rules are necessary for muqarnas projection approaches.

The primary blocks used to build muqarnas are called cells. In the complicated examples of muqarnas, intermediate elements are also present. They are used as subsidiary items between the cells to make a geometric network more complete. Some researchers state that “the primary requirement of prefabrication is that the whole complex has to be decomposed to specific forms with limited variety and quantity” (Dadkhah et al. 134). It enables the development of diverse projections based on specific elements that almost do not vary and can be recognized as three-dimensional items from the beginning. Therefore, each two-dimensional tile is originally a three-dimensional element in the plane projection. To design three-dimensional structures in plane drawings, it is necessary to understand clearly how each element affects the space.

Complicated muqarnas structures are developed by utilizing the modular design. Such design is a construction of a variety of different elements composed of a set of basic modules. Such modules can be applied in the final layout or can be a part of the invisible substrate. Usually, the geometric items of two different scales are used in a certain combination. The large-scale patterns are rather big and recognizable, and the conjunction of small-scale elements is often determined by several key points of the large-scale patterns. For such muqarnas designs, the presence of complicated shapes such as stars, rosettes, and hexagons is widespread. It is noted that “an example of these combinations of stucco and tiling is the entrance portal (iwan) of the Shah Mosque, Esfahan, Iran, built by Shah Abbas the Great between 1611 and 1629” (Gherardini and Leali 138). The semi-dome of this mosque is characterized by the application of several three-dimensional shapes which corners are directed towards the center to create the point of attraction for the other points and the observer.

It is generally recognized that every muqarnas niche-like element has a roof and some vertical facets. The facets are adjusted to form a right angle, a half a right angle, or a sum of these angles with the near elements. Two facets are considered to be placed on a plane surface which is parallel to the ground. It is possible to place a flat surface above them, which is not parallel to the ground, or two curved surfaces to form a roof. This structure is what the muqarnas designers call a cell. The cells which are adjacent to the same level form a tier. The intermediate elements are situated between the roofs of two connected cells. They usually have a shape of triangles. Thus, it is possible to say that muqarnas design is an evolution of a decorative and structural element. The shape of muqarnas tiles is convenient to trap the light and diffuse it to make special visual effects. The final muqarnas structure includes a finite number of items that are logically connected and bounded to a primitive perimeter.

## Latest Design of Muqarnas

The contemporary designs of muqarnas are characterized by utilizing the bifurcated fold approach. This method is easy to apply through computer algorithms as the relationship between the elements is clear. It is also noted that “different from the basic principles of the well-known structural systems such as load-bearing or frame-based systems, the fold comprises an anti-hierarchical load disposition” (Alaçam et al. 288). The notion of bifurcation is defined as a geometrical operation or a process of branching to achieve a stable force redistribution on a surface. It greatly assists in understanding and developing vault-like structures.

For the application of this method, initial plane geometry is required as well. Therefore, three-dimensional forms can be generated from two-dimensional patterns by using computer technologies. This process includes creating a bifurcation for each calculated point along the line of force-flow. The bifurcated fold approach represents the combination of muqarnas encoding and folds technique which includes force-flow, layering, subdivision, and projection.

It is generally recognized that 3D modeling of muqarnas structures might give a new understanding of mathematical methods used to develop its form. Thus, it is possible to investigate the further potential of muqarnas to apply it in modern architecture. A cellular element is considered to be a basic item for developing various solutions for the irregular distribution of columns and plan types.

## How to Design Muqarnas – Size, Dimension, and Form

A simple muqarnas can be designed by determining the location of radial and orbital axes. For this purpose, a circle or a half-circle with an arbitrary radius is identified. Radial axes are determined by dividing it into equal sectors. Traditional muqarnas domes are expanded by using crescent and ray methods. The number, size, and form of the elements are derived from the size of a muqarnas dome, as well as from the height of its arches, which allows filling the spaces between them with tiles. The number of tiers is also dependent on the size and height of the whole structure. The tiers are formed by adding vertical tiles. The traditional domes usually include thirty-two tiles in the center. The domes can be expanded by various methods, which involve applying additional tiles between the determined axes. Each configuration might use various shapes of tiles.

It is stated that the increasing repetition of tiers causes the creation of new focal points (Dadkhah et al. 134). In the highest point of a dome-like structure, the element of the last tier is aligned with the identified axes. The radius and the size of the muqarnas element vary depending on the architect’s style. In contemporary designs, there is a tendency to omit intermediate elements, which results in developing muqarnas structures consisted of simple and uniform geometric patterns.

It is possible to say that each element plays a great role in muqarnas design and projection. The most important element in a flattened dome is an item that is placed at the upper tier, which is usually a big star in the center of a dome. The variations of muqarnas domes depend on the technique applied to their erection. For example, onion domes use flat vertical tiles to narrow the dome in its highest part. The additional tiles used in the designing of such domes create more space and a bigger radius.

## Analysis of Muqarnas Shapes

The geometrical patterns of muqarnas are derived from the equal subdivision of circles, and their forms are based on circle grid templates. The center of the circle is defined as a point to initiate all the patterns in Islamic culture. Some researchers state that “the circle is a symbol of a religion that emphasizes One God and the role of Mecca, which is the center of Islam toward which all Moslems face in prayer” (Abdullahi and Embi 245). Therefore, many geometric patterns used in muqarnas are based on such constructive polygons as octagon and hexagon. Stars are the fundamental elements of Islamic patterns and are designed by connecting the vertices of the polygons. The elements that originate from hexagram and hexagon can be classified as six-point patterns. It is noted that at the certain tier, two adjacent rays of a six-point star become divergent or parallel and create rosette petals in the shape of a deformed hexagon. Still, the polygons and stars are developed from more easily produced forms such as hexagons.

It is generally recognized that muqarnas can be developed with the help of an infinite number of possible elements. Still, all these elements are derived from the basic shapes such as square or rhombus. It should be noted that two-dimensional projections of muqarnas designs include a limited number of simple geometric forms which are shown below.

According to the Il-Khanid description of muqarnas, the element of a square shape has four right angles and ribs with the length that amounts one. They can form a cell or an intermediate element. There is a range of other elements based on the square form. The jug shape consists of two ribs that correspond to the other curved sides of the unit. This element appears only as a cell. The element of a large biped form represents what is left from a square after the utilization of a jug item. It has a diagonal which length is √2 – 1 and two sides whose length is one. This unit is combined with a jug element to make an intermediate pattern. A half square pattern is based on a square divided by diagonal. It is utilized at the muqarnas edge as a cell. Still, it might appear as an intermediate pattern.

The elements that have a rhombus as their basis have one or more angles of 45 degrees. The rhombus elements have four equal sides and two opposite angles which have 45 degrees. They appear in muqarnas both as intermediate elements and cells. The elements of small biped shape and almond can be combined to split or form the rhombus. The almond appears only in such elements as cells, while the small biped shape can be utilized as the intermediate element and in a cell. A half rhombus shape is defined as a rhombus divided by diagonal. Two such elements can appear in muqarnas in conjunction with a square and a jug. The top projection of these combined elements forms the shape of a hexagon.

Sometimes, such an element as a barley kernel can appear in muqarnas. It has a form of a rhombus with one stretched side. This element might occur as an intermediate element in the upper tier to fill the upper and the last part of a vault. All the muqarnas elements are combined by stair steps called layers or tiers to form a complete dome or another muqarnas structural element.

## New and Old Configurations of Muqarnas

The studies of old configurations of muqarnas were based on the analytical studies of traditional drawings made in two dimensions. It is a general opinion that the complex geometry of three-dimensional models was simplified by utilizing digital technologies. For example, for evaluation of muqarnas structures in ancient mosques, such an approach as digital photogrammetry can be used. This method applies three-dimensional scanning and 3D modeling codes to determine morphological and structural features of various configurations of muqarnas.

The form and dimension of muqarnas are dependent on the geographical region where it was built and the period of its construction, as well as on the section of the building where it was applied and the material. For instance, some researchers note that “the usage areas of muqarnases, which are frequently used in Anatolian Turkish Architecture, are quite wide” (Karabörk et al. 141). Apart from the traditional application of muqarnases in domes and portals, they were also utilized in tombs, fountains, street corners. Still, the main principles of old muqarnas constructions remain the same for all configurations. All muqarnases are constructed by making a concave-return surface which is narrowed at the top and contain curved elements to connect vertical and horizontal parts of the construction. The early configurations of muqarnas have rather big cells that are primitive and array-sliced.

The muqarnas variations of the late periods are proved to become more sophisticated and intricate. It is generally recognized that the ancient architects applied muqarnas ornaments that had various complex shapes such as hexagons, octagons, and stars, and were unique. It is stated that “the intricate 16-point patterns remained popular in North Africa and Islamic Spain, but only minimally influenced eastern regions, such as Persia, Anatolia, and the Mughal region” (Abdullahi and Embi 250). In the construction of domes, it is possible to distinguish the flattened and onion domes. Both forms include complicated sets of cells and intermediate elements filled between the rays to form an exquisite structure of muqarnas.

The new muqarnas configurations designed with the help of digital technologies are usually less complicated than the old ones. As it was mentioned before, modern designs are mostly based on a bifurcated fold approach combined with the results of studies of old plane two-dimensional projections and digital analysis of ancient examples of muqarnas. It is possible to say that digital 3D modeling and analysis of muqarnas forms resulted in the attempts to design and build constructions with muqarnas elements applied in them. Still, new configurations are not that intricate as the works of the ancient architects. The contemporary developers usually apply the same approaches to the creation of forms and application of cells with some variations due to modern tendencies.

## Development of Muqarnas by Using Technology

An algorithmic approach is vastly applied in architecture for decoding structural and spatial elements. It is noted that “a layering algorithm in Python programming language was developed as interference of surface explorations which allows the manipulations of the internal relations dynamically via interactive layer line selection by the user” (Alaçam et al. 294). Thus, modern architects can benefit from applying digital technologies in the development of such complicated structures as muqarnas.

There are many programs available for structural analysis and modeling of muqarnas by using various parameters that are applied to its formation. The development of a 3D model starts with one element, a square, or a circle, depending on the expected results. By rotation at 45 degrees, a second element of the same shape is placed on the top of the previous one. This method is applied to get a plane projection of the future muqarnas element in the form of an octagon, hexagon, or a circle. Usually, such projection consists of several repetitive tiles of almost the same shape which can be used for the construction of muqarnas elements. After that, an analysis of possible shapes is performed and compared to the traditional approaches.

Computer technologies allow safely to develop and model such complicated constructions as domes and portals by using the same approaches as in the process of physical modeling. The initial two-dimensional plan is transformed into a three-dimensional model by the tools available in graphic programs such as 3D MAX where the possible variations of cells and their shapes are analyzed to get the final design. It should also be noted that in computer modeling, the calculations are performed for each triangular pattern received in the plane projection to apply force flow and bifurcation rules.

A CAD environment can be used to import the existing projections of muqarnas for analysis or modeling the new ones. Some researchers state that “the analysis of the pattern is a fundamental phase to avoid useless work and take advantage of its modularity” (Gherardini and Leali 147). Thus, muqarnas two-dimensional elements can be classified by a hierarchy which includes plane elements, niche-like patterns, and intermediate items. A single module drawn in the program can be repeated by the available tools such as copy or mirror to multiply it. Thus, various elements can be integrated into the model.

If the patterns are not available, they can be taken from the three-dimensional projection of the muqarnas construction erected out of a two-dimensional model. A photograph can be utilized to make this plane projection of muqarnas. Thus, it is possible to make a correlation between a two-dimensional design and a three-dimensional model using digital technologies.

## How to Use Muqarnas in Modern Business

The application of digital technologies in muqarnas development and analysis made it possible to apply this exquisite construction element in the modern buildings, as well as in the decoration of gardens, squares, and yards. Some researchers note that modern Islam architecture tends to combine state-of-the-art approaches with traditional elements such as muqarnas in the construction of new buildings (D’Agostino 9). Thus, the interior of such businesses as airports, restaurants, and shopping areas can be easily decorated with the variations of muqarnas elements.

It should be also noted that modern architects tend to use muqarnas elements to build creative constructions. One such example is a Hayam Temple to Sunlight presented at the Burning Man festival of modern art. This construction embodies the perfection of Islamic geometry. It is assembled from the plywood boards perforated with flowers, which are joined seamlessly and resembles muqarnas but still is an original work of art that contains only necessary elements. Another interesting idea presented at this festival is a sitting named Reflection, which also resembles the muqarnas design. The application of muqarnas elements was also noticed at the exhibition dedicated to Islamic culture. The entrance to the exhibition was decorated with a muqarnas-like structure made from fabric that hung from the archway in a neo-Gothic style. Thus, it is possible to say that muqarnas is still popular in the modern world and the methods of its design and modeling occupy the minds of many contemporary architects and designers.

The latest tendencies of using muqarnas prove that this decoration and construction element can be utilized in a variety of businesses, such as designing private gardens with Eastern elements or applying muqarnas elements in the interior decoration of shops, airports, hotels, and other public places. Various niches, portals, dome-like elements, and arches can be utilized in constructing pavilions, fountains, creative benches, and entrances. Muqarnas elements can also be used for constructing some interesting pieces of art to be placed in the streets for the decoration and tourist attraction. Thus, the functional potential of muqarnas is very expanded and can be used by modern architects in their models both as a decorative and structural element.

## Works Cited

Abdullahi, Yahya, and Mohamed Rashid Bin Embi. “Evolution of Islamic Geometric Patterns.” *Frontiers of Architectural Research*, vol. 2, no. 2, 2013, pp. 243-251.

Alaçam, Sema, et al. “Reconnoitering Computational Potentials of the Vault-Like Forms: Thinking Aloud on Muqarnas Tectonics.” *International Journal of Architectural Computing*, vol. 15, no. 4, 2017, pp. 285-303.

Dadkhah, Negin, Hadi Safaeipour, and Gholamhossein Memarian. “Traditional Complex Modularity in Islamic and Persian Architecture: Interpretations in Muqarnas and Patkâné Crafts, Focusing on their Prefabricated Essence.” *Proceedings of 2012 ACSA FALL CONFERENCE — Offsite: Theory and Practice of Architectural Production (Temple University, Philadelphia, PA, 27–29 September 2012)*, 2012, pp. 130-138.

D’Agostino, Glauco. “Architecture in Saudi Arabia: An Exciting Challenge Amidst Traditional Islamic Features and Technological Development.”* Geopolitics, Political Geography and Geostrategy Magazine, *Jan. 2015, pp. 1-18.

Gherardini, Francesco, and Francesco Leali. “A Framework for 3D Pattern Analysis and Reconstruction of Persian Architectural Elements.” *Nexus Network Journal*, vol. 18, no. 1, 2016, pp. 133-167.

Karabörk, Hakan, Esra Yaldiz, and Lütfiye Karasaka. “3d Documentation of Portal Muqarnases in Anatolian Madrasahs with Digital Close Range Photogrammetric Method.” *Mediterranean Archaeology & Archaeometry,* vol. 17, no. 3, 2017, pp. 137-148.