Computational Design Potentials Promoting Regional Arab Architecture

Computational Design Potentials Promoting Regional Arab Architecture Ahmed Fathi Ahmad ([email protected]) Assistant Professor at Architecture and Urban Planning Department, Faculty of Engineering, Suez Canal University Ahmed Muhammad Saleh ([email protected]) Associate Professor at Architecture and Urban Planning Department, Faculty of Engineering, Suez Canal University Muhammad Hegazy Ali ([email protected]) Assistant Lecturer at Architecture and Urban Planning Department, Faculty of Engineering, Suez Canal University Keywords: computational design, Islamic patterns, regional Architecture, architectural identity, sustainability.

1

Abstract Computational design was the phase that revolutionized the role of computer in the architectural design process. Generative, Bio morphogenetic, Parametric, and algorithmic design are all synonyms and sub-Disciplines for computational design, aiming to use "Artificial Intelligence" and advanced mathematics to generate and control far futuristic, complex organic forms. Besides, Digital fabrication techniques made it possible to build these forms at astonishing accuracy and time management. Furthermore, computational design has a number of concrete applications in environmental simulations, as well as building modeling and documentation. Unfortunately, these computational design methods were imported to the Arab world not as tools but as copies of the western application to this technology, aggravating the identity crisis and local sustainability, as seen in Dubai, Doha, Abu Dhabi and others. Regional Architecture identity was neglected although it is richness with ritual, religious, sustainable and geometric values, leading to cities with no Identities, nonsustainable buildings and non-efficient spaces. This study aims to review and explore a set of computational design applications to reserve the local architectural heritage and design identity within the Arab World. Firstly, it will introducethrough historical review- the role of mathematics in the development of the sophisticated Islamic architecture, discussing how the Muslim scholars contribute to the building industry at their times, as well as the mathematical features of Islamic buildings. Secondly, the study will focus on the computational nature of Islamic geometric patterns, reviewing a set of historical and scientific evidence to the ultimate mathematical precision of such patterns. Finally, a number of applications of computational design to promote the regional architecture will be studied, featuring the reconstruction of historical buildings, Islamic pattern design.

2

Significance of study This study will be a significant endeavor in preserving the local architectural identity within the Arab world. It will be also beneficial for the Arab architects and designers to make use of the latest digital design technologies, by understanding the core concepts within the Islamic architecture supporting the application of computational design tools. Moreover, this study will provide a set of examples of the main aspects that can make use of these technologies. Objectives of study The study objectives can be summarized as follows:  To review the role of Muslim mathematicians in the progress of building science in the Islamic world.  To study the computational nature of Islamic architecture, specially the Islamic geometric patterns.  To collect historical and scientific evidence to the sophisticated use of mathematics in the Islamic architecture.  To determine contemporary case studies of using computational design to preserve the local architectural identity in the Arab world. Methodology The methodology of the study is based on a qualitative approached applied in three phases:  Historical approaches: aims to review literature about the role of Muslim mathematician in the progress of building industry within the Islamic world.  Descriptive approaches: aims to analyse the computational features of Islamic architecture, especially geometric patterns. This will take place through literature review and analysing historical and scientific evidence.  Case studies: this phase will review and analyse a number of examples of computational design used to preserve local 3

architectural identity. This will take place through analysing previous scholarly work as well as practical experimentation by the author for some computational design tools. Introduction Computational design is a term that differs from, but is often confused with computer-aided design (CAD). Generally, CAD is about using computer as a digital drawing tool, to automate some routine processes and digitizing drawings. In simple words, the computer is not involved in the “thinking” phase of design. In contrast, computational design is more about using the algorithmic power of computer-through coding- to explore limitless iterations of forms, problem solving, very complex geometric calculations, and rationalization. The application of computational design can cover many aspects, including industrial design, animation, simulation and others. However, the architectural application of this technology is very promising, changing the way architects are approaching form finding process and manufacturing. In this case, computational design tools can be used in all phases of building, including design (shape grammars, building information modelling (BIM)), construction (Digital fabrication, construction phases simulation), and management (smart building control, environmental responsive utilities). The use of computational design tools can not only speed up the design process of the building, but it also offer the designer’s imagination free space to explore ultimately complex building shapes, unlikely to be built by traditional tools. It also integrate all the phases of design together in one comprehensive model, whose parts can be precisely fabricated with minimal need for human drafting. However, the adoption of this trend in the Arab world did not serve the local architectural identity. Most of these projects ere designed by foreign designers who aimed to replicate the western 4

glass towers through these tools, but they did not make use of the rich Islamic architectural culture, neither in form nor in behaviour. It is interesting how Islamic architecture, especially geometric patterns, have a genuine mathematical nature, which make it perfect for the application of computational design tools. These tools can be used to produce new forms inspired by the local culture, or preserve the existing architectural heritage through 3D scanning and BIM documentation. Role of Muslim mathematicians in Art and Architecture While the scientists of Saljuq and Mongol Iran (early 10th century) were the masters of their field, it has been estimated that it was the Timurid (14th century) period when the apex of Islamic work in computational mathematics has been reached (Mashayekh, 2003). An example for advanced mathematics in construction is the weight of the double shelled dome of the mausoleum of Uljayto in Sultanieya (Figure 1) in central Iran (45 meter high with a diameter of 24.5 meter), where the ceiling is concentrated on a small number of supporters, without the use of any shoulder or buttress.. So it must has been calculated before to its construction (Figure 2). (Hejazi, 1997).

Figure 1 Gunbad-i Uljaytu, Sultaniya (http://archnet.org/sites/1671)

Figure 2 Structural system of the dome (https://www.studyblue.com/notes/ note/n/midterm/deck/5880919)

Thanks to Abū al-Wafā' Būzjānī's works in geometry and practical mathematics, the 4th century was a milestone for connection between mathematics and architecture. During this era, prominence of Baghdad school on harmonizing theoretical 5

sciences and practical works had strong effects on architectural works. During the Seljuk dynasty (6th century), the interest in studying applied sciences grew more than ever. The existence of professional and resourceful political advisors, including Khawja Nizam Al-Mulk Tusi resulted in geometry positive impact on architecture. (Ebrahimi & Aliabadi, 2015) Scientists including al-Kāshī continued to study theoretical application of mathematics in architecture as a set of practical solutions through writings about application of geometry in building and authoring theoretical expression. During the Safavid dynasty, the peak of geometry application in decoration of monuments can be seen, including using Khayyām's triangle proportions in Nizam Al-Mulk dome of Isfahan's Grand Mosque and using it in order to decorate this monument. In dynasties after Safavid and especially in Qajar dynasty mathematics retreated from practical geometry issues due to stepping Western and theoretical methods, tending toward positivist and pure issues. (Ebrahimi & Aliabadi, 2015) The following table summarize the notable contributions of Muslim mathematicians to the craft of building form 4 th century to the 12th one. Table 1: Muslim mathematicians’ contributions to architecture

Scholar Contributions 4th and 5th Centuries  Profile design to prove the theorem of Pythagoras.  Compilation of literature outlining the method of the two-dimensional geometric girih. Būzjānī  Introduced three main tool for drawing geometry: ruler, compass and Bracket  Sphere divisions.  Jameh Mosque of Isfahan Tiling  Useful information about the names and Al Tabari units of measurement of building and surveying  9th Century 6

 Geometry used in buildings. Addressing the scientific aspects of architecture and building. Calculate the area of regular polygons Based on the square modulus.  Describe Making Muqarnas. Addressing architects to work on the practical way in a side of theoretical ways. al-Kāshī  Compile the application of the theoretical foundations of geometry in architecture.  Management, Design and construction of the observatory in Samarkand.  Build a sundial on the wall that is not in any of the main four directions.  Create a hole in the wall of the mosque to specify the time of evening prayer.  11th Century  Designing triangle tools with Plummet of architect  Recognizing height of symbols and signs in Shaykh‐ I cities. Bahāʾī  Design and build bridges, Dams.  Geometry employed in the construction of buildings, houses and castles.  12th Century  Using the properties of North Dome irrational numbers in the design of the dome Umar  Employment Khayyam on architecture and alrelated arts of Domes. Khayyām  Applications of Pascal's Triangle as a decorative array (Author based on (Ebrahimi & Aliabadi, 2015, p. 226))

Mathematical features of Islamic architecture According to (Kaptan, 2013), Proportional mathematical relations in Islamic architecture depend on the process of preferred dimensions, which is recognized by the unity of its 7

system aspects proportions. These systematic proportions are based on a set of geometric features: a. Repetition: achieved by following a standard module repeated by the multiplications and the parts of the standard module of the same construct volume. This allows the continuity of the structure as a whole by multiplying itself with a different measurement inclusive repetition- in a straight linear shape (Figure 3 and Figure 4).

Figure 3 :Array of arches at Alhambra palace (http://www.virtourist.com/europe /cordoba/11.htm)

Figure 4 :Moroccan arches (https://www.pinterest.com/ pin/14355292536472454/)

b. Symmetry: Islamic buildings layout often based on regular pure geometrical shapes for the entire structure around a point – radial symmetry- or around axis with constructional relations per constant system of dimensions (Figure 5 and Figure 6).

Figure 5: Plan of the palace, Mshatta, Jordan. (Kaptan, 2013, p. 8)

Figure 6 :entral-plan of Selimiye Cami (Mosque of Selim), (Kaptan, 2013, p. 10)

8

c. Balance: achieved by developing a visual balance to the structure among the dynamic shapes like the circle and the static ones like the square at fixed system of dimensions (Figure 7). d. Gradation: Spaces in Islamic buildings was often degraded from secondary towards principal. This order may be a result of orienting towards what is being principal or for its extraordinary scale through the gradation of relations among the part, the parts and the whole (Figure 8).

Figure 7: Cutaway drawing of the Dome of the Rock (Kaptan, 2013, p. 7)

Figure 8: Gradation in Haga Sophia (http://www.archh.com/m/sara/projec ts/1652/hagia-sophia/)

The Divrigi Ulu mosque The Divrigi Ulu is a mosque and hospital complex in Sivas, turkey. It was built in 1228 by the the Mengücekid emir, Ahmet Shah. The chief architect is inscribed in the interior of both the mosque and the hospital and has been read as Khurramshāh b. Mughīth al-Khilātī, which indicated his origins from Ahlat city, known in the medieval sources as al-Khilāt (Pancaroğlu, 2009). It is known for its astonishing geometric patterns and botanic design as well as the highly sophisticated technique of vault construction, and a creative, exuberant type of decorative sculpture– particularly on the three doorways, in contrast to the unadorned walls of the interior – (UNESCO World Hertiage, 2012). It was recognized as a UNESCO world heritage site for its high artistic and historic values. Recent studies show that shadows of different silhouettes appear on the carvings of the outside walls of the entrance during the different hours of a day. Silhouettes of a man looking straight, reading a book and praying (Figure 9), respectively, as well as the silhouette of a praying woman can be seen in formed by shadows 9

combination (Figure 10). These extraordinary features could not have been designed without the using mathematics, astronomy and art altogether. In fact, the scientists observed the positions of the sun and stars for two years before construction, where very careful calculations had been done and applied in the construction of the walls and the carving of the outside doors. (Al-Hassani, 2007)

Figure 9: a Silhouette of a praying man reading a book (http://blog.radikal.com.tr/kentkulturu/divrigi-ulu-camii-vedarussifasi-1985-yilinda-unescodunya-miras-listesine-alinmistir27792)

Figure 10: Silhouette of praying woman (http://www.milliyet.com.tr/gundem /divrigi-ulu-camii-de--namaz-kilaninsan--silueti-1911273/son-dakikagundem/SonDakikaGaleri/13.07.20 14/1911273/default.htm?PAGE=1)

Computational features of Islamic geometric patterns a. Repetition (Tessellation): Islamic patterns are originated from a set of polygons (equilateral triangles, squares, or hexagons) placed in an array or a grid. The mathematical term for these grids is "regular tessellation" (deriving from the Latin tesserae, i.e., pieces of mosaic), in which one regular polygon is repeated to tile the plane. No matter how intricate a design becomes, it is still based on a regular grid of simple shapes (Figure 11) (Islamic Art and Geometric Design, 2004).

10

Figure 11: Tiling unit in an Islamic pattern

Figure 12: Interlocking units showing repetition

(http://www.catnaps.org/islamic/geome try.html)

(http://www.catnaps.org/islamic/geomet ry.html)

b. Illusion of Infinity (Unframed): Geometric decoration is based on the concept that every pattern can be repeated and infinitely extended into space. This means that a frame can appear to be subjective, simply providing a window onto a pattern that continues beyond the bounds of that frame (Figure 13 and Figure 14). Geometric ornamentation in Islamic art suggests a remarkable degree of freedom. The complex arrangements and combinations of elements are infinitely expandable (Islamic Art and Geometric Design, 2004).

Figure 13 :Islamic pattern covering arch outline (http://dickschmitt.com/travels/spain/gr anada_province/granada/Alhambra.ht m)

Figure 14: Star pattern filling a triangular shape (http://teardropsonroses.blogspot.com/2 014/05/geometric-wood-panels.html)

c. Symmetry: is created in Islamic patterns by the repetition and mirroring of one or more basic units—usually shapes such as circles and polygons. Although the design can be expanded and made complex, the basic symmetrical repetition and mirroring of these shapes creates a sense of harmony (Primary Characteristics of Islamic Geometric Decoration, 2013). d. Two-Dimensionality: Islamic patterns are often twodimensional. Because it is generally applied to not only flat surfaces, but also the patterns themselves do not have shading or background-foreground contrast. In some instances, however, an 11

artist will create interlocking or overlapping designs that create the illusion of depth and produce an aesthetically pleasing and visually playful composition (Figure 15 and Figure 16) (Primary Characteristics of Islamic Geometric Decoration, 2013).

Figure 15: colored geometric fabric shows illusion of depth

Figure 16: Interlocking rhombi (http://2hpencil.com/category/pattern/)

(https://www.etsy.com/)

e. Shape Combinations: Combinations of interweaving floral forms and vegetal patterns are also used (Figure 17). The former set as foreground and the latter as contrasting background. The contrast can be created by varying the shades of the same color or by varying the colors. Sometimes a combination of a pattern and calligraphy is used involving principles of symmetry (Khan, Zaffar, & Ansari, 2011, p. 64).

Figure 17: Vegetal patterns combined with geometric ones (http://pixshark.com/islamic-arabesque.htm)

Girih tiles Girih tiles are a set of five basic tiles that were used in the creation of tiling patterns in Islamic architecture (Figure 18). Girih patterns contain properties of quasicrytalline patterns, predating concepts defined by mathematicians like Roger Penrose by over five centuries. The term Girih is derived from the Persian word “‫”گره‬, meaning "knot". They have been used since about the year 12

1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453. (Prange, 2009). All sides of these figures must have the same length; and all their angles are multiples of 36° (π/5). All of them, except the pentagon, have bilateral reflection (symmetry through two perpendicular lines) or may have additional symmetries. Specifically, the decagon has tenfold rotational symmetry (rotation by 36°); and the pentagon has fivefold rotational symmetry (rotation by 72°). The five shapes of the tiles are: (Nicanor, 2009) -a regular decagon with ten interior angles of 144°; -an elongated (irregular convex) hexagon with interior angles of 72°, 144°, 144°, 72°, 144°, 144°; -a bow tie (non-convex hexagon) with interior angles of 72°, 72°, 216°, 72°, 72°, 216°; -a rhombus with interior angles of 72°, 108°, 72°, 108° -a regular pentagon with five interior angles of 108°.

Figure 18 the five basic Girih tiles (http://psdg.pbworks.com/w/page/19548743/Geometry%20in%20Islamic %20Architecture)

Applications of Computational design in Regional Arab Architecture The previous sections have clearly showed the major role of mathematics in the development of Islamic architecture, as well as its elements. Such computational nature of forms can grantee promising applications of computational design tools to replicate 13

the vocabulary of Islamic architecture. In the following section, a number of case studies will be reviewed in the fields of form finding, historical documentation, fabrication, and environmental simulation. a. Historical Building Computational Reconstruction The following example is based on the works of (Baik, boehm, & Robson, 2013). The aim of the project was to use computational documentation approach to establish a building information model for historical buildings in Jeddah. Terrestrial laser Scanning and Architectural Photogrammetry are used as tools. Farsi House was chosen as a test case for the project. The resultant BIM model will automatically provide full engineering drawings orthographic, sectional and 3D models. The workflow of the project can be described as follows: Image Survey: The project started with the images survey to discover the Farsi house characters. A professional Canon 18 Mega Pixels camera was used to take free images of the house. Laser Survey: The best locations for scanning station and scan targets were chosen. To offer perfect visibility can be produced. Three targets at least must be used in common between these laser scanner stations to give more accuracy, where the collected scans have sufficient overlapping area to allow for subsequent integration. (Figure 19) Data Cleaning and Point Cloud Registration: The Cyclone program was used to remove the noises. This step took around three days to be completed. (Figure 20). Different scans corresponding points in overlapping areas were used for the registration. Revit modeling: After getting the cloud points from the laser scan, Autodesk Revit was used to turn point cloud into architectural elements. It was chosen because it produces high quality construction documents and high level of flexibility. (Figure 21 and Figure 22) 360BIM Glue: The 3D Revit model was linked to the Autodesk BIM 360 Glue to provide multidiscipline model coordination and clash detection. 14

Figure 19: Using laser scanners Figure 20: Using computer to generate the point cloud of the algorithms to clean the point building cloud data and make it more BIM (Baik, boehm, & Robson, 2013, p. friendly 75) (Baik, boehm, & Robson, 2013, p. 75)

Figure 21: 3D point cloud model after registration (Baik, boehm, & Robson, 2013, p. 75)

Figure 22: the reconstructed building in remodeled in Revit software (Baik, boehm, & Robson, 2013, p. 75)

b. Girih-Edit The girih tile as geometric shape grammar for Islamic patterns was discussed previously. Girih-edit.com is a free web-based application, meaning it does not need download and can work on any browser. Its script is based on WebGl (a JavaScript API for rendering interactive 3D computer graphics and 2D graphics within any compatible web browser without the use of plug-ins). 15

Girih-edit uses the five preset girih shapes (decadon, rhombus, elongated hexagon, pentagon and bow tie) as building units for sophisticated digital Islamic patterns. It uses simple translation operations (Move, Place, and Rotate by 36 º).

Figure 23 Girih-Edit interface featuring the main tabs (Author)

The interface is quite simple. It consists of four main tabs (Figure 23): Tiling Tab: it is the modeling tab including the five-girih tiles and other operations (zoom, clear view, erase girih unit and rotate) (Figure 24). Style Tab: Where user can choose different display presets, the tiling preset is the default style showing the outline of girih tiles (easier for modeling), the other styles (specially Clearing) removes the construction lines, giving thickness and shadows to the pattern to look similar to Islamic patterns seen in real world (Figure 25). SVG Export: which stands for “Scalable Vector Graphic”; an XML-based vector image format for two-dimensional graphics with support for interactivity and animation. This tab enabling exporting the pattern to use it in other 2D or 3D software packages. File Tab: To save a working file on the cloud using cookies.

16

Figure 24 Tiling tab showing the five girih tiles (Author)

Figure 25 Style tab showing different display sets (Author)

Figure 26 A pattern displayed in girih outlines (Author)

Figure 27 The final pattern in clearing style (Author)

c. Parametric Pattern Generator PATGEN is a script developed by (Çolakoğlu, Yazar, & Uysal, 2008) for 3ds max environment, dedicated to design parametric Islamic geometric patterns through a shape grammar algorithm. Computational design was used as an approach to generate parametric star patterns. First, the shape grammar (rules) for the pattern generation was defined mathematically. Then, maxscript was used to develop a plug in for 3Ds max following the same parametric rules of the previous description. The generated iterations are limitless and can be exported to other CAD software for fabrication.

17

Figure 28: PATGEN interface and a sample pattern generated in 3DMAX (Author)

d. Digital Fabrication of Islamic Patterns Nomad Inception is a design studio that adopts computational design as an approach to regional themed projects and motifs. A set of design tools that assist in the creation of a new generation of Islamic geometric patterns are used. They have developed technology to produce large non-periodic Islamic geometric compositions, respecting every rule of the age-old art form. They are specialized in parquet floors, wall decorations and partitions motifs. Certain algorithms generate huge compositions of Islamic patterns with every sort of traditional elaboration techniques, such as interlaces or double star lines, other computer programs dissect them into pieces. Computational design provides us with a mathematical understanding of each of the hundreds of thousands of pieces in a large geometric composition, and their relation with each other and the 3D space. (Nomad Inception, 2014) Then, the technical teams work on the design development and working drawings phases, to find the proper arrangements of the details. Every repetitive task is fully automated, where the resulting data is inferred to the rest of the pieces in the design algorithmically. At this stage, the technical work is done in whichever CAD or BIM platform that is integrated with the client’s framework. (Nomad Inception, 2014) 18

Finally, to ensure that every issue is resolved in the most efficient and cost effective way. In house developed technological solutions are used to produce CAM operations programs directly from within working environment, in order to supply the contractor with ready-to-cut files, accompanied by algorithmically generated step by steps instructions on how to assemble the puzzle. (Nomad Inception, 2014)

Figure 30: CNC millers Figure 29 : algorithms used to fabricating detailed forms generate complex patterns (https://vimeo.com/nomadinceptio (https://vimeo.com/nomadinceptio n/videos) n/videos)

Conclusions It is clear that the role of computer is getting larger and larger in the architectural design process, turning from just a digital drawing tool to a “thinking” device that can use algorithms to design and explore very complex forms with seamless support for construction and optimization. Moreover, this technology can also be used in more aspects of architecture like 3D scanning for historical buildings and environmental simulations for the building elements. at a time of retract for the contemporary Islamic architecture, driven by globalization and the limited contributions of local designers, the computational design used to be a goal, not a tool, replicating western building forms within the Arab world, as seen in Qatar, Dubai and others. At this point, the rich heritage of Islamic architecture is being ignored, despite the promising potentials of its elements and reliability to the hot environment. As computational design is based originally on mathematics, it was important to explore the role of mathematics in Islamic architecture. It is obvious that since the early 4th and 5th centuries, mathematics was not only used to overcome technical 19

issues, like structure optimization, and geometric shape accuracy, but also to boost the creativity of the Muslim artisans, showed in the sophistication of geometric patterns. Moreover, the Islamic building concepts are based on geometrical features such as symmetry, and repetition. In the divrigi ulu mosque, it was clear how advanced mathematics, along with astronomy and building crafts helped expressing cultural values of the society in a miraculous way. Islamic geometric patterns are the best example of computation in Islamic architecture; they show ultimate complexity and unparalleled precision. Unlike the traditional explanation stating they are based on ruler and compass, recent studies have found that Islamic geometric patterns were based on advanced mathematical rules, as seen in the girih tiles, following certain algorithms to form complex shapes easily. Computational design can help preserving the architectural identity of the Arab world in many ways. For example, through documenting historical buildings by 3D scanning, so that they can be rebuilt at maximum precision. Also, "Girih edit" and "PATGEN" are examples of scripts dedicated to digitally model parametric Islamic geometric pattern, with flexible variable and support for computer aided manufacturing (CAM).Such technology is used to pre fabricate highly complex Islamic patterns, overcoming the lack of professional manual artisans. The reviewed cases are a few examples of the promising applications of computational design to preserve Islamic architectural identity in contemporary buildings. In facts, the potentials are limitless and local architects have the responsibility to explore the real power of computational design not as a fashion or copycat, but as creative tools to fulfill the environmental, social, aesthetical needs within local architecture nowadays. Recommendations The study recommends the following:  Arab architects should adopt the concept of computational design as an approach to introduce a new face of local architectural heritage, a face that integrate the environmental 20

national identity and globalized futuristic approaches of architecture.  Any building should be related to its environment, in a way that reflects the unique architectural heritage of this particular place. At the same time, it should feature contemporary trends in architecture.  When applying computational design in Arab countries, a local architect should be involved in the design process along with the hired professionals, to be a source of cultural inspiration and social fulfillment.  National architectural competitions should prioritize preserving local identity in the design as a major criterion to win the competition  Multiple computational design courses should be introduced to undergraduate architecture students, as well as applied throughout different design projects. Bibliography Al-Hassani, S. (2007, April 25). New Discoveries in the Islamic Complex of Mathematics, Architecture and Art. Retrieved May 22, 2015, from Muslim Heritage: http://www.muslimheritage.com/article/new-discoveriesislamic-complex-mathematics-architecture-and-art#ftnref107 Baik, A., boehm, J., & Robson, S. (2013). JEDDAH HISTORICAL BUILDING INFORMATION MODELING "JHBIM" OLD JEDDAH - SAUDI ARABIA. XXIV International CIPA Symposium (pp. 73-78). Strasbourg, France: International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Çolakoğlu, B., Yazar, T., & Uysal, S. (2008). Educational Experiment on Generative Tool Development in Architecture. eCAADe Conference (pp. 1-7). Yildiz Technical University. Ebrahimi, A. N., & Aliabadi, M. (2015). The Role of Mathematics and Geometry in Formation of Persian Architecture. Asian Culture and History, 7, 220-239.

21

Hejazi, M. M. (1997). Historical Buildings of Iran: Their Architecture and Structure. WIT Press. (2004). Islamic Art and Geometric Design. New York: The Metropolitan Museum of Art. Kaptan, K. (2013). Early Islamic Architecture and Structural Configurations. International Journal of Architecture and Urban Development, 3, 5-12. Khan, K., Zaffar, A., & Ansari, M. R. (2011). Islamic Art, Mathematics and Heritage of Sindh. The Sindh University Journal of Education, 40(2010-2011), 58-73. Mashayekh, H. (2003). Wisdom in Art: Mathematics in Islamic Architecture in Iran. ISAMA-BRIDGES Conference (pp. 582582). Granada, Spain: University of Granada. Nicanor, P. (2009, March 5). Geometry in Islamic Architecture. Retrieved May 20, 2015, from pbworks.com: http://psdg.pbworks.com/w/page/19548743/Geometry%20in%2 0Islamic%20Architecture Nomad Inception. (2014). Retrieved May 23, 2015, from http://www.nomadinception.com/about-us.aspx Pancaroğlu, O. (2009). The Mosque-Hospital Complex in Divriği: A History of Relations and Transitions. Anadolu ve Çevresinde Ortaçağ 3. Prange, S. R. (2009, October). The Tiles of Infinity. Saudi Aramco World, pp. 24-31. Primary Characteristics of Islamic Geometric Decoration. (2013, January 8). Retrieved May 9, 2015, from The Metropolitan Museum of Art: http://www.metmuseum.org/learn/for-educators/publicationsfor-educators/art-of-the-islamic-world/unit-three/primarycharacteristics-of-islamic-geometric-decoration UNESCO World Hertiage. (2012, January 4). Retrieved May 22, 2015, from http://whc.unesco.org/en/list/358

22