伊斯蘭建築的宇宙觀反映了一個烏托邦的創造，對於信徒而言是建造一座虛擬的天堂。圖騰與裝飾在實現這宇宙觀中扮演著至關重要的角色，透過的內部空間建造，將建築物的内殼脫離外部的現實世界。在建築中，圖騰透過裝飾掩蓋的"真實"，呈現了建築所表達的結構與構成的關係。如果將伊斯蘭建築只是視為一種符號性的宗教象徵體時，建築的價值是以"皇家藝術"的觀點傳承與擴散；有關伊斯蘭建築定位的討論，通常優先考慮模仿與複製，而卻未充分考量材料性質和結構等表達之區域變化。

本研究的目的是通過現有伊斯蘭建築的裝飾與圖騰，提取設計元素並將其轉換成為模組與鑲嵌式構築系統，重新詮釋伊斯蘭建築為新的數位形態。研究聚焦於兩大伊斯蘭元素，以不同研究的出發點深入探討：‘阿拉伯窗花’鑲嵌結構系統之皺摺呈現, 以及由‘鐘乳石簷口’元素所發想的伊斯蘭構築透明性。透過對於線條、平面和立體讀形式進行分析與探討，創造以聚合結構相互連接的模塊單元。

研究的成果以空間和建築細節為基礎並進行合理化，涵蓋了如宣拜塔（Minaret）、拱門（Iwan）、洗禮間（Wudhu）、遮陽棚（Brise Soleil）、鐘乳拱亭（Muqarnas Pavilion）、與圖騰窗花（Mashrabiya）。這些成果將視為對於現有伊斯蘭建築元素中木材結構的重新詮釋，因此實現了傳統與當代設計觀點的和諧融合。

The cosmology of Islamic architecture reflects the desire to create a virtual utopia for worshippers, evoking a sense of heaven in the eyes of believers. Patterning and decoration play a crucial role in realizing this cosmology by constructing an enveloping shell within a building, shielding worshippers from the outside reality. In architecture, this embodiment of "truth" expresses the structural composition that enables the building to stand. When considering Islamic architecture as a prestigious form of religious symbolism, operating within the framework of "Royal Art," discussions about Islamic identity often prioritize imitation and replication, without sufficient regard for regional variations such as materiality and tectonic articulation.

The objective of this research was to reinterpret Islamic architecture in a new digital form by deriving design elements from existing decorations and ornamentation and incorporating them into a modular and articulated tectonic system. The study focused on two specific Islamic elements in different contexts:  Representation of Drapeness in the Mashrabiya Tessellated Structure System, and Structural Transparency of Islamic Tectonic Based on Muqarnas Element. The research involved analyzing and developing the design by exploring line, planar, and 3D block forms to create modular units that can be interconnected in an aggregate structure.

The research output will provide a rationalized approach to spatial and construction details, incorporating elements such as the Minaret, Iwan, Wudhu, Brise Soleil, Muqarnas Pavilion, and Mashrabiya. These elements will be reinterpreted in terms of timber articulation within the existing Islamic architectural context, aiming to achieve a harmonious blend of traditional and contemporary design approaches. The focus will be on developing a comprehensive understanding of the spatial and construction aspects of these elements, resulting in innovative and cohesive design solutions.

Table of Content
Chapter One  –  Introduction 
1.1	Research Background	1
1.1.1	Islamic Architecture and Its Identity in the Perspective of Tectonic Culture.	1
1.2	Research Motivation	4
1.2.1	The Identity Crisis of Architecture in Rapid Developing Middle East cities.	4
1.2.2	The Evolution of Timber Appearance in Architecture along Technology Intervention	5
1.2.3	The Presentation of Timber Architecture in the Current Postmodernism Era	8
1.2.4	The Intrinsic Value of Tectonic Study in Architecture Understanding	10
1.3	Research Objective	11
1.3.1	Reinterpretation of Islamic Architecture in New Digital Form via Timber Material.	11
1.3.2	Deriving Ornament Patterning in Architecture into a Design System.	12
1.3.3	Deriving Architecture Tectonic Design base on the Nonstandard Material Module.	13
1.4	Research Structure Flowchart	15
Chapter  Two  –  Literature Review
2.1.	Tessellation from Art to Tectonic	16
2.1.1.	Tessellation in the Form of Nature	16
2.1.2.	Tessellation in the Form of Art – M.C. Escher	17
2.1.3.	Tessellation in Cultural Aesthetic	18
2.1.4.	Tessellation in Digital Tectonic	21
2.2.	Theoretical Discourse on Articulation in Architecture	23
2.2.1.	Kenneth Frampton’s Architecture in Tectonic Culture Perspective	23
2.2.2.	Kengo Kuma in Natural Materiality	25
2.2.3.	Buckminster Fuller in Synergetic Structure	27
2.2.4.	Mario Carpo in Design in the Digital Turn	28
2.3.	Islamic Geometric Tessellated Composition	30
2.3.1.	Classification by Symmetry and Repetitive Strategy	31
2.3.2.	Classification by Numeric Quality	32
2.3.3.	Classification by Plane Symmetry Group	33
2.3.4.	Classification by Grid	36
2.3.5.	Classification by Polygon Technique	37
2.3.6.	Tridimensional Tessellated Ornament / Muqarnas	40
2.4.	Islamic Architecture in Malaysia Context	41
2.4.1.	Regional Characteristics of Malaysia’s Traditional Architecture	41
2.4.2.	Chronology of Islamic Influence in Malaysia Architectural History	43
2.4.3.	Mosque Architectural Timeline in Malaysia	46
2.4.4.	The Islamic Architecture of Malaysia’s Identity Inheritance	49
2.5.	Summary	50
Chapter Three  – 	Representation of Drapeness in Mashrabiya Tessellated Structure System 
3.1	Islamic Patterning in Architectural Expression	55
3.2	Digital Generative Grid Patterns	59
3.2.1.	Threefold Tessellation Pattern	60
3.2.2.	Fourfold Tessellation Pattern	61
3.2.3.	Islamic Pattern Generative Grasshopper Plugin – Parakeet	62
3.3	Translation from Line to Geometrical Interlocking Articulation	67
3.3.1.	Lattice Interlocking	67
3.3.2.	Planar Interlocking	79
3.3.3.	Stick Interlocking on a Curve Surface	83
3.4	Summary	88
Chapter Four – Structural Transparency of Islamic Tectonic Based on Muqarnas Element
4.1	Transparency and Islamic Architecture Expression	90
4.2	Muqarnas from Decoration to Structure	92
4.2.1	Muqarnas Formation	94
4.2.2	Muqarnas Translation to Structural Transparency	99
4.3	Strip Interlocking Modular Units Derivation from Muqarnas Element	104
4.3.1	Module S	110
4.3.2	Module S1	111
4.3.3	Module M	112
4.3.4	Module L	113
4.4	Digital Aggregatory Reassemble of Muqarnas Cell	114
4.4.1	Line Field Aggregation	118
4.4.2	Geometry Field Aggregation	119
4.4.3	Digital Aggregatory on Interlocking Modular Units	122
4.5	Summary	125
Chapter Five – Architecture Digital Design Based on New Islamic Decoration through Timber Structure
5.1        The Presence of Timber in Islamic Architecture	127
5.2	Minaret	128
5.3	Wudhu	137
5.4	Iwan	143
5.5	Brise Soleil	150
5.6	Muqarnas Pavilion	155
5.7	Mashrabiya	160
5.8	Summary	166
Chapter Six – Conclusion  169
References  173
Appendix  177

List of figure
Figure 1.1:	Arches colonnade in Great Mosque Cordoba shares similar structural composition and elements with Gothic architecture.
Figure 1.2:	Element of patterning create by carving or attaching (mosaic) as a decoration that expresses Islamic Identity for the architecture.
Figure 1.3:	Architecture of vernacular and symbolism in the Middle East. New Barris Village, Egypt – Hassan Fathy (Left). Museum of the Future, UAE – Killa Design (Right).
Figure 1.4: 	Timber material for construction fabrication chain from mass production to mass customization.
Figure 1.5: 	Timeline of technological evolution in fabrication tools involving hardware and software.
Figure 1.6: 	Representation of timber architecture and its signification in three major eras of industrial advancement.
Figure 1.7: 	The comparison of dendriform in present with tectonic value, Interior of Johnson Wax Building (Left) and as decoration, Interior of Neue Staats Galerie’s lecture room (Right).
Figure 2.1: 	Tessellation pattern from nature (left to right) cactus, pineapple skin, fish scale, and snakeskin.
Figure 2.2: 	Art of M.C. Escher (left to right) ‘Sky and Water - 1938’, ‘Angels and Devils -1960’, ‘Day and Night - 1938’.
Figure 2.3: 	Compilation of Owen Jones in ‘Grammar of Ornament - 1856’. Ornament from Greek, Renaissance, Hindu, Chinese, and Roman. (Sequence from top left to bottom right) 
Figure 2.4: 	Cover image of the book titled - Digital Fabrication by Lisa Iwamoto (left), and AD volume 89 Discrete by Gilles Retsin (right).
Figure 2.5: 	Cover image of the book titled - Studies in Tectonic Culture by Kenneth Frampton (left), The History and Antiquities of The Doric Race by Karl Otfried Muller (center), and Modern Architecture by Manfredo Tafuri (right).
Figure 2.6: 	Cover image of the book titled - Architecture of Defeat (left), Small Architecture (center), and Natural Architecture (right) by Kengo Kuma.
Figure 2.7: 	Triangle and tetrahedron: synergy 1+1=4; two triangles combined to form a tetrahedron, a figure volumetrically embraced by four triangles, therefore one plus one seemingly equals four. (Synergetic 108.01) (Left) subdivision of dome’s frequency based on triangle module. (Right)
Figure 2.8: 	Cover image of the book titled – Synergetics (left), and Pattern Thinking (right) by R. Buckminster Fuller.
Figure 2.9: 	Cover image of the book titled – The Second Digital Turn by Mario Carpo
Figure 2.10: 	Cover image of the book titled – Islamic Geometric Patterns by Jay Bonner.
Figure 2.11: 	(Left) Hexagonal pattern based on a diagonal isometric grid. (Middle) Triangular pattern based on a hexagonal grid. (Right) Square pattern based on the orthogonal grid.
Figure 2.12: 	Two sizes hexagon threefold pattern.
Figure 2.13: 	Miller indices plane symmetry group, composed by Jay Bonner.  
Figure 2.14: 	Example of Islamic geometric pattern modular extraction based on plane symmetry group type, composed by Jay Bonner.  
Figure 2.15: 	Classic fourfold (top) and threefold (bottom) tessellated pattern generated by a 45°orthogonal grid. 
Figure 2.16: 	Classic star pattern in various expressions. Basic line grid (top left), tiling treatment (top center), widening line (top right), interweaving line (bottom left), double line (bottom right)  
Figure 2.17:	Pattern chart of acute, median, obtuse, or two-point in various angles. Composed by Jay Bonner.
Figure 2.18:	Muqarnas is applied to various architectural elements.
Figure 2.19:	Traditional Malay house building by large part assembling (left). House moving event carried out by the village community (right).
Figure 2.20: 	List of timber classification and species harvest in Malaysia. Information from Malaysia Timber Industry Board (data last updated on December 2019)
Figure 2.21: 	Chronological of architecture appearance from early to current (sequence from top left to bottom right) Kampung Laut Mosque, Kampung Kling Mosque, Jamek Mosque, Malaysia National Mosque, Kuala Lumpur Mosque, Iron Mosque.
Figure 2.22: 	Mosque architecture timeline in Malaysia composed by Siti Dalila Mohd Sojak. Source from ICRP 2019.
Figure 3.1: 	The Bedouin tent in Arab nomadic culture. Textile is the main material for shelter structures.
Figure 3.2: 	Calligraphy embroidery textile as a symbol of the Islamic universe at Kaaba.
Figure 3.3: 	Meshrabiya in Cairo, Egypt. Source from Development Workshop digital archive by John Norton.
Figure 3.4: 	Lighting effect of Louvre Abu Dhabi Museum and composition of the roof layers. Source from Ateliers Jean Nouvel.
Figure 3.5: 	Interior lighting effect of Institute Du Monde Arabe, and kinetic mechanism of sunscreen.
Figure 3.6: 	Architectural representation of pattering in different periods and materials.  Textile on Bedouin tent (left), mosaic tiles on Dome of the Rock (middle), digital perforated metal sheet on Doha Tower (right).
Figure 3.7: 	Grasshopper configuration of threefold tessellation pattern.
Figure 3.8: 	Grasshopper configuration of fourfold tessellation pattern.
Figure 3.9: 	The result of pattern generation from parakeet via six main grid systems (from top to bottom) – Elongated triangular, Rhombi-trihexagonal, snub square, snub trihexagonal, trihexagonal, and truncated hexagonal, in combination with Genotype pattern (left to right) genotype C, K, and L.
Figure 3.10: 	Grasshopper configuration of attractor constrain in parakeet and results of pattern generation (above – point attractor, below – curve attractor)
Figure 3.11: 	Grasshopper configuration of parakeet pattern morphing three hyperbolic paraboloid surfaces.
Figure 3.12: 	Grasshopper configuration of parakeet pattern morphing Mobius ring surfaces.
Figure 3.13: 	Module derivation from the fourfold square grid.
Figure 3.14: 	Horizontal aggregation based on chainmail interlocking.
Figure 3.15: 	Module derivation from the fourfold octagonal grid.
Figure 3.16: 	Horizontal aggregation of module two.
Figure 3.17: 	Vertical aggregation of module two.
Figure 3.18: 	Module derivation from the threefold hexagonal grid.
Figure 3.19: 	Horizontal aggregation of module three.
Figure 3.20: 	Module derivation from the threefold triangular grid
Figure 3.21: 	Horizontal aggregation of module four.
Figure 3.22: 	Module derivation from the threefold triangular grid.
Figure 3.23: 	Horizontal aggregation of the module in node-to-edge connection.
Figure 3.24: 	Horizontal aggregation of module mirrored connection.
Figure 3.25: 	Module derivation from rosette/star pattern.
Figure 3.26:       Parts of circular aggregation from the combined module. – Inner, outer, and centered star. 
Figure 3.27: 	Interlocking panel for hexagon tessellation pattern.
Figure 3.28: 	Interlocking panel for quarterly octagon tessellation pattern.
Figure 3.29:	Interlocking panel for octagon tessellation pattern.
Figure 3.30: 	Interlocking panel for four-angle star tessellation pattern.
Figure 3.31: 	Interlocking panel for dove shape tessellation pattern.  
Figure 3.32: 	Curved surface interlocking panel for four hexagon tessellation patterns.
Figure 3.33: 	Comparison of interlocking angle for line expansion and line direction/degree one (left) and degree two (right)
Figure 3.34: 	Penrose, Genotype D, E, and K line patterns in four density iterations. 
Figure 3.35: 	Grasshopper configuration for interlocking batten and the transformation process from surface, lines, and batten geometry.  
Figure 3.36: 	Configuration of Genotype D in various density iterations and forms.
Figure 3.37: 	Configuration of Genotype E in various density iterations and forms.
Figure 3.38: 	Configuration of Genotype D in various density iterations and forms.
Figure 3.39: 	Configuration of Penrose in various density iterations and forms.
Figure 3.40: 	Close-up interlocking relation among each batten of the outcome. 
Figure 3.41:	Mirrored duplication of the outcome for extended structure.
Figure 4.1: 	Representation of ‘Transparency’ in Le Corbusier’s works. Maison Cook (left) and Villa Stein de Monzie (right).
Figure 4.2: 	Structural advancement in the Gothic era that enables transparency of building which allows exquisite opening design.  
Figure 4.3: 	The expression of architectural transparency by timber articulation in Asia’s mosque.
Figure 4.4: 	Square lattice style Muqarnas in Abraham Palace (image source from shiro1000.jp)
Figure 4.5: 	Polar coordinate style Muqarnas in Isfahan Mosque (image source from shiro1000.jp)
Figure 4.6: 	Original style Muqarnas in the entrance of Suleiman Mosque (image source from shiro1000.jp)
Figure 4.7: 	Formation of cells based on square and rhombus.
Figure 4.8: 	Existing entrance Iwan at Malik National Museum, source from Google map (left). Blow up muqarnas detail, source from shiro1000.jp/muqarnas (right)
Figure 4.9: 	Malik National Museum Muqarnas composition and characteristics on planar projection and 3D remodeling.
Figure 4.10: 	Existing North chamber niche at Jameh Mosque source from Google map (left). blow up Muqarnas detail, source from shiro1000.jp/Muqarnas (right)
Figure 4.11: 	Jameh Mosque Muqarnas composition and characteristics on planar projection and 3D remodeling.
Figure 4.12: 	Existing entrance Ivan at Shah Cheragh Mosque, source from Google map (left). blow up muqarnas detail, source from shiro1000.jp/muqarnas (right)
Figure 4.13: 	Shah Cheragh Mosque Muqarnas composition and characteristics on planar projection and 3D remodeling.
Figure 4.14: 	Sectioning representational of Muqarnas at Malik National Museum in timber articulation
Figure 4.15:	Sectioning representational of Muqarnas at Jameh Mosque in timber articulation
Figure 4.16: 	Sectioning representational Muqarnas at Shah Cheragh Mosque in timber articulation
Figure 4.17: 	Formation of cells based on square and rhombus, extension from previous figure 4.7 in addition of board and stick.
Figure 4.18: 	Stick formation structure derivate based on Jameh Mosque Muqarnas profile.
Figure 4.19: 	Corbel arch structure tomb during the medieval age.
Figure 4.20: 	Bucket arch or Dougong structure in Chinese architecture.
Figure 4.21:	 Load distribution relation in Muqarnas.
Figure 4.22: 	Stick form interlocking module derivation.
Figure 4.23: 	Base module A (left), module B (center), and module C (right).
Figure 4.24:	Module S wall structure developed by base module A (figure 4.23).
Figure 4.25: 	Module S1 wall structure developed by base module A (figure 4.23).
Figure 4.26: 	Module M wall structure developed by base modules A & B (figure 4.23).
Figure 4.27: 	Module L wall structure develops by base modules A, B & C (figure 4.23).
Figure 4.28: 	Formation of cell in muqarnas of Jameh Mosque. 
Figure 4.29: 	Information of aggregation for Wasp operation.
Figure 4.30: 	Wasp grasshopper configuration (above) Combination possibility of aggregation based on given geometry and rules of duplication (bottom).
Figure 4.31: 	Four variations of combination output.
Figure 4.32: 	Muqarnas aggregation generate from line field.
Figure 4.33: 	Muqarnas aggregation generates from geometry field (curved wall).
Figure 4.34: 	Muqarnas aggregation generate from geometry field (Dome).
Figure 4.35: 	Muqarnas aggregation of dome field generate by attribute proxy replaced from cell to board. 
Figure 4.36: 	Proxy composition in stick form modular for aggregation form finding. 
Figure 4.37: 	Modular stick form aggregation in line field constraint. 
Figure 4.38: 	Modular stick form aggregation in geometry field constraint. 
Figure 5.1: 	Mineret of Jamek Mosque, Malaysia (Left), Kalan Mosque, Uzbekistan (Middle), Al-Azhar Mosque, Egypt (Right) 
Figure 5.2: 	Design outcome based on research of timber articulated Minaret.
Figure 5.3: 	Exploded view of minaret’s structural tiers composition.
Figure 5.4: 	Exploded view of minaret’s tower head structural tiers composition.
Figure 5.5: 	Perspective view from tower (top), and entrance (bottom).
Figure 5.6: 	Blow up construction detail on Muqarnas cantilever support (top), and awning batten (bottom).
Figure 5.7: 	Exploded detail of Muqarnas awning batten from inner view (top), and outer view (bottom).
Figure 5.8: 	Muqarnas interlocking module dissection and arrangement per unit on timber board for CNC milling.	
Figure 5.9 : 	Wudhu area of New Valide Sultan Mosque, Turkey
Figure 5.10: 	Design outcome based on research of timber articulated Wudhu.
Figure 5.11:	Connection details of roof support to wall interlocking structure.
Figure 5.12: 	Exploded view of Wudhu’s structural tiers formation.
Figure 5.13: 	Blow-up detail on roof batten structure connection and main wall interlocking connection.
Figure 5.14: 	Exploded construction detail on Wudhu’s timber roof structure.
Figure 5.15: 	Muqarnas interlocking module stick arrangement on timber board for CNC milling.
Figure 5.16: 	Iwan in Qaboos Mosque, Sohar (Left) and Jameh Mosque, Isfahan (right).
Figure 5.17: 	Design outcome based on research of timber articulated Iwan.
Figure 5.18: 	Parakeet generated pattern in three parameters. – Vertices 0.2, 0.6, and 0.8 and translation from planar to curved surface (top left). Parametric configuration from pattern generation to structural rationalization.
Figure 5.19: 	Iwan’s dissection of structural tiers formation.
Figure 5.20: 	Exploded view of Iwan’s structure (combined).
Figure 5.21: 	Exploded diagram of Iwan’s structure (blow up).
Figure 5.22: 	Exploded diagram of Iwan’s structure (partial).
Figure 5.23: 	Exploded diagram of Iwan’s structure (substructure connection).
Figure 5.24: 	Brise Soleil / Umbrella in Medina Haram Piazza.
Figure 5.25: 	Design outcome based on research of timber articulated Brise Soleil.
Figure 5.26: 	Modular composition deviated in chapter four developments into column formation.
Figure 5.27: 	Relation of articulation between block composition and steel column support.
Figure 5.28: 	Brise Soleil dissection of structural tiers formation.
Figure 5.29: 	Exploded diagram of the column to truss articulation.
Figure 5.30: 	Exploded diagram of column articulation.
Figure 5.31: 	Muqarnas interlocking module stick arrangement on timber board for CNC milling.
Figure 5.32: 	Muqurnas formation in Imam Mosque, Isfahan (left & middle), St Petersburg Mosque, Russia (right).
Figure 5.33: 	Design outcome based on research of timber articulated Muqarnas pavilion.
Figure 5.34: 	Perspective view of the pavilion from the bottom.
Figure 5.35: 	Pavilion composition of the primary structure (left) and Muqarnas aggregation (right).
Figure 5.36: 	Exploded diagram of modular Muqarnas board units assembly sequence on the primary structure.
Figure 5.37: 	Muqarnas board module assembly sequence and configuration (top). Modular variation and numbers of total units in the entire pavilion formation (bottom). 
Figure 5.38: 	Mashrabiya at the old street of Al Balad quarter, Mecca.
Figure 5.39: 	Design outcome based on research of timber articulated Mashrabiya wall.
Figure 5.40: 	Façade view of Mashrabiya wall from the interior (top) and exterior (bottom).
Figure 5.41: 	Mashrabiya wall dissection of structural tiers formation.
Figure 5.42: 	Partial segment of Mashrabiya wall from the interior (top) and exterior (bottom).
Figure 5.43: 	Exploded diagram of Mashrabiya structure formation. 

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