İslâmi yıldız geometrik örüntülerin biçim grameri yöntemleri ile kurallı üretimi
Rule for generating Islamic star patterns with shape grammer methods
Yazar: VOLKAN DALAĞAN
Danışman: PROF. DR. SİNAN MERT ŞENER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Mimarlık Ana Bilim Dalı / Mimari Tasarım Bilim Dalı
Derece: Yüksek Lisans, 2012
Konu: Matematik = Mathematics ; Mimarlık = Architecture ; Tarih = History
Dizin: Örüntü algılama = Pattern perception ; Örüntü sınıflama = Pattern classification ; Örüntü şekillendirme = Pattern forming ; İslam kültürü = Islamic culture ; İslam mimarisi = Islamic architecture ; İslam sanatı = Islamic art ; İslam tarihi = Islamic history

Özet:
1970'lerde Stiny ve Gibs'in biçim üretim metodu olarak kullandıkları biçim grameri ve kural setleri ile yeni biçim türetimlerini yaratmışlardır. Kurallı üretim yöntemleri daha sonraları birçok disiplinle birlikte tasarım dahilinde de kullanılmıştır.Çalışmanın konusu olan İslâmi geometrik örüntüler biçim grameri disiplini yardımıyla kurallı üretimleri yaratılmaya çalışılmıştır. Bugüne kadar birçok kişi tarafından İslâmi geometrik örüntüler farklı kurallarla çizilmeye çalışılmıştır.Çalışmada on, altı, sekiz ve on iki kollu düzgün İslâmi rozet ve yıldız örüntülerin biçimsel ve çizim özellikleri incelendikten sonra formülize edilmeye çalışılmıştır. Bununla birlikte kol sayısı ve açısal ilişkilerden doğan birim üçgenin rozet veya yıldızların çizilmesinde kullanılmasıyla kurallar seti ortaya çıkarılmıştır. Birinci bölümde çalışmanın amaç, kapsam ve yöntemi üzerinden yapılacak çalışma ve hedefler açıklandıktan sonra ikinci bölümde İslâm sanatı konusu üzerinden tarihsel gelişimi, geometrik örüntülerin ve süsleme olan arabeskin bulunduğu mimari eserlerden dönem bazında bahsedilerek tarihten örnekler tanıtılmaya çalışılmıştır.Erken İslâm dönemi ve Emeviler, Abbasiler ve Anadolu Selçuklu ve Osmanlı devletleri dönemi mimari süsleme örnekleri üzerinden örüntülerin biçimsel özellikleri anlatılmaya çalışılmıştır. Diğer tasarım disiplinleri bazında mimari haricinde seramik, çini, halıcılık  dokuma, ve kaligrafi gibi belli başlı alanlarda görülen geometrik biçimlerden de örnekler gösterilmiştir. Bu yolla İslam sanatı üzerinden süsleme sanatı olan arabeskin özellikleri de anlaşılmaya çalışılmıştır.Bir sonraki bölümde dil ve onun kurallı kümesi olan gramerin tanımı yapıldıktan sonra biçim gramerinin tanımı ve kullanıldığı farklı disiplinlerde örneklere yer verilmiştir. Biçim gramerinin İslâmi geometrik şekiller üzerinde uygulandığı Kaplan, Salesin, Lee, Abas ve Salman'ın yarattıkları üretimlerden örnekler verildikten sonra simetri ve simetri gruplarından doğrusal türeyen yedi friz grubu ve x ve y aksında türeyen on yedi duvar kağıdı grubu açıklanmıştır. Şablon yaratımı olarak İslâmi örüntüler incelenmiş ve Ostromoukhov, Schattscheider ve Kaplan'ın çizimleriyle örneklendirilmiştir.Dördüncü bölümde yıldız kollu rozetlerin biçim grameri kuralıyla yeni bir üretim biçimi yaratılmaya çalışılmıştır. Kol sayısına bağlı olarak çizilen birim üçgen yıldız ve rozetlerin yaratımında açısal ilişki kurmaktadır. Rozet motif iki ayrı parça olarak merkezdeki yıldız ve çevresindeki halka olarak düşünülüp çizilmektedir. Daha sonraki aşamada kolları düzgün olmayan ve farklı açılara sahip rozet ve yıldızların üretimi kural setleriyle gösterilmiştir. Sonuç olarak bu bölümde yaratılan yeni formlarda motifler kol sayısı ve açısal farklılıklar ile yaratılabilmiştir. Üretilmiş olan rozet ve yıldız motiflerin bir araya getirilerek yaratılması amaçlanmıştır. Tasarım mantığı eskiden referans alarak modern araçlarla yeni olanı yaratmaktır. Daha sonraki aşama bu simetri gruplarını kullanarak kendi şablonlarımı yaratmak olmuştur. Bu şablonların yaratımından sonraki adım içlerinin çeşitli rozet veya yıldız motiflerle doldurulması olmuştur. Farklı açılarla düzenlenebilen motifler şablona işlenebilir. Son olarak da yaratılan örüntülerin çizgi kalınlıkları, kesişim noktalarındaki boşluklar ve renklendirilmeleri ile örüntüye farklı anlam ve algı katılması amaçlanmıştır.Son bölüm olan sonuç bölümünde çalışmanın genel bir değerlendirilmesi yapılarak, ileride üretilmesi olası olabilecek bir programın nasıl olabileceğine dair bilgiler verilerek çalışma sonlandırılmıştır.

Abstract:
In 1970's shape grammar and rule sets have used as shape generation method by Stiny and Gibs for generating new shape deriving. Later sets of generative methods used within design principles in various of disciplines. Islamic geometric patterns that is the subject of studying aimed ruled productions by help of shape grammar discipline. Islamic geometric patterns drawn by many researches with different set of rules with using effectively usage of computers. In research, the approach was formulating of production after studying carefully of shape and drawing properties of ten, six, eight and twelve stars and Islamic rosettes. Within this by using an unit triangle that inference of number of arms of rosette and angular relations, this triangle used for drawing of rule sets of rosettes and stars.Islamic civilization comprises one of the richest period of cultural heritage of humanity of world. From China to Spain they spread of a vast geography and produced rich creations in most of art disciplines. Roots of Islamic art touches to traditions of Helen, Byzantine, Sassanian and Turk. The difference of Islamic art is recreation of these traditions by mixing up original and unique way. Art was reflecting language of Qur?an and imitating mortals meant recreating them in other words. This restriction was appeared by fear of becoming an idol of someone else. Islam artist who obeyed this rule and concept started to stylize and abstract his or her art. Decoration artist, architect or calligrapher worked for reaching to this geometric order in their works.After the Four Caliph period that started with death of the Prophet Muhammad, Omayyad Dynasty found the first dynasty. Changing the location of the capital city from Medina to Damascus enables them acquaint to Roman and Hellenistic art and the first serious architectural building of Dome of the Rock built between 687  691. In year 750 Abbasid Dynasty ended Omayyad period and for the first mission they carried the capital city from Damascus to Baghdad and within this the first city was settled by Muslims was Baghdad. Between years 848 ? 852 Samara Mosque built. In the Anatolian Seljuk period in Anatolia, Divrigi Ulu Mosque (1228/9) has had compositions of geometric stone carving on its portal. Islamic architecture carried by conquests to the west and east, east and west Europe by Ottoman Empire and with its art. This also means trading culture and art. Bringing artists to Istanbul after Caldiran conquest can be shown as an example.Geometric ornamentation that used in various disciplines examined as calligraphy, miniature, bookbinding, ceramics and glazing, carpet and textile. In these works geometric patterns searched. In this chapter also similarities of patterns and decorations searched and six properties clarified. Then six, eight, ten and twelve star rosettes drawn and given examples from buildings.In third chapter after giving the description of the language and its ruled group grammar, samples from different disciplines that uses shape grammar as a design tool.Language as a thinking and expression tool and also a team defined for creating symbols and words or a set of rules of word compositions for creating sentences. Examples for set of rules in spoken language is one of the most well know studies of Samuel Morse and his patented Morse Alphabet. Later to our modern age in WWII Enigma crypt machine used for sending and receiving codes by German army at war. After giving these examples for the study of shape grammar can be classified into three titles as topological relations, geometrical relations and traditional relations. Star patterns can be examined by geometrical relations because of geometric elements have characteristics by editions of their centers, directions, values or the applied transformation processes on coordinate planes. So inherently every language uses its elements (words) and grammars as rules. For these two groups, two set of rules enables us to generate meaningless sentences. These are ?semantic? and ?syntactic? rules.And for the transformation tools for basic design or computer aided design while we are working with shape in design we can classify these operations into two groups. These are geometric operations and Boolean operations. Most well known operations that applied to the shapes are move, rotate, scale and mirror reflecting according to an axis. Boolean operations used for creating a new shape from two solid forms or shapes. Complex forms can be generated by this transformation rules. In design field, shape grammar used in many disciplines such as front head light design of Buick cars or town planning of Beirao and Duarte and for the architectural works a design model by fractals and row house design of Malagueira houses of Alvaro Siza.Within this approach Seljuk Mulayim presented geometrical analysis of wooden carvings of Nigde Sungurbey Mosque's north facade door. Kaplan and Salesin generated their own rules as a starting from one line and producing an symmetrical view of it on horizontal axis and arraying it with the number of star rosettes points. The extension of inner lines of star intersects and creates a detail and this detailing categorized by giving a s value to the shape.Main aim is with the help of the symmetry rules multiplying stars and rosettes in a row to create patterns that produced in previous chapters. Symmetry groups titled in two groups as a result of analyzing patterns in a mathematical classifying way. These are orderly first seven frieze groups and second one is seventeen wallpaper groups or patterns. In online dictionary Websters the symmetry means in mathematical term; as an attribute of shape or connection; absolute reflection of shape to the both sides according to section line or plane. Seven frieze groups are groups of shapes that transforming with different operations on one direction. They named shortly F1  F7. Firstly the difference from the first group rule sets of the seventeen wallpaper groups derived on two directions. Seventeen rules derived from five different units that are square, rhombus, rectangle, parallelogram and hexagon. We can also named these first template as a grid and every grid unit transforms on two vectors named V1 and V2.Further achivement is explaining symmetry groups the next step is examining the methods for generating Islamic geometric patterns. With these rules Ostromoukhov worked with Cayley diagrams for analyzing and reproducing Islamic patterns. For Kaplan the polygons and their connecting systems Islamic patterns can be generated by connecting relations of each other. Approach is placing a (X) in the middle of edge of a polygon and then extensions of these (X) lines intersects with the others. So that there the grid scheme produced. For Islamic patterns generating them with rules of planar symmetry rules, seventeen wallpaper groups used producing star and rosettes that approached in the previous chapter. First purpose is creating templates and with the Islamic decoration elements like polygons, stars and rosettes filling the template to create an Islamic pattern. Lastly produced patterns wanted to present with different visual images accept the native line work. In section 4.3.1 to create a template aim is to create a polygonal grid system by placing motifs main edges as a polygon on folding center of planar symmetry group. But after these process as mentioned in second chapter in Islamic decoration art arabesque tiling created an empty space fear so that empty spaces can be filled after extending edge lines. In another words the motifs must be seen as a unique or as one. From previous chapter the unit triangles that are derived from the angular relations of star rosettes and these relations now wanted to implement to planar symmetry groups to create new templates for Islamic geometric patterns.In fourth chapter after examined other examples then the production of set of rules for Islamic star pattern generated. Generally we see that star patterns have two part. The first one of these is star that has n numbered arms and an outer ring for surrounding star. For example of N=10 pointed star we must use 18, 72, 90 triangle. From this triangle now we can draw a circle with one unit radius and a second one which has hypotenuse ? 1 radius. We must divide 360 degrees into the twice of numbers of arms. So 360/20 = 18 degrees is the key angle and because of this the 18, 72, 90 triangle drawn. The isosceles triangle gives us the guide lines for the outer ring and if we draw a line from its left bottom point and intersect it with its bisector line and mirror it twice with according to the hypotenuse four lines of outer ring can be drawn the other operation is arraying it within a center point of the circle. Inner circle represents the range of the star and by diving the perimeter into ten points by drawing a line through the the points on perimeter and from the center point, a second line must drawn with the 18 degrees according to the center line. Then the lines transformed by arraying ten times around the center point of the rosette and then deleting the lines that pass through the center. After these steps ten pointed star can be produced by a set of steps after the two shapes summed up over the same centers ten pointed star rosette could produced. Within same directions of rules in research from 4 to 36 pointed Islamic rosettes produced. Also the numbers that can't properly dividing into 360 degrees produced with very small refracting. Not only a certain angular degree, any kind of angles with intersecting of rosettes arms can be produced with set of rules in chapter 4.2.Patterns which has odd arms or points are already symmetrical and have 2n edges. This means their symmetry and central rotations are itself again. Designs that includes more than one motifs can be arranged firstly the mid motif and other motifs that arrange around the central shape. After these arrangement of their polygonal template can be multiply by symmetry group rules. Second steps is filling the polygons of templates with rosettes or stars or leave them empty. The next and final step is visualizing patterns that created only in line type in study for researching. So the properties added to the patterns orderly giving width to lines, giving gaps to intersection points of pattern and coloring empty regions of the pattern. So that the pattern have different identities and perceptions.In conclusion chapter the overall process summarized and some thoughts shared about developing a software for designers. There is also a common program derived by Kaplan named Taprats. The next step maybe developing a program that will start by organizing templates, rosette motifs and star patterns.