A Shape Grammar: The Language Of Traditional Turkish

conditions of land and climate. This classification was not made in chronological order, butit shows the stages of development in time (Eldem, 1984). In some large houses (i.e.konaks) and palaces of differing sizes, more than one type of plans may be combined.These combinations were not new plan types; they were generated by using more than oneplan type or repeating a certain plan type twice or more. Large houses and palaces withone, two, three halls were designed by using this method.Plan Type without a HallThis is the most primitive type of the traditional Turkish house and consists of one or morerooms in a row. There is a circulation area in front of the rooms in the shape of a courtyard.When the rooms are above ground level, this area takes the form of a balcony.Plan Type with an Outer HallThis type constitutes the first stage in the development of the plan. In this plan type, therooms in a row are connected with each other by means of a hall. In the primitive plans ofthis group, the hall was an open place with pillars and only the top was covered. With theimprovement of living and housing standards, the open hall was closed by using glassbetween the pillars. After the 19th century, windows were added. While some plans inthese type have recesses (eyvans) between the rooms, some others have pavilions (kiosks)at one end or both. In some cases, the pavilion and the recesses are used together; in others,the recesses are two in number, and in still others the pavilions are projected from the endsof the hall. L- or U-shaped plan layouts come out as a result of these additions (Fig. 2a).Variations and different combinations of the spaces in this plan type constitute differentplan layouts in this group. In some cases, the corners of some rooms are inflected in orderto provide entrance.Plan Type with an Inner HallIn this type, both sides of the hall are surrounded by rows of rooms. This plan type isdeveloped by adding another row of rooms onto the outer side of the hall. In some plans,the inner hall is extended towards a room which is smaller than the other rooms in the row.In some other plans, the hall is extended by adding another hall or an eyvan. This type mayhave several sub-types because of these variations (Fig. 2b). In some cases in this group,the corners of some rooms are also inflected in order to provide entrance.7

1231Room 2 Rooms 3 Rooms4567With aneyvan4 Rooms5 Rooms5 Rooms with aneyvanA1 Plan typewith anouter hallA2 Plan typewith ansupplemen.hallA3 Plan typewith onekioskA4 Plan typewith twokiosksA5 Plan typewith oneprojectingkioskA6 Plan typewith twoprojectingkiosksA7 Plan typewith semicentral hallA8 Plan typewith acorner hallFigure 2a. Plan types with an outer hall (Eldem, 1984, pp.26-27)8

B1Plan type withan inner hallB2Plan type with asupplementaryhallB3Plan type witha subordinateroomB4Plan type witha supplementryhall and asubordinateroom121 Room2 Rooms 3 Rooms3456With aneyvan in themiddleWith aneyvanat the sideWith acentralhallFigure 2b. Plan types with an inner hall (Eldem, 1984, p.28)Plan Type with a Central HallThis type represents the third and the last stage in the development of the plan layouts. Thehall is located in the middle of the house and is surrounded by rows of rooms on all foursides. It is oval or square in shape and has curved or inflected corners in some cases.Among the rows of rooms are one or two eyvans in the form of recesses, which are alwayslocated on the axis of the hall. By changing the numbers of eyvans from two to four,variations and combinations are generated in this plan type (Fig. 2c).9

C1Plan type with acentral hallC2Plan type with acentral hall and aneyvanC3Plan type with acentral hall and twoeyvansC4Plan type with acentral hall and twoeyvansC5Plan type with acentral hall and threeeyvansC6Plan type with acentral hall and foureyvansC7Plan type with along hall12345With acentral hallWith asquare hallWith aninflectedhallWith asupplemt.hallWith anoval hallFigure 2c. Plan types with a central hall (Eldem, 1984, p.29)10

A Parametric Shape GrammarIn this section, a parametric shape grammar developed by the author to generate the plansof traditional Turkish houses is presented. Parametric shape grammars are variations ofshape grammars in which shape rules are defined in terms of shape rule schemata. A shaperule schema (α β) consists of the parameterized shapes α and β (Stiny, 1980b, p.349). Indesign, the term schema is often used to represent the properties of a formal structure. Inthe parametric shape grammar, a shape rule schema is applied by the replacement of theshape on the left-hand side (α) with the shape on the right-hand side (β). As Mitchellstated, “The shapes that appear in rules may be actual construction elements and spaces, orthey may be abstract shapes and volumes that serve as construction lines, grids, axes,place-holders for later substitution of something else, and other devices that guide thedevelopment of a design,” (Mitchell, et.al., 1991, p.19).In a syntactic or a compositional context, a design can be defined as a complex of shapesand the relationships between these shapes. A shape grammar (SG) contains a vocabulary(V), a set of spatial relations defined by shape rules (R), and an initial shape (I) made up ofthe shapes in the vocabulary. By applying the shape rules recursively to the initial shape, aformal composition of design can be generated (Stiny and Gips, 1972, pp.1461-1462).Shape grammars are formed using various language-theoretic operations, such as shapeoperations, set operations, and substitution (Stiny, 1980a, p.459). While in shapegrammars, shapes made up of lines and points constitute the vocabulary elements, in setgrammars, which are conceptually simpler forms of shape grammars, discrete elementsconstitute the vocabulary. As Coyne stated, set grammars have certain implementationaladvantages compared with shape grammars. Set grammars are more amenable torepresentation within a computer-aided design system, and they also seem to conformbetter to the designer’s world (Coyne, 1988, pp.102-103).In generating grammars, two different approaches can be used by applying variousgrammar rule-sets. In the first approach, a rectangular schema or a grid is generated at theinitial stage and then refined in order to generate a plan composition in further progressive11

stages. In this approach, spatial relations are represented through hierarchical rule-sets asdefined in the Palladian grammar, the Bungalow grammar, and the grammar of Japanesetearooms. In the second approach, the generation process starts by locating a certain spaceand proceeds by adding the other spaces to the plan composition. In this approach, spatialrelations are represented through multiple rule-sets as defined in the Queen Anne grammar(Oxman and Oxman, 1992, p.121).In this paper, the second approach is used for generating the plans of traditional Turkishhouses. However, an imaginary grid is used for guiding the progression of the generationprocess. The spatial relations between the vocabulary elements of the grammar aredescribed through shape rule-sets. In these rule-sets, polygons representing the vocabularyelements are placed in a grid to determine the possible locations of the walls, in otherwords, to determine the topological configurations of the blocks. These rules areconsecutively substituted to generate the plan layouts. The grammar is formulated as aparametric shape grammar which is based on shape rule schemata. As the vocabularyelements of this parametric shape grammar are represented as blocks, this grammar can beconsidered a set grammar. The vocabulary elements of the grammar (i.e. the spaces in thehouses) are treated as modules in the block grammar.As Stiny states, “Spatial relations for a given vocabulary, sometimes allow for its shapes tointerpenetrate in designs. Interpenetration like spatial ambiguity can be a valuabletechnique in design. Architects and designers often conceive of designs in terms ofinterpenetrating masses or volumes. In those cases, however, where interpenetration is feltto be undesirable, it can be prohibited by labelling the shape rules used to constructdesigns,” (Stiny, 1980a, p.440). Stiny developed a labelling scheme for preventinginterpenetration in designs constructed by shape rules. This scheme can be used to labelshape rules based on spatial relations that can be specified by sets of shapes defined in adiscrete, cubical grid (Stiny, 1980a, p.441). In the grammar of traditional Turkish houses, agrid is used in representing the blocks and their spatial relations so as to prevent spatialambiguity and to control interpenetration of the blocks, and consequently of the spaces.Vocabulary Elements12

As Downing and Flemming stated, all shape grammars dealing with the generation ofarchitectural plans create, at the initial stage, a geometric pattern which determines thecompositional characteristics of the plans (Downing and Flemming, 1981, p.276). Thegeneration of Palladian plans start with the definition of a grid which determines thepossible locations of walls (Stiny and Mitchell, 1978). In the grammar of Bungalows, arectangular schema is divided into two horizontal and two or three vertical zones at thefirst stage of the generation (Downing and Flemming, 1981). In the grammar of Japanesetearooms, the initial shape of the grammar is the smallest bilaterally symmetric grid(Knight, 1981). In the grammar of Queen Anne houses, the vocabulary elementrepresenting the hall is located at the first stage of the generation; at the progressive stages,the rooms, the kitchen, and the stair hall are located so as to generate the plan layoutsaccording to the shape rules. In the grammar of traditional Turkish houses, the initial shapeof the grammar is a labelled point (K) which is placed on a coordinate system. Thegeneration process begins by locating the hall, represented by a polygon, whose upper leftcorner coincides with point K and proceeds by applying the shape rule schemata.The main vocabulary elements in the language of traditional Turkish houses are rooms andhalls with their particular extensions. As Stiny states, two-dimensional shape grammarscan be used in plan compositions (Stiny, 1976, p.209). The vocabulary elements in thisgrammar are represented as polygonal blocks, which correspond to the spaces in traditionalTurkish houses. As the dimensions of these spaces may vary in different plan layouts, theblocks are fully parameterized as shown in Figure 3, where both x and y coordinates of theend points of the lines representing the edges of the blocks in a schema are defined asparameters.Figure 3. Two-dimensional parameterized blockThe polygons and their spatial relations constituting the set grammar are defined by a gridsystem so that the knowledge can be translated into descriptions easy to manipulate by a13

computer. For the symbolic and graphical representation of the knowledge, a declarativeform of representation is considered. A grid-based representation system can combinegraphical and abstract descriptions of vocabulary elements and thus it treats linessymbolically rather than mathematically according to the coordinate system (White, 1992,p.384).In this shape grammar, straight lines are used; relative dimensions of these lines and theangles between them may vary; they are not limited to orthogonal orientations. Therefore,this grammar can be used in defining the language of shapes with proportionalrelationships represented by a grid system.The main vocabulary elements in the shape grammar are rectangular and triangular blockswith some constraints on their parameters. The other vocabulary elements used in thegrammar are produced by combining two or more elements of this vocabulary. In otherwords, the main vocabulary elements are actually sub-shapes of the shapes already defined(Fig. 4). The vocabulary of traditional Turkish houses needs the generation of designs withsub-shapes that already exist in the vocabulary but that have to be combined to make up aspace in a plan layout.Figure 4. Vocabulary elements of the grammarTwo types of knowledge about the polygons representing the vocabulary elements and therelationships between these polygons are considered: Knowledge about the formal properties of the polygons;14

Knowledge about the dimensional properties of the polygons.The knowledge about the formal properties of the polygons and their relationshipsconcerns topological configurations of the blocks. Each polygon representing a block isdescribed by a matrix. While the matrix describing a polygon (square, rectangle, or righttriangle) has nine elements (3x3) (Fig. 5a), the matrix describing the topologicalconfigurations of the sub-shapes have a different number of elements depending on theformal properties of the configurations (Fig. 5b). The sub-shapes of the polygons areindicated by construction lines (dashed lines) in the figures.a) Representations of polygonsb) Representations of topological configurations of sub-shapes in polygonsFigure 5. Representation of knowledge about polygonsThe first element of the matrix is the north-west corner of the coordinate system, and thelast element of the matrix is the south-east corner of the coordinate system. The elementsof the matrix are integer numbers. “0” indicates an empty cell, and other integer numbersindicate the cells occupied by a polygon or by a sub-shape. All the sub-shapes in a blockare represented by the same integer numbers in the matrix, and this indicates that thesesub-shapes show only one single space in a plan layout. This representation allows the subshapes within a compositional configuration to be easily orientated and positioned with15

respect to one another. The representation of a polygon by using a matrix with nineelements, or by using a matrix with more number of elements for the configuration of subshapes, is necessary in order to convert the symbolic representations into the graphicaloutputs of the compositional configurations according to the algorithms developed in thisstudy.The dimensions of the blocks are described by a list of coordinate pairs (x, y) whichindicate the endpoints of the edges of the grid cells. It is considered that at least two edgesof the polygon are parallel to the axes of the coordinate system.Spatial Relations Between the Vocabulary ElementsTopological relations like adjacency indicate the location of a vocabulary elementrepresenting a space with respect to another element representing a different space in theplan layout (Fig. 6). These are:a) Corner relations;b) Partial relations;c) Complete relations.Figure 6. Representation of spatial relations between spaces.Stiny states that, in a shape grammar, the spatial relations between three-dimensionalblocks satisfy the following requirements (Stiny, 1980a, p.420): Each partial relation is specified by a pair of blocks; Οne block overlaps with another block on the edge shared by two blocks; The blocks do not interpenetrate in any way.16

In the shape grammar of traditional Turkish houses, which has two-dimensionalvocabulary elements, spatial relations satisfy the three requirements similar to those statedby Stiny. Multiple spatial relations between shapes shown in Figure 6 are employed toconstruct designs by adding and subtracting shapes. Different combinations of those spatialrelations are used in this grammar. The spatial relations are described by using theknowledge representation technique explained above (Fig. 6). While the same integernumbers are used in representing the sub-shapes of a polygon, different integer numbersare used in representing the spatial relations between polygons. In other words, differentintegers represent different polygons and consequently different spaces. The firstdescription is used to define the relations of the sub-shapes in a polygon and thus in aspace; the second description is used to define the spatial relations between the polygonsrepresenting the spaces in a plan composition. The dimensions of each composition can bevaried according to the parameters given in the rule-sets to define plan layouts of differentproportions. The exact location of the shape replacing another shape is specified withrespect to the Cartesian coordinate system. This can be accomplished by defining a shaperule schema that indicates the exact coordinates of each shape in that schema.This representation, which is not limited only to orthogonal polygons, allows the separatepolygons within a grid system to be easily orientated with respect to one another (Fig. 7). Italso prevents the polygons from overlapping in the same configuration. The process ofgenerating plan layouts from descriptions of polygons is carried out with a bottom-upapproach, in which simple elements are combined to form more complex ones.Figure 7. The final representation of the plan layouts A54 by a grid-based systemRule-SetsTwo groups of rule-sets are defined for the parametric shape grammar of traditionalTurkish houses (Fig. 8): Rule-sets belonging to the plan types with outer halls (ROn);17

Rule-sets belonging to the plan types with inner halls (RIn).The first rules (RO1, RI1) of both groups are the starting rules that have to be used in thegeneration of each plan type. The left-hand side of the shape rule schema, which indicatesthe first rule, is the initial shape, which consists of a labelled point (K); and the coordinatesof this labelled point are (x1,y1). It is the point where the upper left corner of the hall mustbe located. The right-hand side of this schema consists of a parameterized polygon withvertices at the points (x1,y1), (x2,y2), (x3,y3), and (x4,y4), and a labelled point (O). When thefirst rule is applied, the point label (K) is replaced with the point label (O), so that the firstrule cannot be applied again. The RO1 and RI1 replace the initial shape with the hall,labelled (H), to generate the cores of the plans.The RO2 and RI2 locate rooms around the halls. The first rules of these sets (RO21 andRI21) show the complete relations between the halls and the rooms. In other words, thehall length is equal to the room length in those rules. These shape rule schemata indicatethe plan types with one room each. The RO22 and RI22 rules show the complete relationsbetween the halls and the rooms that are aligned with one side. The RO23 and RI23 rulesalso show the complete relations except the alignment relations between the halls and therooms. These shape rules are recursively applied to generate plan types with more than oneroom, where the hall length is increased as seen in rules RO22, RO23 and RI22, RI23. Inthese shape rules, rooms are added either to one side or to two sides of the hall, so the halllength is increased to accommodate them. The label (M) seen in the shapes on the righthand sides of these schemata is used to represent variable labels that mark the end of theaddition (E) or the continuation of the process (O). In other words, if the shape has thepoint label (E), the rule for adding a room is not applied; but if the shape has the pointlabel (O), the rule for adding a room is applied.18

Figure 8a. Shape rule schemata to generate plan types with outer halls

Figure 8b. Shape rule schemata to generate plan types with inner halls

The rules RO31, RO32, RI31, RI32 and the rules RO33, RO34, RI33, RI34 allocate theeyvan, labelled (E), to the corner and between the rooms in a row, respectively. Byapplying these rules, the hall is labelled (HE). The

The parametric shape grammar for traditional Turkish houses developed by the author in this research is based on the