A generic shape grammar for the Palladian Villa ...mason.gmu.edu/~jgero/conferences/dcc12/DCC12DigitalProceedings... · A generic shape grammar for the Palladian Villa, Malagueira

Design Computing and Cognition DCC’12. J.S. Gero (ed), pp. xx-yy. © Springer 2012

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A generic shape grammar for the Palladian Villa, Malagueira House and Prairie House

Deborah Benrós and Sean Hanna University College London, United Kingdom

Jose Pinto Duarte T U Lisbon, Portugal Shape grammars are formulations consisting of transformation rules that describe design. Previous studies have focused on recreating the style of family-related solutions [1], [2], [3]. This study does not aim to recreate a specific architectural style but is part of wider research aimed at inferring shape grammars. It is believed that more than one grammar can be developed for the same style, but no one has ever demonstrated this possibility. In addition, no one has ever developed a grammar that can describe more than one style. The aim of this work is to demonstrate both possibilities. Firstly, it proposes a shape grammar that can produce three different design styles, and, secondly, it uses a process that is distinctively different from other tested examples yet still produces the same corpus of designs. It also enables a new corpus of designs to be produced, which had not been possible using the previous (or original) grammars. A selected case study of three grammars, namely for Palladian, Prairie and Malagueira houses, allowed for comparison and observation of the different processes and shape rules and for a new set of rules to be proposed, combined in a shape grammar. This was followed by the recreation of a new subdivision type of grammar with a top-down approach and a set of generic design rules. The result is a generic shape grammar that enables three different house styles to be designed from the same formulation. Shape grammars, generic grammar, generic shape rules, housing grammars

Introduction

Shape grammars, like rule systems, are formalisms that allow rules to be combined in a structured way to create a set of designs that share a similar root, are part of the same family or, in stylistic terms, belong to a certain

D. Benros, J.Pinto Duarte and S. Hanna 2

style [4]. Beirão [5], working on urban shape grammars, proposed a generic grammar for design and illustrated an application for urban design. Stiny [6] showed how shape grammar rules may be classified into a finite set of rule types or schemas expressed algebraically to suggest how different grammars may share a common structure. In the past, many different shape grammars were used to describe a certain architectural style or signature design. The concept was first introduced by Stiny and Mitchell [1], [7] as a response emerging from the architectural and computing world to address the study of grammars described by Chomsky [8]. The controversial Palladian grammar showed how a style could be recreated using a set of rules. This enabled a set of housing layouts originally designed by the architect and a new corpus of solutions to be produced which obeyed the same rules and were intrinsically related to the existing corpus The same grammar theory was later put into practice by Duarte using the work of a living master, the Malagueira housing project [3]. This allowed expert feedback on the rule inference process from the author and, also for the trial and criticism of the new solutions by the creator of the system, as a quality control check. This study does not aim to recreate any specific architectural style previously tested by others but is part of wider research aimed at inferring generic rules and exploring a generic grammar. No one has ever tried to create two grammars for the same style. Usually, when capturing a particular style, researchers try to create the most elegant grammar, that is, the one that contains the smaller number of rules. Once a valid grammar is developed for a particular style, the need to create another, less elegant grammar becomes redundant. In addition, no one has ever developed a grammar that can describe more than one style. It is believed that a grammar needs to be exclusive of a particular style or it fails its descriptive, analytical, and synthetic purposes. This work aims to demonstrate the possibility of developing more than one grammar for the same style and the possibility of one grammar being able to generate more than one style. Firstly, it proposes a shape grammar that can produce three different design styles and, secondly, it uses a process that is distinctively different from the shape grammars previously inferred for these styles, yet still produces the same corpus of designs. It also enables a new corpus of designs to be produced, which had been impossible using the previous grammars (or the original forms). The methodology started with the selection of three grammars for a case study, the comparison and observation of their different processes and shape rules and, finally, the proposal for a new set of rules combined into a new shape grammar.

A generic shape grammar for the Palladian Villa, Malagueira Houses and Prairie House

3 The grammars selected reflect the three types of shape grammars identified and described in Knight’s grammar classification as quoted by Prats [9]. The grammars, namely the Palladian villas by Palladio [1], [11], the Prairie houses by Wright [2] and the Malagueira houses by Siza [3], address the grid, addition and subdivision types respectively. One important feature that influenced the case study selection was the fact that all the grammars are applied to single-family housing and, at the same time, featured distinctive differences in style, layout, history, and architect’s background and signature, in addition to different geographic locations and periods of construction. The next step involved comparing the study case data and identifying differences and similarities within the rule sets. The proposal for the new set of rules addressed and encoded all three styles. The process selected was the one that seemed more flexible and allowed for the production of all three types – the subdivision process. The subdivision grammar type used is clearly distinct from previous attempts to recreate new Palladian-like designs since involves a grammar formulation and proposes a method combining parametric shape rules based on polygon division. This was the system used to generate the original Malagueira grammar, and also the process selected and described in an alternative Palladian grammar [12]. The alternative grammar for the Palladian villas grammar is, to the extent of our knowledge, the first attempt to propose a grammar that being intrinsically different in structure, rule formulation, and derivation process, still allows the design of the same corpus of designs described by the original grammar, the existing corpus designed by Palladio and a group of villas not addressed by the original grammar. The grammatical structure developed for the Palladian Villas, a top-down subdivision of rectangles, was then applied to the Prairie houses. The house starts with the inclusion of a house boundary and production opts for a top-down approach to the generative process. The system proposes a self-contained boundary shape that encompasses the limits of the building work. Subdivision starts as process of refining a succession of recursive divisions that generate different space subdivisions. A series of parametric shape rules are proposed to provide accuracy in the generation


process. It is the manipulation of these parameters that enables a specific house type, either Palladian, Wright or Siza, to be produced. The rules are generic, but potentially specific. Within each rule the parameterisation assures that the right house type is designed even though the same rule is put to practice. Labels and other agents maintain and propose restrictions. In addition to shape, function was also taken into account (unlike the Palladian grammar). The existing plans were observed and analysed in order to introduce functional spatial meaning. Segregation and integration were considered in the spatial assessment [13]. The spatial adjacency of each room, its dimensions and communication with other rooms were also considered. As original research, the work aimed to automatically infer shape rules, starting by reflecting on three distinct shape grammars. All three original grammars were extensively tested and proved to be operational. However, the scope of their design was specific and bound by the limits of each designer. As formulations encompass a large amount of information, design know-how and consistent design style, they are not much use outside their corpus of action. This study attempts to make full use of the potential of these generative formulations, commonly known as shape grammars, by attempting to come up with a generic shape grammar formulation. The first step was to prove that one specific style can be produced by more than one formulation. The second step was to create one grammar that can produce more than one style, thus refuting certain assumptions concerning the hermetic nature of these structures. This paper is divided into five sections. The introduction is followed by a description of the case study and of the generic grammar formulation. The fourth section concerns the generation of solutions and derivations and the paper concludes with comments on the results and on future work.

The case study and grammar comparison Three grammars were used as a case study: the Palladian villa [1], Prairie house [2] and Malagueira house [3] grammars. The differences between them enriched the study and the similarities allowed for comparisons to be made, since all refer to single-family housing.

The Palladian grammar – a grid grammar The formulation of the Palladian grammar atypically resembles the grid grammar type. It is atypical because in order to generate a grid it goes through an addition process whereby cells are added individually to the design. The basis of the design begins with the construction of a grid or matrix that reflects the interior design. This resembles a traditional orthogonal grid, even though it is constructed by adding individual cells.


5 The original and first grammar formulation for the Palladian grammar had eight design stages. The grammar formulation is illustrated in Figure 1 as a grammar tree diagram. The first stage combines ten rules for grid definition. These rules are additive processes that allow a grid scheme to be recreated by cell addition. The second stage proposes the introduction of a containing boundary shape and the inclusion of a single rule for defining the exterior walls. The third stage incorporates the room layout rules. This stage proposes seven concatenation rules. Special rooms are designed by joining consecutive cells to create larger spaces with spatial complexity. Stage 4 allows for wall realignment. At this point, the manipulation of the grid cell borders can be altered to create less rigid

Fig1. Original Palladian Grammar tree diagram


configurations. Stage 5 proposes 23 set of rules to introduce the main entrance. These are additive rules which add an obtrusion to the main envelope in the shape of a portico, loggia or ornamented column entrance. Stage 6 is dedicated to the decoration of the façade true to the classical style and is also an additive step that includes classical features. Stage 7 constitutes a typical subtractive process that involves creating openings in the walls for windows and doors. Stage 8 is a technical stage for deleting labels and terminating the design. The grid grammar described effectively produces design solutions that fit the style criteria. The rules are coherent but the formulation does not necessarily follow an intuitive architectural design procedure.

The Prairie house grammar – an addition grammar

The Prairie house grammar was one of the first implementations of a 3D grammar and uses a typical addition process. The design follows the prescriptions of Frank Lloyd Wright and is initiated by the insertion of the main focal point of the family dwelling - the fireplace. Spaces are sequentially arranged around it in an orthogonal, biaxial manner, from the living and dining areas (the social areas) to the kitchen and pantries (the service areas) and the intimate family divisions (bedrooms, closets and bathrooms). This grammar structure is shown in Figure 2. The grammar is mainly composed of additive steps, as shown in the illustrative tree diagram. The first stage combines four rules for positioning the fireplace. Two possible fireplace placements are available. The second addition stage involves the insertion of the first social area adjacent to the fireplace. This constitutes another innovation in terms of the Palladian grammar, which did not address spatial function. There are four rules for this first room design. The third stage adds and extends the core living space, proposing the addition of an extra space adjacent to the one previously allocated. The fourth stage is responsible for the so-called obligatory extensions to the social area immediately adjacent to the spaces previously added. It is another additive step. The fifth stage, with six addition rules, allows for the creation of functional social zones. The overall ground floor layout is then concluded. The seventh stage adds detail to address the style features of Wright’s Prairie creations. The concave corners of the envelope are filled with exterior elements such as terraces, porches, verandas or small extensions decorated with features that are true to the original style. The other rules are mainly subtractive and address certain issues relating to the ornamentation of this style.


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Fig2. Original Prairie houses Grammar tree diagram

Some corners are truncated, chamfered or simply subtracted to create the level of detail and refinement evident in the existing design corpus. The eighth stage terminates the design with the deletion of labels. Other stages are proposed by the grammar to design the top floor. However, as it is similar to the entrance floor and the upstairs design recursively repeats the


main level procedure, the need to address this is minimal. It can be concluded that the Prairie house generation is mainly an addition process, with the exception of the detailing, for which uses subtraction as the operative means, and the termination stage. The design is conceived using a bottom-down approach in which a single element (such as the fireplace) is included at an early stage and the whole design subsequently develops from this. It is a very different approach to the grammar previously described in which the self- contained boundary is proposed at the outset. This addition grammar drives its formulation directly from Frank Lloyd Wright’s design concept and intentions. It is therefore intuitive and spaces are created in a sequential manner. The additive process seems to an appropriate choice which is easy to implement.

The Malagueira house grammar – a subdivision grammar

The Malagueira house grammar uses a top-down approach and a subdivision grammar type to address plot and house design. The design is driven from the fixed plot space and adjacencies between surrounding buildings. The design concept inspired by Siza is based on the plot available. A percentage is allocated for exterior space and for the remaining indoor construction. The indoor construction is then detailed progressively through a series of divisions. The original grammar tree diagram can be seen in Figure 3. Although it consists mainly of subdivision stages, the first stage is an additive stage. The design is initiated by the addition of the plot layout and boundary, which establishes the design limits. The second stage is a fundamental step in the design concept. The grammar allows for two subdivision rules that determine the location of the house within the plot and the exterior yard. That is achieved by dividing the surrounding polygon into two smaller elements and is replicated further in the following steps with different aims. The third step starts detailing and assigning functional areas for the interior. Living spaces are designed and selected. The fourth stage, also proposing subdivisions, creates circulation spaces such as corridors or staircases.


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Fig3. Original Malagueira houses Grammar tree diagram

The fifth stage subdivides the space further by creating and allocating service areas such as kitchens and pantries. The sixth stage is the last subdivision stage and applies to small rooms and divisions, utilizing the remaining spaces. It is a design refinement stage that uses particular division rules.


The seventh stage breaks the routine proposing subtraction. It is a detain stage in which openings are created in interior walls for doors and in exterior walls to generate windows, and other elements such as risers and chimneys are detailed. The eighth stage terminates the design and erases the construction labels. Despite the approved efficiency and operability of this subdivision grammar, close observation led to the possibility of converting this into a grid grammar, as the floor plan resembles a complex grid plan. The key question concerned which grammar would be more efficient and thus more economical and the answer is probably subdivision, due to the level of grid complexity involved. However, this gave rise to the idea that more than one grammar could lead to the same design, as explained in the next section.

The case study analysis, methodology and comparison

The three grammars presented above describe three different processes and approaches to shape grammar inference. Firstly, they describe different content and styles. These differences derive from the fact that the existing designs were originally created by three different architects, of different nationalities, working at different periods, with dissimilar social and cultural backgrounds, specific clients, aesthetics and, more impor-tantly, a characteristic, easily identifiable design language. The common ground they shared was that all the grammars focussed on single family housing and which allowed comparison. Their processes follow different approaches. The Palladian villa and Malagueira house grammars use a top-down approach, starting with the general aspect of the building and detailing it as they progress, whilst the Prairie house grammar uses a bottom-up approach starting with one particular feature, ‘ the fireplace’, and progressing to the other parts of the design. This is intrinsically related to the nature of each grammar. Grid and subdivision grammars first consider the big picture, either the boundary or design limits, and then work their way inwards, whereas an additive grammar typically starts with one of its parts and adds other elements sequentially. This also leads to another assumption, namely that grid and subdivision grammars often start with a self-contained element, whereas addition grammars is much harder to envisage the future containing shapes. If all three tree diagrams from each grammar are juxtaposed as shown in Figure 4, the main differences and similarities between them can be seen. Despite the differences, all three grammars appear to start from a common point. They also present a similar number of steps from start to finish. The first stage is usually an addition process. This initial step always involves the addition of an element to start the design.


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Fig4. Grammar tree diagram comparison

Fig5. Generic Grammar Shape Rules

Likewise, the final step, involving the deletion of labels and the termination of the design, is very similar. The penultimate or seventh stage, which is the detailing stage and is subtractive, is also very similar in all the grammars. . The main purpose of the detailing that occurs in these


housing grammars is to create openings, such as windows and doors, in the walls. Other conclusions reflect the similarities between grid and subdivision grammars. They share the same top-down approach and main addition processes. Grid and addition grammars also have some formulations in common. As shown in the comparison tree, both have six additive processes in the early design stages. Despite the differences in the top-down and bottom-up approaches, both mainly use addition to achieve design solutions. Close observation of the set of shape rules for the grammars revealed other similarities. Four types of rules were identified as very common: addition, offset, subtraction and concatenation. These could be observed countless times in all the grammars, sometimes involving certain particularities and on other occasions with different parameterizations. However, it seemed that a generic rule could be implemented to address all cases. The idea of a generic grammar now seemed feasible. These core studies on each grammar also led to other conclusions. If so many similarities were found, it seemed only reasonable that there could be more than one way to generate a design. The Palladian grammar proved to be operative and effective in reproducing existing designs and generating a new corpus of solutions. However, it was less intuitive than expected and the grid creation process did seem particularly complex at times. A grammar does not have to recreate the designer’s vision and process to produce consistent results, but sometimes this can be an effective way of tackling design or even helping to create a more economical grammar. The idea of developing an alternative grammar for the Palladian grammar seemed feasible when the research indicated that there could be more than one way of achieving results. Due to the similarities between the grid and subdivision grammars and due to the intuitive manner in which subdivision operates, it was chosen for this endeavour. Furthermore, this methodology was also extended to the Prairie house grammar. However, it implied an added level of complexity to obtain the same corpus of results. The overall rules were reconfigured, re-planned and parameterized to accommodate all the examples from the three-grammar case study, as will be explained in the following section. Generic Shape Grammar formulation A generic shape grammar was developed for the creation of Palladian villas, Prairie houses and Malagueira houses, supported by the choice of a top-down approach using a subdivision grammar. A new grammar structure and a new set of parametric shape rules were developed.


13 The alternative grammar for the Palladian villa used a methodology developed by Duarte [4] for the Malagueira house and later adapted to an urban context for the Marrakech grammar [14]. The subdivision grammar famously implemented by Stiny in the Ice-ray grammar [15] encompasses a very simple shape rule set of sequential subdivisions of polygons. The grammar showed how a polygon could be divided in two, generating complexity just by introducing diagonal cuts into a rectangle and sequential cuts to triangles and pentagons. The end result was a complex ice-ray window frame that resembled the traditional Chinese ice-ray lattices. This proved how a simple five-rule grammar could lead to an almost endless set of new solutions. The Malagueira grammar used a similar process, starting with the boundaries of the plot and evolving through subdivision into smaller inner spaces. Since Palladio’s villas always propose a rectangular envelope geometry, and taking into account that the use of subdivision is a common design choice for architects, it was the process selected to accomplish this task. A new set of rules was developed to address all three grammars. The selected grammar does not try to replicate the process of the designers’ work or methodology. It aims for a generic formulation that can accommodate three instances of design that are not only independent but also dissimilar. It attempts to achieve a consistent solution as efficiently as possible, whilst also creating a system that is easy to use. The grammar adopts a top-down approach and uses subdivision. The new generic grammar allows for eight stages from start to completion and the design of three types of houses, namely Palladian, Prairie and Malagueira. Any misuse of the grammar or rule manipulation will generate a hybrid version of the houses. This does not mean that the grammar implies an intelligent and careful use. The parametric mechanisms embedded in the grammar account for that, avoiding the occurrence of undesirable hybrids that do not represent any of the three styles. The shape rules should therefore be used intelligently but not freely. The generic grammar does not classify as


Fig6. Generic Grammar tree diagram – Palladio’s Villa La Malcontenta

unrestricted since it does follow a strict ordering process and imposes several restriction in the shape of parametric rules according to Knight’s classification [9]. As shown in the tree diagram, the first stage designs the envelope or container shape. In all cases it is a 4-sided polygon or rectangle. For non-rectangular envelope geometries such as those of the Prairie houses, further geometric transformations are required to detail the envelope. The second stage introduces the subdivision. Two rules can be applied at this stage, namely horizontal divisions or vertical divisions. Vertical divisions provide double divisions for cases like the Palladian villas, where bi-symmetry has to be observed. At this stage, both rules can be applied a number of times recursively to the point where the maximum grid with the maximum number of cells is reached (a condition for the Palladian villas) or the divisions reach the minimum space needed to accommodate a living or circulation area. Other proportional aspects are monitored to ensure that design consistency is maintained. At the end of this stage the outline of the interior layout should be patent or at least foreseeable. This outline will be made clearer in the next stage. Stage Three encompasses two basic design rules of concatenation and cell merging or, to be more accurate, cell border deletion. Both rules follow the


15 symmetry conditions for the Palladian villas and involve a simple formulation for the Prairie and Malagueira houses. Rules Four and Five present two simple border deletion methods for vertical and horizontal situations, as shown in Figure 5. The final interior layout is now complete and the design progresses to other aspects of construction. The fourth stage proposes wall thickening. Limits and spaces had previously been represented by bi-dimensional lines but at this point, Rules 6 to 9 are responsible for converting either lines or corners into proper wall representations with a double line to represent a specific thickness. In the Palladian case, the thickness of the interior walls reflects the masonry technology used and they are relatively thick in comparison with the other examples, whilst the exterior walls are incrementally thicker. The rules address these differences and convert corners and intersections from 2D abstractions to standard thicknesses. The fifth stage of the generic grammar proposes an addition step. This allows for certain features of each style to be added to the exterior, complementing the envelope with entrances, porticos, porches, exterior spaces and/or ornamentation. In the case of the Palladian villa, this is the stage when the entrance is defined and porticos and ornamentation, such as decorative classic columns or loggias, are added. For the Prairie house, elements such as the corner volumes occasionally fitted to concave corners of verandas or terraces are now incorporated. For the Malagueira houses, the small divisions or service spaces also added to concave corners can be introduced at this stage. This constitutes the second additive process in the procedure. The sixth stage includes internal functions. The introduction of functions constituted an innovation in terms of the original Palladian grammar. Space and function is the issue covered least in Palladio’s Four Books [11] and never addressed or labelled in plans or other drawings. It relates to the social nature of the 16th century aristocratic Italian villas built for the purpose of entertaining, whose main floors contained a series of rooms ranging from ante-chambers to ballrooms, drawing rooms, libraries and studies that are not always easy to identify. It was therefore necessary to research this area. Observation and comparison allowed for some spatial


assumptions that were introduced into the generic grammar. Both the Malagueira and the Prairie house grammars addressed functions and originally proposed shape rules associated with special meaning. The seventh stage constitutes a subtractive stage to introduce a greater level of refinement. At this stage openings are made in walls and interior walls can be removed to create internal circulation and incorporate doors. The exterior walls and facades can accommodate entrances and windows. Geometry, proportion and window positioning varies greatly from one house type to another. The rules that were written accommodate these differences and take into account the symmetrical features needed for the Palladian villa. A specific function is associated with each space, created in accordance with the shape rules in order to maintain spatial flow and coherence and avoid the overlapping of functions, awkward adjacencies or spatial relations not envisaged as part of the original style. The eighth and final stage completes the design by deleting the construction labels. Generation of solutions and derivation process The recreation of original designs using the method described above is illustrated in Figures 6 to 9. Derivation is the exemplification from start to finish of the phased application of the shape grammar rules. Often, the faster the derivation, the more efficient, elegant and easy the grammar is to use. In this experiment three existing houses designed by the original architects were selected to illustrate the generic grammar. Villa Malcontenta is an example of a typical Palladian villa, the Robbie House, one of Wright’s most famous creations, illustrates the existing corpus of Prairie houses and the Malagueira two-bedroom Ab type house (according to Duarte’s labelling) exemplifies a typical Malagueira family housing unit.


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Fig7. Generic Grammar derivation – Palladio’s Villa La Malcontenta

La Malcontenta derivation

La Malcontenta was originally designed, built and completed in Venice between 1559 and 1560 and is pictured in the ‘Il quatro libri’ [11]. Its orthogonal features and grid-like floor plan features a matrix that resembles a 5x3 grid organisation. Whereas the original grammar used a grid process, achieving the same design with subdivision allows us to economise on certain steps (namely extensive concatenation). The new tree diagram featuring the generic grammar is shown in Figure 6 and the Malcontenta derivation in Figure 7.


The envelope is thus designed and established from the start. This results in the first derivation step with the application of Rule 1 (adding a four sided polygon). Step 2 addresses the first main stage of the subdivision process by applying Rule 3, the vertical subdivision. As shown, this subdivision is doubled to address the symmetrical nature of the design. Steps 3 to 6 use the division rules 2 and 3 recursively (in the case of Rule 3, repeated again and again). Steps 7 and 8 start the space merging or concatenation process. This is a fundamental step for spatial configuration in a Palladian villa. The core space or social area is often the, largest, most central and geometrically complex area in the villa. This complexity is achieved by combining adjacent cells to form a broad regular polygon. Other larger rectangular spaces are allocated at the edges of the construction facing the facades. With the layout settled, the 9th derivation step continues with the wall thickening, applying Rules 6 to 9. Step 10 adds new elements attached to the exterior of the envelope, namely the entrance portico. The 12th step assigns functions for the spaces previously designed, and the next step creates detail and prepares the spatial articulation with the insertion of openings such as doors and windows. The villa is finished in Step 14 with the deletion of labels. In comparative terms, the derivation of the Malcontenta using this alternative method is faster than the derivation used in the original grammar.

The Robbie House derivation

Fig8. Generic Grammar tree diagram – Wright’s Robbie House derivation

The derivation of Prairie houses using the generic grammar takes a certain level of abstraction into account (Figure 8). Most of the existing Prairie houses have a floor plan composed bt polygonal shapes assembled


19 orthogonally. With the exception of the rectangular, self-contained Wright Winslow House that can easily accommodate the rules and derive an operative alternative derivation in a few steps, most have a butterfly/crossed shape envelope, this is explained further by Granadeiro [16]. Prairie houses are created by the generic grammar using a container that extends to its extreme edges. A new rule was introduced to erase the container edges after the core house was completed. For this reason, the example chosen to illustrate the Prairie house is the Robbie House, which is a singular, characteristic and well-known example. As in the Palladian example, the containing envelope shape is inserted in the first step using Rule 1. This rectangular shape does not contain the construction boundary, but illustrates a containing shape that encompasses its maximum limits. Step 2 initiates the subdivision process. The horizontal and vertical division rules, Rules 2 and 3 respectively, are used recursively in several stages until all the floor plan lines have been replicated. Step 2, which extends to the next design stage, resumes the lengthy process of subdivision and is not the most intuitive or efficient of processes at times. The process combines analysis of the maximum lines (the lines that connect opposite sides) and their replication using subdivision. The trick lies in establishing the butterfly cross placing by using the double division first, then continuing to the finer details. Once all the lines are illustrated, the design is one step away from completion. At this point some adjacent cells need to be concatenated to remain true to the style, creating a flow of spaces that are oblong and have large areas. This constitutes Steps 9 and 10. In Step 10 all the basic interior design features are represented, including the container envelope shape. This shape is then modelled to fit the design criteria for the style. The unwanted edges are erased in accordance with Rule 10 and the line from the external vertex to the connecting indoors line is erased, leaving the end results as expected. Steps 11, 12, 13 and 14 resemble much of what has been described previously and involve wall thickening, the detailing and creation of openings, and the completion of the design, respectively.


Fig 9. Generic Grammar derivation –House type Ab derivation

Malagueira two-bedroom single-family house type Ab derivation

The derivation of Malagueira houses using the generic grammar involves a slight adaptation of the original Malagueira grammar rules. The original grammar is a typical subdivision grammar and, as explained, is the driving force behind the design of this generic grammar [3]. The example illustrates a typical two-bedroom, two-storey, terraced, semi-detached house, type Ab under the classification system devised by Duarte. The proposed derivation uses the subdivision rules previously explained, plus particular shape rules that address Siza’s special configuration (Figure 8). After the subdivision is performed, the steps that follow diverge from the original grammar and are closer to those tested in the previous derivations. Step 1 is the plot insertion, which involves applying a self-contained rectangular shape. In the case of the Malagueira houses the envelope shape is not parametric, but has a fixed size that reflects the available plot space with the same dimensions and area for each house. Step 2 applies Rule 3 for horizontal subdivision, segregating interior from exterior space. At this stage the yard/exterior space is allocated. Step 3 applies the vertical division, creating a division between the interior functional areas. The house layout now begins with the allocation of (service versus living) zoning. Due to the true nature of this subdivision, recursive vertical and horizontal divisions are performed to carry out the zoning and spacing. Steps 2 to 10 continue the recursive application of the division rules. Step 10 includes specific rules for the Malagueira design which replicate Siza’s intention to create oblique cuts to produce smaller spaces and generate some spatial complexity. These rules


21 are no more than parameterizations or generalizations of the division rules exemplified. The subdivision continues until Step 14. In the 14th step concatenation is performed for the first time, offering the designer the flexibility to generate complex polygons with an incremental number of sides. This is replicated up to stet 17, where the design progresses as usual with wall thickening, detailing, the creation of openings and the completion of the design.

Conclusion – Discussion of results and future work The work described above presents a generic shape grammar that allows for the generation of not one, but several signature styles. Unlike previous work, this is not a typical shape grammar, but a generic formulation that allows for the replication of more than one design style, which is believed to be a contribution to shape grammar research. To this end, the generic grammar uses shape grammar structure and shape rules. The rules are formulated as parametric and that can be manipulated to generate a particular design. A case study composed of three types of grammars, namely the Palladian villa, Prairie house the Malagueira house grammars, was selected to illustrate the scope of this generic grammar. The aim was twofold: firstly, to produce an alternative grammar that allowed for the alternative generation of a previously developed grammar, and, secondly, to use this new grammar as a generic grammar capable of producing more than one design style. The methodology started with a cross comparison of the grammars previously inferred and a study of their underlying styles. Each grammar was decomposed and its structure analysed. The complex sets of rules for each grammar were also analysed and similar rule formulations were pinpointed. The grammar comparison and knowledge acquired led to the idea of using subdivision grammars to construct the new generic grammar. This choice reflects the ease of use and intuitive nature of this grammar type and the adaptable nature of the subdivision process in comparison with other creative concepts. A new set of rules was developed for this new generic grammar in order to produce stylistically consistent designs. The set of rules incorporated important subdivision


rules for the required conditions, such as minimum spacing and bilateral symmetry. To the best of our knowledge, all the previous work on shape grammars has proposed a unique grammar to describe a particular corpus of designs. No one has proposed more than one grammar for the same style or a grammar that can describe more than one style. However, we believe that the effort of developing of an alternative grammar, different from the original grammar developed for that style, can tell us more about the essence of the style. We also believe that developing a grammar that can describe more than one style, which we call generic grammar, helps us to understand the commonalities among the different styles and the structure of the common underlying type. In this paper we present a grammar for single-family homes of three different styles. This work refutes certain assumptions regarding shape grammars, namely the uniqueness of the design style that one grammar can produce. Given that there is more than one way to reproduce designs, more than one suitable grammar and that one grammar that can produce more than one style, many different representations are potentially viable. This represents a breakthrough in shape grammar methodology and research. Shape grammars are no longer exclusive, but can potentially be manipulated to generate a larger corpus of new designs. This allows for efficiency in exploring shapes and analysing results, thus widening the scope of grammars. Future work will focus on the effectiveness and implementation of the generic grammar, such as the exploration of a new corpus of designs and the analysis of generated design hybrids. It is expected that the mutation of these design styles or the overlapping of rules will produce new consistent designs with a new hybrid style. This is currently not allowed by the restrictions implemented. Moreover, computerised implementation will represent a positive development, allowing for the exploration of design solutions and even the enumeration of design corpus results. The potential of this generic grammar will be fully tested with a computerised tool, as was the case with previous work developed for housing shape grammars, such as the ABC system and the Haiti gingerbread house grammar [12].

Acknowledgments

The authors would like to thank the contributions of Prof. Stiny and Prof Knight at MIT and Prof. Steadman at UCL at different stages of this research project.


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References

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