Application of shape grammar to vernacular houses: a brief case study of Unconventional villages in the contemporary context

ABSTRACT

Shape grammar, as a design reasoning method, offers a graphical approach to decoding formal languages and implementing the emergence of results through recursive shape rules. Since its introduction in 1972, it has been increasingly utilized in researching vernacular houses’ inherent value and adaptive regeneration. This paper explains the principles of shape grammar and summarizes relevant research cases from the past four decades. Three representative cases are selected to demonstrate shape grammar’s positive impact on studying vernacular houses. Subsequently, the paper focuses on the “Unconventional Village” undergraduate graduation design from Shandong Jianzhu University. It uses it as an example to illustrate the design generation process of “unified construction” houses in rural China through rule reasoning. Finally, the research value of shape grammar is summarized, and the significance of studying contemporary vernacular houses is elaborated.

KEYWORDS:

• Shape grammar
• vernacular houses
• case analysis
• generative design
• unconventional village

1. Introduction

Vernacular houses are often considered to be several common building types of a particular time and region (Upton, Wenwen, and Yin 2009). According to the traditional concept, when Oliver defined the vernacular houses, he kept the common sayings of Rudofsky’s (1964) mass architecture, architecture without architects, and even people’s architecture, and defined them as a kind of localized construction (Oliver 2006). From the micro level, vernacular houses are produced by the inevitable needs of local people’s life and production. They embody a form of expression or an amalgamation of buildings that incorporate the accumulated wisdom of previous generations in adapting to the environment. These structures reflect the underlying and recurring intentions deep within human consciousness. Specifically, they are a combination of a way of life and a specific type, and “the vernacular design process is one of models and adjustments or variation” (Rapoport 1991), which sharply contrasts the accidental works produced by professional architects. From the macro level, vernacular houses encapsulate the material and spiritual cultures shaped by climate, regional characteristics, economic conditions, and social values (Wang et al. 2017). They significantly shape the local environment’s distinct style and features, embodying harmony and diversity. Their diachronic characteristics are more general, abundant, and inherited, and they respect the law of their metabolism. While scholars often define vernacular houses based on traditional and primitive principles, it is essential, from a contemporary standpoint, to find a harmonious synthesis between present-day needs and vernacular culture. This symbiotic relationship will continue to generate the necessary strength and vitality to support sustainable development (Lim 2003). Based on this, Maarouf (2020) pointed out that when studying the inheritance of this type of building, at the request of uses different types of design models having existing technology to generate optimal enhanced architecture under the title of the broad spectrum of globalization, symbolism, and updatable architectural themes. To comprehensively explore the traditional and contemporary characteristics of vernacular houses, research on their inherent value and adaptive regeneration has always been an academic focal point within architecture. Regarding intrinsic value, the focus lies in examining vernacular houses’ fundamental characteristics, including customs and culture, material composition, spatial layout, structural forms, intricate textures, and decorative elements. In terms of adaptive regeneration, while preserving the authenticity of vernacular houses, aligning them with the functional and material needs of the times is necessary. This approach facilitates reviving their inherent value while ensuring their continued lifecycle. Lim and Shan (1998) summarize this type of research as “a conscious pursuit to express the unique responses of tradition to local conditions, climate, and to externalize these customary and symbolic features into creative new forms that reflect the values, culture, and lifestyle of contemporary reality”.

At present, the action plans supporting the above research mainly include information registration (2D or 3D), planning and construction (repair, revitalization, and new construction), and conservation management (information or manual), and the related technical means include field mapping, human interview, and artificial intelligence. Shape grammar (SG), in particular, represents a concrete application of artificial intelligence. On the one hand, researchers can utilize SG to delve into the concealed logic and organizational rules of vernacular houses with remarkable precision. This enables the extraction of valuable information regarding the morphological and mathematical characteristics, spatial relationships, and functional typology of vernacular houses. Consequently, these architectural forms’ classification, analysis, and evaluation become feasible. On the other hand, researchers can “regularize” the gathered information by constructing computerized databases and employing search algorithms to generate “unpredictable” results. This allows for exploring potential avenues for the adaptive regeneration of vernacular houses. Because of this function, more and more domestic and foreign research is directed at studying the association between vernacular houses and SG. These efforts aim to preserve traditional architectural styles and safeguard the inheritance of vernacular values. Among them, the JY502 Studio of Shandong Jianzhu University also carried out a series of studies on “unified construction” housing in Chinese villages through the method of SG titled “Unconventional Village”.

2. The basic principles of SG

SG emerged from Chomsky’s linguistic theory. As a structural linguist, Chomsky proposed the theoretical ideas of Universal Grammar (Chomsky 1957) and Generative Grammar (Chomsky 1965), respectively. He argued that every human language possesses inherent rules that can generate infinite grammatically correct phrases or sentences using a finite set of words. Inspired by this, Stiny and Gips (1971) proposed SG, defining it as a generative method that can transform a set of initial shapes into more two-dimensional or three-dimensional shapes with “harmony and difference” characteristics according to specific rules. In his book “Shape: Talking about Seeing and Doing”, Stiny emphasized that SG provides a visually driven process for the “unpredictability” of graphical computation (Li 2017). It allows for the visualization of shape derivation and iteration processes, thereby enhancing researchers’ ability to inspire thinking and assist in design tasks.

Stiny (1980) further elucidated the fundamental elements of SG, which consist of four types: SG = (S, L, R, I). S is a finite set of Shapes, which refers to a specific set of geometric shapes; L is a finite set of Labels, which refers to a set of indexical relations between the above geometric shapes; R is a finite set of Rules, which refers to a set of shape retrieval rules needed to establish the above indexical relations; and I represents Initial Shapes, which can be characters, coordinate points, or the simplest or complex shapes derived from reality. It specifically refers to the initial shapes that match the rules and generate new shapes through a recursive application. The interconnection between the above elements can be expressed as follows: first, R ∈ (S, L), shape rules need to be represented by a set of shape or label variations; second, I ∈ (S, L), the initial shape should match at least one shape or label; third, I is usually regarded as the “initiator” for the effective operation of R. In other words, SG as an algorithm can be used to explain the generation characteristics of the initial shape, the decomposition rules of its sub-shapes, and the Boolean logic for the sub-shapes. Based on the above understanding, the application process of SG can also be described as the process of filling the grammatical architecture. It consists of the initial set of shapes I and the set of rules R with the set of shapes S and the set of symbols L as optional corpus, the process of formulating shape rules by the researcher. In this process, the shape rules exhibit obvious if-then statements, the left-hand side (LHS) shape A is converted to the right-hand side (RHS) shape B by “if” followed by “then” command, or “if” followed by “termination” command to generate the right-hand target shape RHS-C. In which, when the shape rule consists of multiple subrules, the LHS-A and RHS-B between its different subrules should have a mutual matching relationship, RHS-B in rule 1 is equivalent to LHS-A in rule 2 to realize the recursive application of the rule.

To describe the process of shape transformation more clearly and to reflect the “computation-friendly” nature of SG, Krishnamurti (1982) generalized two processes of formulating shape rules based on the inducements of shape transformation. One is the Subshape-driven SG, where the transformation of shape rules is influenced only by the set of shapes, and the RHS shapes are matched with the LHS shapes through the recognition of shapes. As in Figure 1., the shape rule can be applied when the initial shape C₁ is matched with the shape A (LHS) in the shape rule. This process involves various Euclidean geometric transformations, such as translation, rotation, symmetry, and deflation, and Boolean operations, like union, intersection, clipping, combination, and splitting. These transformations convert shape A into shape B, generating a new shape. Rule application in this process relies solely on shape transformations, resulting in a certain level of unpredictability. Therefore, this approach is particularly suitable for art design and automated design reasoning through tools. The other type of SG is label-driven, where the transformation of shape rules is influenced by both the set of shapes and the set of labels, with the labels usually playing a decisive role in the process. As demonstrated in Figure 1.2, labels added to the shape rules assign different properties or meanings to the shapes, thereby driving the shape transformation in a predetermined direction until the desired target shape is achieved. Subsequently, the labels are removed, effectively terminating the shape rule inference. Therefore, label-driven rule application is purposeful, can generate predetermined targets with relative accuracy, and is more applicable to fields such as architectural design.

Figure 1. Shape rule application source: drawn by the author.

In the subsequent research on SG, some scholars have been expanding the theoretical connotation of SG by combining the practical needs and application directions in art, engineering, architecture, and products (Figure 2) (Wang et al. 2022). For example, to decode the change laws of complex shapes and simplify the reasoning process of rules, Stiny (1980) proposed parametric shape grammar, which has now become one of the most widely used SG. He further advanced the concepts of descriptive grammar (Stouffs 2015) and parallel grammar (Stouffs 2018) to enhance the theory of SG. In 2015, he proposed a method incorporating improvisation, perception, and action based on SG, along with a computational theory supporting the generation of shape matrices (Knight and Stiny 2015). By modifying the material pedigree of shapes, Stiny established the material pedigree of objects or things, aligning the computation of SG with the computation of things. Influenced by it, many researchers engaged in the theory of SG have enriched and interpreted the theoretical connotation of SG. For example, Kunkhet et al. (2016) proposed an SG framework inspired by the field of natural language processing to solve the context and coordination problems in SG. This new SG framework includes four levels of analysis: morphological, syntactic, semantic, and pragmatic to enhance the overall design process. At the same time, influenced by the development of computer science, some researchers began to pay attention to the development and possibility of combining SG with computer, mathematics, and other related majors (Ning and Amini Behbahani 2021). Jabi (2013) theoretically highlighted that SG could be understood as a mathematical model based on grammar processing systems. In practice, SG serves as a general-purpose computer language that directly manipulates formal rules to generate designs. Previous SG theories were reinterpreted using algebraic methods and a bridge was built between theory and computer implementation (Stouffs 2018, 2015). Furthermore, this type of research encompasses investigating computer-implemented algorithms, advancing shape grammar interpreters（SGI）, and related areas of study.

Figure 2. Shape grammar and its related theoretical development Source: Ning and Amini Behbahani (2021).

3. A study on the association of SG and vernacular houses

One of the pioneering applications of SG in the analysis of architectural works is evident in the paper “the Palladian Grammar” (Stiny and Mitchell 1978). This study focused on the planar analysis of Palladian-style villas and employed shape rules derived from a parametric SG. By reshaping the proportional relationships and architectural language of Palladian houses into a modern generative language, they demonstrated the potential of SG in architectural analysis and design. Following this landmark study, SG’s relevance in analyzing serial architectural works, including vernacular houses, gained attention. Initially, researchers aimed to verify the scientific accuracy of SG by analyzing the stylistic characteristics of vernacular houses. However, as researchers deepened their understanding of SG, it evolved into an established method for the systematic study of vernacular houses (Wang et al. 2021). At present, SG has gained some influence in the field of vernacular houses research, and the value of the results is that it can thoroughly combine morphology and mathematics to analyze the structural characteristics of vernacular houses, such as obtaining the external shape characteristics, exploring the proportion of shape composition, defining the functional space pattern, and determining the correlation between elements, and then coding them into a design language (Hussein and Ismaeel 2020). Moreover, SG facilitates exploring and reproducing these structural features within the same context, supporting researchers in continuing adaptive regeneration studies focused on local residential styles. In order to highlight the correlations and significance of SG in the examination of vernacular houses, this research draws upon a comprehensive collection of 31 documented cases from relevant domestic and international literature spanning since 1978 (Figure 3). The analysis focuses on six aspects: research scope, purpose, method, strategy, implementation, and form (Hussein and Ismaeel 2020; Wang et al. 2022; Xie and Ding 2021). Through this examination, the study highlights the contributions of SG in the analysis of vernacular houses and their potential for future research (Table 1).

Figure 3. Statistics on the application of shape grammar in vernacular houses research Source: Stiny and Mitchell (1978); Koning and Eizenberg (1981); Downing and Flemming (1981); Flemming (1987); Herbert, Sanders, and Mills (1994); Chiou and Krishnamurti (1995); Cagdas (1996); Chiou and Krishnamurti (1996); Colakoglu (2005); Duarte (2005); Duarte, Rocha, and Ducla-Soares (2006); Said and Embi (2008); de Godoi and Celani (2009); Eilouti and Jamil Hamamieh Al Shaar (2012); Tching, Paio, and Reis (2012); Barros et al. (2013); Güzelci (2014); Erem and Selen Abbasoğlu Ermiyagil (2016); Lambe and Dongre (2019); Ena (2018); Chokyu and Maria Angela (2018); Lee and Gu (2018); Hadighi and Duarte (2019); Yousefniapasha et al. (2019); Verniz and Duarte (2020); Hussein and Hani Ismaeel (2021); Wang, Zhao, et al. (2021); Wang, Agkathidis, and Crompton (2021); Gholami et al. (2021); Zihao (2021).

Table 1. The cases of vernacular houses using shape grammar application for analyzing.

Titles			Research scope		Research purpose		Reasoning method		Research strategy			Implementation approach		Expression form
Time	Researchers	Research Subjects	Single house	Settlement	Feature analysis	Comprehensive generation	Manual reasoning	Automatic iteration	Addition	Subdivision	Grid	Totality reasoning	Selective reasoning	Shape diagrams	Semantic diagrams	Description diagrams
(1978)	G. Stiny	Palladian villa	•		•		•				•		•	•
(1981)	H Koning	Wright’s Prairie Houses	•			•	•		•			•		•
(1981)	F Dowing	Bungalows of Buffalo	•		•		•			•		•		•
(1987)	U. Flemming	Queen Anne Houses	•		•		•		•			•		•
(1994)	T. Herbert	Linear Ndebele Homesteads		•	•		•				•		•			•
(1995)	S. Chiou	Taiwanese traditional houses	•		•		•		•			•
(1996)	G. Çağdaş	Turkish Houses	•		•		•	•	•				•		•
(1996)	S. Chiou	Taiwanese traditional houses	•		•		•		•			•		•
2003	B. Colakoglu	Hayat Houses	•			•	•		•				•	•
(2005)	J. Duarte	Siza’s Houses at Malagueira	•			•	•	•		•		•		•		•
(2006)	J. Duarte	Medina Houses		•	•		•			•		•		•
(2008)	S. Said	Malay Long-Roof Houses	•		•			•	•				•	•		•
(2009)	G. Godoi	Monte Alegre Do Sul Houses	•		•		•		•			•		•
2008	M. A. Ramli	Rudinara Houses	•		•			•	•				•	•
(2012)	B. Eilouti	Damascene Houses	•			•		•			•		•	•		•
(2012)	J Tching	Campinas Houses	•			•	•		•				•	•
(2013)	P. Barros	Maputo´s Houses		•		•		•		•			•	•
(2014)	OZ Güzelci	Turkish Houses	•		•			•	•				•		•
(2016)	Ömer Erem	Turkish Houses	•			•	•		•			•		•
(2018)	V. Ena	Janeiro’s Favelas		•		•		•		•		•		•
(2018)	M. Lica	Rocinha houses	•			•		•		•			•	•
(2018)	J H Lee	Murcutt’s Rural Houses	•			•	•		•			•		•
(2019)	N. Lambe	row houses of Ahmedabad	•		•		•		•			•		•
(2019)	M. Hadigh	single-family house	•		•			•		•			•	•
2019	C. Teeling	Mazandaran Vernacular Houses	•			•	•		•			•		•
(2020)	D Verniz	Santa Marta Houses		•	•			•		•		•		•
(2020)	K A Hussein	Mosul’s Vernacular Houses	•		•		•		•			•		•
(2021)	Yuyang Wang	Beijing Hutong		•	•		•		•	•			•	•
(2021)	Gu Zihao	Jiaoxi Vernacular Houses	•	•		•		•		•			•	•	•
(2021)	S. Gholami	Ekbatan Houses	•			•		•	•				•		•
(2021)	Wang Jiang	North China Rural Houses	•			•	•			•		•		•
percent（%）			81	22	55	45	65	42	58	35	10	52	48	90	13	16

Source: The same as Figure 3.

(1) Research Scope: from Single House to Settlement

The research scope of the above literature mainly involves the single house and the settlement. The former includes the analysis and generation research on the plan layout, structural composition, functional organization, facade section, and detailed decoration of vernacular houses. For instance, Hussein and Hani Ismaeel (2021) examined the facades of traditional houses in Mosul’s old city, employing SG analysis to extract form elements and mathematical features. These were translated into shape rules to reconstruct the digital model of the residential facade. At the same time, the latter includes research related to the grouping relationship, road network, and spatial texture among vernacular houses. Wang, Agkathidis, and Crompton (2021), for example, reconstructed the digital model of a Beijing Hutong block using procedural modeling based on SG. This method facilitated restoring and reproducing the spatial structure unique to Hutong blocks, shedding light on their emergence and development. Furthermore, studies have been conducted on the inherent spatial evolution mechanisms in informal settlements like Rio de Janeiro and Mozambique.

(2) Research Purpose: from Feature Analysis to Comprehensive Generation

SG can be used as a research method for analytical research with a single purpose and comprehensive research with multiple purposes. Analytical research focuses on the case study of vernacular houses and reproduces their creation process through graphical language simulation to categorize, analyze, and evaluate the research object. For example, Flemming (1987) analyzed the correlation between internal functions and the Queen Anne style house’s logic through two stages: planar functional layout and three-dimensional form generation. The accuracy of SG as an analysis method is positively correlated with the number of samples in the target corpus. The larger the number of samples, the higher the accuracy of the analysis. For comprehensive studies, Knight (1981) proposed a method to create a new grammar based on the existing one. This approach involves recursive reasoning according to established grammatical logic to generate new residential design schemes. Colakoglu (2005), for instance, constructed a comprehensive SG consisting of three levels: original house generation, new house generation, and house evolution. Their research focused on exploring the diverse characteristics of traditional Ottoman-style Hayat houses using eight typical houses as a corpus.

(3) Reasoning Method: from Manual Reasoning to Automatic Iteration

Reasoning is the process of concluding existing facts based on specific rules. In the early research of vernacular houses, Manual Reasoning was a common way to extract the shape rules from the corpus and present them in a graphical representation by collaborative hand-brain drawing. Later, with the popularity of computers, the above work can be achieved by automated reasoning and generation. Some researchers have developed SG interpreters with the help of computer programming to interpret predefined SG, enabling the mapping of shape rules to shape simulations. In addition, a growing number of studies have shown that the combination of SG with other methods is also an effective way to use it for automated generation. For example, the Technical University of Dublin, Murphy of TUD (Virtual Lab Dublin), and others have been devoted to the research of historical building information modeling (HBIM) (Dore and Murphy 2013; Murphy et al. 2021). A method of generating HBIM from image data is proposed, and SG is used as the primary means of building generation modeling. The former obtains basic 3D or 2D model information employing laser scanning and photogrammetry, but it does not have modification and optimization. The latter can be considered a semi-automatic modeling approach. By translating the model information into corresponding shape rules with the aid of the former, procedural modeling is achieved within the designated BIM software. This method enhances the adjustability and interactivity of the model, ensuring both its precision and intricate detailing. Computer reasoning has significant advantages over manual reasoning in terms of “emergent” shape results, but in practice, the two are often complementary and can be applied synergistically. On the one hand, manual reasoning is a shape evolution process based on visual calculation, which is easier for others to understand and learn. On the other hand, computer reasoning is a digital model construction method based on computer programming language, which is easier to adjust and optimize. In essence, SG belongs to an expert system, which is better at assisting researchers in carrying out generative research. However, it is difficult to be used independently for the “deep learning” of the research object, so SG cannot replace the design behavior of architects.

(4) Research Strategy: from Addition, Subdivision to Grid

In the process of rule inference, two strategies that are often used are addition and subdivision, which are derived from mathematics. The former is transformed from the sum operation of numbers to the sum operation of shapes. In this process, a pivotal shape or label is initially defined within a finite set of shapes. Subsequently, elements are incrementally added based on their priority, thereby completing the reasoning of rules. This strategy is often used to study irregular borders or complex shapes. Conversely, the latter generates the layout relationship between elements from top to bottom by continuously splitting the “parent element” into “child elements” (Wang et al. 2022). Here, the external contour of the research object is generally regarded as the initial shape of shape rule deduction, so this strategy is mainly used for shape rule reasoning with fixed boundaries. For example, Chiou and Krishnamurti (1995) used an additive strategy to reason about the floor plan of a traditional Taiwanese house by adding functional rooms in 17 stages, starting from the main room. Downing and Flemming (1981), in their study of Bungalows of Buffalo, defined the exterior boundaries of the residence based on the logic of its internal spatial organization and then reasoned about the functional relationship of the residence’s floor plan through a subdivision strategy. In addition, there is also a grid method that is often used. This approach entails first obtaining the minimal set of shapes representing individual elements within the subject of study. Subsequently, a Coordinate Grid is established, allowing for the positioning and delineation of shapes within the grid. This strategy primarily serves the purpose of inferring shapes that possess specific mathematical relationships. For example, in their study of Palladian grammar, Stiny and Mitchell (1978) used this strategy to define the external boundaries of a house and then gradually subdivided the relative relationships of the functional plans based on a grid.

(5) Implementation Approach: From Totality Reasoning to Selective Reasoning

In researching the relationship between vernacular houses and SG, some studies require a comprehensive examination of all the object-oriented details, including the plane function organization, the number of doors and windows, the number of colonnades, and even detailed decorative components. These aspects are analyzed and reasoned according to authenticity principles. Other studies focus only on selecting one or several representative architectural elements of the object, considering both local residential style and contemporary design requirements. For example, Lambe and Dongre (2019) constructed a generative grammar of row houses in 13 stages in an analytical study of row houses in Ahmedabad (India). The study involved generative simulations of the first-floor plan, second-floor plan, roof forms, and window and door openings in achieving authenticity reproduction of the research object. In his study on the generation design of residential monoliths in Jiaoxi Village, Zihao (2021) focused on the spatial relationship known as the “central axis” within the traditional Fujian residential plan. Drawing upon this key aspect, he “subjectively” tailored the shape rules of the double-axis layout to produce a novel house form characterized by a sense of “siege”. The above two implementation methods consider the respect and inheritance of the original local residential style. The former pays more attention to the analysis of the original corpus and has the characteristics of “following the map”. At the same time, the latter is more inclined to the characteristic interpretation of rural houses and has the characteristics of “keeping pace with the times”.

(6)Expression Form: from Shape Diagrams, Semantic Diagrams to Description Diagrams

SG is mainly used to express and convey the design intent through diagramming. In the specific application, the diagrams can be subdivided into shape, semantic, and description diagrams. Shape diagrams reproduce the object’s shape characteristics, aiding researchers in visually reasoning shape during the rule reasoning process (Rivollier et al. 2010). These diagrams usually maintain relatively fixed proportions and scales for traceability. Semantic diagrams abstract the object’s shape, obscuring precise “size” details and deleting unnecessary shape information. They present the relationship between shapes in a concise form. Dual diagrams and bubble diagrams (Xie and Ding 2021) fall under this category. Moreover, the description diagrams are a new representation after computer-intervention, representing the graphic information through programming and coding and then converting the digital information into specific shapes with the help of visualization tools. For example, Koning and Eizenberg (1981) constructed a comprehensive SG based on a corpus of 11 Prairie Houses and reproduced the generative reasoning process of Prairie Houses through shape iconography (Figures 4–1). Gholami et al. (2021), in the study of vernacular houses in Ekbatan, abstracted the functional shape of the floor plan and illustrated practical information and correlations using basic color blocks (Figure 4-2a). Bubble diagrams were also employed to present logical relationships better (Figure 4-2b). Herbert, Sanders, and Mills (1994) used shape diagrams to demonstrate the regular reasoning process of the layout of the Ndebele house in Africa. Descriptive diagrams were then used to illustrate the algorithm related to the shape diagram (Figures 4–3).

Figure 4. Three expressions of shape grammar source: 1) Koning and Eizenberg (1981), 2) Gholami et al. (2021), 3)Gholami, Soheili, and Manesh (2021).

It can be seen from the inductive analysis in Table-1 that the application of SG in the process of vernacular houses is adjusted due to the different independent variables of the research object, which leads to the application structure of the dependent variables such as research scope, purpose, method, strategy, implementation, and form. Notably, there is a significant focus on single-house levels in most studies (81%), which predominantly employ visual representations through shape diagrams (90%). Furthermore, there is a discernible shift from manual to automatic reasoning approaches. In general, the research on the application of SG in vernacular houses has the following characteristics: ① uniqueness, meaning that each set of SG corresponds to the actual vernacular houses case; ② similarity, meaning that the application structure of SG is convergent mainly in the specific research process; ③ diversity, meaning that a large number of studies on the application of SG can contribute to the construction of a rich vernacular houses research case base (Figure 5).

Figure 5. The case of vernacular houses research based on shape grammar source: drawn by the author.

4. Reinterpretation of typical cases of vernacular houses

To provide a comprehensive validation of the positive impact of SG in the study of vernacular houses, we will select three representative cases to illustrate how researchers can effectively analyze the generative process of plan functions in vernacular housing. This will be accomplished by employing three specific strategies: addition, subdivision, and grid. These cases are reinterpreted following the steps of first dimensionality reduction, and then dimensionality increases to help understand the analytical strategies used by the researchers in the case studies. Firstly, the studied case corpus will be simplified to extract the fundamental geometric shapes. Subsequently, the corpus will be further simplified to identify the related information about residential functions, which will be visually represented using bubble diagrams as a foundation for establishing shape rules. Lastly, the initial shapes will be carefully selected, and a recursive design process will be executed by applying the defined shape rules.

4.1. Analysis of vernacular houses in Mazandaran, Iran, based on additive reasoning

To explore the climatic adaptation and ontological sustainability of vernacular houses in Mazandaran (northern Iran), Teeling selected 44 dwellings from four local settlements as a corpus through fieldwork and classified the dwelling types into four categories based on the architectural outer contours formed by the residential climate interface: as basic type (RH) as well as L-type (HSH), U-type (SH) and composite type (Figure 6) (Yousefniapasha et al. 2019). After combining the local climate factors, Teeling establishes the two-dimensional SG generation system of local vernacular houses in stages and involves the layout of floors, enclosed spaces, and semi-enclosed spaces. Finally, a proposed initial shape is used as the starting point for reasoning, and the required set of residential design results is gradually generated to verify the effectiveness of SG in the study of vernacular adaptive regeneration.

Figure 6. Shape grammar of vernacular houses in Mazandaran, Iran Source: Yousefniapasha et al. (2019).

The reasoning process of this study is mainly carried out through the following 7 stages: ① Selecting a coordinate point within the proposed house site as the initial shape. ② Defining the living space specifically involves 8 rules; for example, the living room (L) is generated through the definition of rule 1 and rule 3, including room size, optimal orientation, and space extension direction. ③ Defining the main function room involves 3 rules, for example, the expansion of new functional rooms through rule 9, and rule 10, then generating the most basic RH type plan, and then generating SH type, HSH type, and other plans, respectively through multiple invocations of relevant rules. ④Defining the auxiliary functional room involves 11 rules, for example, through rule 13 and rule 15 to change the label and add shape to adapt to the user’s selective rule reasoning according to their own needs and preferences, to generate the same. ⑤ Regarding the climate interface, it is necessary first to define the climate boundary formed by the above functional rooms and then define the SG of the composite residence through a total of 17 rules (such as the use of Rule 23 to define the wall of RH-type residence) to generate a diverse layout of the residence and its physical space. ⑥ Regarding semi-enclosed spaces such as porches and convex balconies, it is necessary to generate them by addition, combining different residential types and the location of semi-enclosed spaces, mainly defining 25 rules, such as a rule 59 defining the location of the porch and rule 64 defining the number of door posts, and then selective reasoning of rules for the actual residential needs. ⑦ Finally, defining details such as windows and doors and completing the residential all-reasoning process by modifying and deleting redundant labels. Here, it is essential to emphasize that some necessary rules need to be added to the research on the design of new houses that continue the vernacular house style, and they are usually related to details such as doors, windows, and column heads.

4.2. Analysis of vernacular houses in fabulo, USA, based on subdivisional reasoning

In the study of The Bungalows of Buffalo, Dowing selected seven related houses for mapping, used them as a corpus, and constructed an SG after clarifying their functional and other relevant features (Downing and Flemming 1981). The reasoning process of the study was carried out in 12 stages. In the first 3 stages, a subdivision strategy was used to define the basic spatial layout relationships of the dwellings. In comparison, in the subsequent 9 stages, with the increase of plan details and shape complexity, a comprehensive study based on multiple strategies was used, which will not be described here for focus.

Based on this, four different plan types are selected here for the derivation of functional layout generation (Figure 7), focusing on presenting the research logic of the first 3 stages: ① Defining the initial plan, firstly, two sizes of structural exterior walls are defined through rule 1, and the interior residential space is equally divided into two areas in front and back, and then the above two interior spaces are subdivided into new units through rules 2 and 3, respectively, and given their labels “a”. ② Defining the main functional rooms, converting cell label “a” to generate different functional rooms by rule 4–7, and defining the location relationship of each functional room, e.g., dining room (d) adjacent to the living room (l), kitchen (k) adjacent to the dining room (d). ③ Defining the auxiliary functional rooms, for example, rules 8 and 9 define the location of the stairs (s) to be adjacent to the kitchen (k), and rule 10 defines the bathroom (t) to be adjacent to the bedroom (b). Through the above three stages of research, the “emergence” of the functional relationship of residential plans can be achieved to a certain extent.

Figure 7. Shape grammar of vernacular houses in Fabulo, USA Source: Downing and Flemming (1981).

4.3. Analysis of vernacular houses in Ndebele, Africa, based on grid reasoning

Through fieldwork, Herbert studied the invisible logic between the layout of vernacular houses in Ndebele and the local polygamy and established an SG for it (Figure 8) (Herbert, Sanders, and Mills 1994). He defined the relationship between residential layout and residential units as “father and son, son and grandson”; that is, the layout logic of “Father’s houses” is composed of several “son’s houses” and “grandson’s houses”. The case mainly adopts the grid method to add “son’s houses” based on “Father’s houses” and finally obtain the “emergence” of “Father’s houses” layout results. According to the operation of the family life cycle, the layout results generated by each stage of rule inference here can represent a final pattern of Ndebele vernacular houses layout.

The study is divided into two steps. First, the definition of “son’s houses”: Herbert first sorted out the examples of the Palace of the Parapets, the Symmetrical Palace, the Palace of the Jets, and the Pediment Palace based on the literature review. Based on this, several residential plans were selectively standardized to form typical plans, including the prototype, L-shaped, diagonal. To adapt to the various stages of the “son’s houses” process in the family’s life cycle, the above plans are built according to the same dimensional module (or modules) with the possibility of expansion. Secondly, for the derivation of the “Father’s houses”, we should follow the plan layout relationship as shown in Figure 8, take the “family formation period” as the starting point for the study, and generate the house layout form in stages: ① Firstly, define a set of the coordinate grid as the initial shape. ② Then define the layout of “son’s houses”, mainly through rules 2 and 3 to generate the relationship between the location of spouse 1 and spouse 2’s homes, respectively, by the local concept of right-handedness, spouse 1’s home is arranged on the right side, and spouse 2’s home is symmetrically distributed with it along the vertical axis. ③ Reasoning about the evolution of “son’s houses” and replacing “son’s houses” according to rules 18, and 22, to adapt to the needs of different home layouts during the life cycle of a family. ④ Over time, the “grandson’s houses” derived from the “son’s houses” are defined mainly based on rules 26 and 27, and usually, the “grandson’s houses” are located below and on the same side of the “son’s houses”. ⑤ Finally, the evolution of the “grandson’s houses” is inferred, and this stage is mainly realized by rules 40, 62.

Figure 8. Shape grammar of vernacular houses in Ndebele, Africa Source: Herbert, Sanders, and Mills (1994).

5. The application of SG in Chinese Unconventional Village design

The above case study illustrates that SG can assist researchers in analyzing the inherent value of vernacular houses more effectively, especially in presenting the characteristics of vernacular houses that are “harmony and difference” in a graphical logic. Research on “harmony and difference”, Wang (2020), an Academician of the Chinese Academy of Engineering, has also clarified the significance and value of this type of research in his article “Much the Same” and “harmony and difference”. In the cultural philosophy of Confucianism in China, the pursuit of “harmony” and “difference” has long been emphasized. The study of “harmony” typically revolves around the temporal dimension, while exploring “difference” necessitates focusing on the spatial dimension. However, when we look at the contemporary vernacular “unified” houses, which have the same root as our traditional vernacular houses, some of them reflect the mismatch between “harmony” and “difference.” The “harmony” here is not implemented in the temporal dimension but in the homogenization of space, and the “difference” is not implemented in the spatial dimension but often highlights the fracture of two spatiotemporal images of the countryside before and after. Considering this observation, the JY502 Studio at the Shandong University of Architecture has responded to the demands of contemporary vernacular house design since 2015. They have guided 8 sessions of the “Unconventional Village” undergraduate graduation design series, employing SG as the theoretical foundation. This series of design teaching is done based on the previous theoretical application cognition (Wang et al. 2021), and focuses on exploring the SG rules defined by the house base as the initial shape (Figures 9–1). The corresponding research strategies involved two types of addition and subdivision, and the reasoning process included the following four stages.

Figure 9. Example of the shape grammar of rural “modular” houses and their related design teaching results.

Source: 1). 2). 3) Drawn by the author 4) Belong to architecture design works of Shandong Jianzhu University

• About the house base. The entrance direction of the house base is defined first, and this stage is mainly related to the location relationship between the house base and the surrounding roads. To make the suitability of the house base to the residential plan contour higher, the shape ratio of the house base is predefined as Type A (4:3), Type B (5:3), and Type C (1:1). In addition, the plan dimensions of the above house base need to be predefined to make the subsequent reasoning process more practical.

• About the residential plan profile. The reasoning process in this stage is based on two-dimensional mathematical relationships. The ratio between the width of the house base and the width of the main house and its depth is defined as n:1:1.5 (n ≥ 1 and integer) under the premise of meeting the natural lighting and ventilation of the house. Following this, specific elements are positioned and added using an additive strategy. The main house is gradually formed, starting from a “single-room” plan. Following that, the courtyard, located to the north or south, must ensure its adjacency to the main room. The north courtyard also fulfills ventilation and lighting requirements for the north side of the main room while avoiding potential shadow shading between the north and south residences, resulting in a relatively more minor depth. On the other hand, the south courtyard has a relatively larger depth. Finally, the definition of the auxiliary room, its location is near the outer boundary of the south yard.

• About functional rooms. Firstly, based on the area of a given target room, its plan geometry is predefined, and the relationship between its dimensions and the number of openings in the main room is determined. Secondly, the residential plan contour is subdivided starting from defining the living room, and labels are gradually added to its functional rooms. Finally, the plan dimensions of functional rooms are optimized and adjusted to meet each functional room’s residential plan flow and the lighting and ventilation requirements.

• About the conversion rules. This phase mainly defines conversion rules such as adding rooms, label merging, or replacement to adapt to different stages of the family life cycle and the residential space needs of different types of rural families, to achieve the iterability of the plan generation scheme. For example, the conversion rules can be adopted for the main house to reduce the room depth and add a greenhouse or a north-south picket.

In addition, the residential plan relationships generated by the two-dimensional rules can be matched with the predefined profile types (Figures 9–2) to “Dimensionality Reduction”, the two-dimensional generative results of rural residential buildings (Figures 9–3). Figures 9–4 is one of the results of the undergraduate architecture design work of the 2019 class of Shandong University of Architecture, which was completed based on the above rules and was awarded the Young Talent Architecture Award 2020 (YTAA 2020) finalist certificate by the Mies van der Rohe Foundation.

6. Conclusion

This paper focuses on exploring the application of SG in vernacular house research. Through the collection, analysis, and induction of relevant cases, the characteristics of SG in this type of research are identified and discussed from six aspects: research scope, purpose, reasoning mode, strategy, implementation mode, and expression form. SG is a key method for decoding vernacular houses’ “harmony and difference” characteristics. The case studies from Iran, the United States, Africa, and China reveal common characteristics of SG in the study of vernacular houses:

1. SG visually represents perceptual design elements such as spatial texture, membership relationships, and climate characteristics through spatial relations of geometric shapes. It regularizes the generation logic of these spatial relations, enabling the visual display of different vernacular houses’ shapes and characteristics through regular graphic means.

2. SG can visualize the design process and stages and express the ruling hierarchy through a tree diagram or single chain shape rule recursion, thus enhancing the design logic. This logic helps designers to effectively understand the inherent attributes of vernacular houses and protect and inherit them using design retrospectives.

3. SG realizes the “emergence” and “unpredictability” of design results through rule reasoning and generates the alternative scheme of the design style while generating the given design results. At the same time, the related technology realized by computers benefits the adjustability and predictability in developing and evolving vernacular houses.

In addition, in the study of these four cases, the applied study of SG also shows some different characteristics:

1. Differences in purpose: The cases from Iran, the United States, and Africa primarily focus on the analysis and representation of their respective vernacular spaces, constituting analytical research. The case from China, on the other hand, emphasizes the possibility of design outcomes within this style, making it generative research.

2. Variations in implementation strategies: To generate the plan layout of vernacular spaces, the Iranian and Chinese cases employ the addition strategy, combining and superimposing spaces. The American case utilizes a step-by-step subdivision strategy to divide the space, while the African case is based on the grid for a generation.

3. Varied levels of shapes: The cases from Iran, the United States, and Africa discuss the generation of single-plane spaces using two-dimensional SG. In contrast, the Chinese case employs two-dimensional and three-dimensional SG, generating a three-dimensional model of the house and exploring the spatial form and combination of units within the village.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Jiang Wang

Jiang Wang is Ph.D. Associate Professor at Shandong Jianzhu University (School of Architecture and urban planning). He was a visiting scholar in School of Architecture, University of Miami, USA. His research interests include Generative Design, Mass Customization, and Housing Typology.

Sheng Zhang

Sheng Zhang is present master at Shandong Jianzhu University (School of Architecture and urban planning).

Wei Fan

Wei Fan is Phd student at Tianjin University (School of Architecture). He has studied for a master's degree at the School of Architecture and Urban Planning, Shandong Jianzhu University from 2019 to 2022.