Exploring Architectural Shapes Based on Parametric Shape Grammars: A Case Study of the “Three Lanes and Seven Alleys” Historic District in Fuzhou City, China

Abstract

With the development of information technology, the introduction of information technology into architectural modelling and façade design and the systematic definition of historic districts is a problem that the architectural industry continues to explore and pursue. As a shape-based and self-defining generation rule, shape grammar provides significant help in the process of the automatic generation of architectural shapes to obtain design results that meet the requirements of the original historic district. Based on the simple combination of the application of shape grammar in architectural design, combined with the field investigation method, the representative buildings in the “Three Lanes and Seven Alleys” historic district are investigated and understood in detail, and the corresponding shape grammar rules are established. The courtyard types of the historic district are divided into: “” shape, “T” shape, “=” shape, “” shape, “” shape, “” shape, “” shape, “U” shape, “” shape, and garden. In detail, the façade components include the entrance, patio, main seat, wings, cloister, pavilion, etc. The elements of its façade include saddle walls, grey sculptures, carved stones, grey tiles, wooden grilles, wooden railings, wood grain flowers, etc. On this basis, parametric design is introduced to convert the design syntax into parametric programs. Grasshopper in Rhino is mainly used to visualize and simulate the regulation, and finally, achieve the purpose of automatically generating the architectural shape and façade of the “Three Alleys and Seven Alleys” historic district by adjusting its parameters.

1. Introduction

With the advent of globalisation and the advance of technology, urban areas are developing at a rapid pace, and many historic districts are being reshaped in terms of their architectural shapes and interiors. However, in urban regeneration, due to its over-rapid and shortened design processes, the architecture in historic districts lacks the “spirit of place” (the activity of people or objects endowed with a certain social, cultural, historical, or physical significance is defined as a place). To achieve this goal, it is necessary to classify and redesign the traditional district style; however, this often requires a huge time investment, which is not compatible with the fast-paced rhythm of urban development. The difficulty in preserving the architectural style while adapting to the fast-paced design rhythm is the current problem we face. Existing design methodologies, which are primarily based on the experience of individual architects, are often biased and impede the development of rational design solutions or a systematic approach to the renovation of historic districts. Additionally, while computers have become widely used as design tools, they have mainly functioned as substitutes for traditional pencil and paper methods. Their full potential for improving design efficiency or enabling automated processes remains largely unexplored [1]. Parametric design, which facilitates automated design, exists; however, its practical applications are numerous and complicated [2]. The focus of this paper is to explore methods for achieving quantitative design, streamlining the design process, and developing visually adaptive solutions while preserving the regional characteristics in the refurbishment of historic districts.

Located in Fuzhou, the “Three Lanes and Seven Alleys” historic district has a strong cultural heritage and is known as a “museum of the Ming and Qing dynasties” because of the number, type, and history of its historic buildings, which are second to none. In 2010, the “Three Lanes and Seven Alleys” district was named a national 5A tourist attraction; in 2012, it was selected as one of China’s World Cultural Heritage sites and in 2015, it was a winner of the UNESCO Asia-Pacific Awards for Cultural Heritage Conservation. The district as a whole displays an urban pattern divided by lanes and alleys, which is the basic character of the area, is complete and uniform in form, and has strong regularity. In terms of individual buildings, however, their spatial organisation and layout follow a certain logic but are not archaic and are colourful. As a manifestation of Fujian culture, courtyard-style houses are ubiquitous in Fuzhou, featuring white walls, gray tiles, saddle walls, and gray carved decorations, with highly regular courtyard layouts (Figure 1) [3].

When updating old buildings in historic districts, it is crucial to develop a methodology that can effectively generate a diverse range of design options for decision makers to choose from. However, the design concepts of this methodology must align with the architectural design concepts of the historic district. Shape grammar is a combination of the fields of computing and morphology, is compatible with architectural design in terms of generative thinking, and can be combined with technical methods to achieve the automatic generation of an architectural design [4]. Shape grammar can deconstruct the architectural shapes and façades of the “Three Lanes and Seven Alleys” district, establish the basic architectural shapes and façade types, formulate the arrangement rules, and compute the possibilities of various arrangement rules.

In this study, we hope to experiment with this methodology in the “Three Lanes and Seven Alleys” historic district in Fuzhou City, China, and use shape grammar to help designers to deconstruct its grammatical rules based on the logical rules of the abstract architectural design. The focus is on combing the architectural shapes and façade designs of the “Three Lanes and Seven Alleys” Historic District, both of which embody the rich and colourful traditional culture. The Rhino-based Grasshopper plug-in is a useful tool for parametric and automated generation in design preparation, as its visualization features allow for adjustments to be made iteratively over time [5]. The final choice when judging the results of the screening and deciding to increase the in-depth analysis program is based on personal experience, which reduces the time and workload in the pre-design stage [6]. Therefore, based on shape grammar, the parametric design can be used for the automatic generation of architectural shapes and façade design of the “Three Lanes and Seven Alleys” historic district. At the same time, it is hoped that this methodology can be applied to different historic districts, using the rules of shape syntax to deconstruct the shapes and façade elements of buildings in historic districts in need of renovation, and ultimately to automatically generate design solutions with local characteristics.

Finally, this design method is expected to reduce human and material resources. The design can be revised several times without repeated operations, and the optimal solution can be communicated effectively in good time. The combination of the two can prevent the use of a single commercial design, reflect the character of the local historic district, and protect the local cultural characteristics to a certain extent.

2. Literature Review

2.1. Review of Shape Grammar Theory and Methodology

Shape grammar was introduced in the 1970s by Stiny and Gips [7] as a logical theory that can be used in the conceptual design of architecture. Shape grammar is usually a quadruple, G = < S, L, R, I >. S, which is a given set of shapes and the root of the operations of the shape grammar. L is a given set of symbols, which indicates the object to which the grammar rules are applied. R is a given set of shape rules, such as C-A, C, A of <S, L >. I is a symbolic initial shape, whose genus < S, L > is called the initial state. It may also be understood that shape grammar is built by creating a set of shapes, setting up rules for generating them and evolving them from the initial state. Shapes and rules are key to the study.

The definition of the concept of shape grammar is as follows: shape grammar can be considered a design reasoning method that uses a shape with a label as the basic unit and generates a new shape by analysing the grammar rules. This method is an algorithmic design grammar based on “shape”, with “shape perception” and “possible substitution of shape” as its core components [8].

“Shape perception” can be understood as a shape rule and an initial state; the new shape can be generated by continuously applying the rule to the initial state or the current shape, and the new design result is the “possible substitution of shape” [7]. This process fits well with the general architectural design process. Therefore, shape grammar helps scholars to develop logical rules for abstract architectural design.

The definition of grammar is the first step when applying shape grammar in architectural design, because it dictates the directions of the next steps. When defining grammar rules for individual buildings, the initial set of shapes is often defined in more detail, and the subsequent rules that are generated become more complex. In 1978, Stiny used shape grammar to create language rules for Palladio’s villa plan. There were six main rules: (1) generate regular squares; (2) regularize some of the squares; (3) generate rectangular arrays with different aspect ratios; (4) generate the contour lines of the walls from the rectangular arrays; (5) generate the layout of the rooms; and (6) generate the exits and the passages between the rooms from the contour lines. The resulting planes have similar characteristics to those of Palladio’s villa, i.e., “possible substitution of shape”.

Shape grammar, as a rule-based generative modelling method, has demonstrated great potential in analyzing and regenerating traditional architectural languages. Wang et al. [9] utilized shape grammar to reverse-engineer the generative process of Beijing hutongs, discovering the grammatical logic implied in their spatial forms. Wang et al. [10] developed a design system combining shape grammar and rural housing needs, achieving an algorithmic representation of local language features. In this study [11], we proposed a generative design method for mountain settlements through algorithm optimization. AL-Masri et al. [12] established a shape grammar system to reproduce the traditional façade style of old Mosul. It can be seen that shape grammar can not only decode the grammatical rules of traditional patterns but can also reproduce these rules for digital regeneration. As an extensible rule set, it can encode architectural languages at different scales and combine them with optimization methods to achieve innovation. Current research on computationally decoding and reconstructing traditional design knowledge using shape grammar opens up possibilities for sensitively regenerating architectural heritage. Enhancing shape grammar’s ability to replicate and extend styles can promote its role in inheriting traditional architectural wisdom in contemporary settings.

2.2. Review of Parametric Design Theory and Methodology

Parametric design is a new stage in the development of digital design, and the core of its method is the collective operation of the prototype to adapt it to the set target of design. In this process, architects operate the generation rules of architectural prototypes and the variables set, i.e., the parameters, rather than the form itself. Form as a geometric representation is a function of a parameter threshold in three dimensions under a given design rule, so the result of such an operation is often an infinite number of solutions rather than a single solution. In front of a computer screen, an architect chooses between countless solutions and, based on the information that is returned, modifies the rules or re-substitutes the parameters [13].

Parametric design is reversible compared to the previous continuous and irreversible architectural design; on the other hand, when a problem occurs in one step of the design and needs to be modified, it is time-consuming to correct the design after that step has been completed, whereas parametric design does not focus on the result but rather on designing a usable and bug-fixable system to solve the problem [1,14].

The parametric design follows a top-down design and, in the case of the secondary school design proposal in Malawi, the design parameters were developed according to the requirements of the mission statement, and the parametric model used a ladder of “modules” to add more educational functions, thus forming a system with a structural nature (parametric model). The components of the “ladder” are arranged step-by-step via an independent variable path (a path that connects indoor and grey spaces in series), and the functions of the indoor and outdoor areas can determine the size of the slope, especially theatres, outdoor work areas, and recreational activities [15]. In the case of shape grammar, the shape set is set first, the generation rules are determined, and multiple results are generated based on the rules. In both cases, the rule generations are performed from the bottom-up, and the focus is on the previous settings rather than the final results. This paper takes advantage of the fit between the two to convert the rules of shape grammar into corresponding parametric design rules for automated generation.

The visual programming and modelling tool is easy to use, scalable, and customizable, so Grasshopper was chosen as the digital modelling platform to generate models with shape grammar logic. There are few existing technical approaches for the transformation of historic districts from shape grammar definition to parameterisation. This paper, therefore, focuses on combining cultural analysis and shape grammar digitisation in an attempt to offer a reference for the renewal, preservation, and management of historic districts.

2.3. The “Three Lanes and Seven Alleys” Historic District

Fuzhou is located in the southeast, with the sea to the north, and has been the political and cultural centre of Fujian throughout the ages, as well as an important city along the Maritime Silk Road (Figure 2). Located in the heart of Fuzhou City, the “Three Lanes and Seven Alleys” historic district covers an area of 39.81 hectares and has a rich history dating back over 1100 years to the Jin Dynasty. The distinctive pattern of the alleys was established in 901 CE and has remained largely unchanged since the Song Dynasty [16]. Most of the existing residential buildings in “Three Lanes and Seven Alleys” were constructed during the Ming and Qing Dynasties and have undergone numerous repairs and renovations over the years. (Figure 3). The residents of the “Three Lanes and Seven Alleys” have developed a unique architectural style that harmonizes with Fuzhou’s natural environment, contributing to the growth and development of the local culture [17]. Many private gardens within the district have also evolved, reflecting the changing trends in gardening and the aesthetic preferences of different historical periods. These gardens serve as a testament to the multicultural fusion that has occurred throughout the history of the district. The district now boasts 270 historic houses and 131 protected buildings. As the city has grown, “Three Lanes and Seven Alleys” has expanded to include not only historical buildings but also museums, exhibition halls, and a variety of shops [18].

The whole historic district is divided into three main areas: Nanhou Street (north–south); Yijinfang, Wenrufang, and Guanglufang (west); and seven lanes (east), namely Yangqiao Lane, Langguan Lane, Ta Lane, Huang Lane, Anmin Lane, Gong Lane, and Jipi Lane. Its name is inherited from the Song Dynasty, and the road pattern follows the pattern of Tafangg from the Tang and Song Dynasties. The “Three Lanes and Seven Alleys” historic district is dominated by 12 representative buildings (Figure 3): Shuixie Stage, Liu Family Compound, Yan Fu’s Former Residence, Wang Lin’s Former Residence, Yan Family Flower Hall, Ye’s Former Residence, Lan Jianshu’s Former Residence, Suian Hall and the Provincial Literature Museum Ermei Bookhouse, Lin Cong Yi’s Former Residence, and Xiaohuanglou [3]. In this study, the shape grammar is established based on these 12 buildings.

Most of the studies on the “Three Lanes and Seven Alleys” historic district are part of the Chinese body of literature, with 1287 studies available in the Chinese “CNKI” database. Of these, 359 studies are related to architectural science and engineering. The visual analysis of these 359 articles (Figure 4) reveals that the majority of the studies on the “Three Lanes and Seven Alleys” focus on three specific sub-areas.

The studies in the green section primarily focus on the colour of the streets and the utilisation of GIS to evaluate fire risk. These studies explore the visual aspects of streets and examine how the colour of the streets can impact the overall aesthetic appeal of a district. Additionally, the use of GIS technology helps in the assessment of fire risk and the implementation of appropriate safety measures.

The works found in the red section primarily discuss the spatial organisation and layout of the district. These studies employ spatial syntax analysis to understand the spatial characteristics of the “Three Lanes and Seven Alleys” and how the arrangement of streets and buildings contributes to the district’s overall functionality and experience.

The studies in the purple section mainly focus on district reconstruction and preservation. These studies provide recommendations and strategies for renovating and protecting historic buildings and streets, ensuring their long-term sustainability and preserving their cultural significance.

The papers in the blue section concern themselves with a specific analysis of individual buildings within the district. It is evident that there are deficiencies in the integration of new technologies, and it is difficult to determine the number of parameterisations. These findings indicate there is still potential for further research in this area. By addressing these deficiencies and exploring new technologies, it is possible to enhance the integration and parameterisation of individual buildings within the district.

3. Research Subjects and Methodology Results

3.1. Simulation and Analysis of Cases

In this paper, a parametric case from the same historic district was chosen as a reference, as it encompasses the uniqueness of the building itself, as well as the cultural and regional characteristics of the “Three Lanes and Seven Alleys” historic district. In addition to the digital archiving and the modelling of buildings, the combination of cultural analysis and digitalisation was also considered. In this paper, we took modern houses on Gulangyu Island as an example, defined 3 types of house layout schemes and their 39 subtypes, established shape grammar and rules for modern house plans on Gulangyu Island, and finally used Grasshopper software to create a digital generation method based on the results of shape grammar. At the same time, the quantitative heritage culture analysis example and the rapid heritage modelling methods were satisfied, which provided a reference for the construction of a heritage culture database and digital heritage management in historic districts [20].

3.2. Analysis Method and Procedure

In this study, the shape, façade form, and layout of “Three Lanes and Seven Alleys” courtyards were used as the subject. For shape, a total of 10 courtyard types and 13 façade forms were used. The main focus of the rules was on the longitudinal and horizontal growth of courtyards, and the rules of the façade were defined based on the entrance, patio, interior, and garden. The labels were closely integrated with shapes, which limit the method of linking the courtyard and the façade forms. The initial state was the courtyard form that exists in the “Three Lanes and Seven Alleys” historic district. Based on this rule, the existing information on the courtyard shapes and layouts in the “Three Lanes and Seven Alleys” district was used as the basis for the establishment of parametric automatic generation.

The research steps are shown in Figure 5. In Step 1, the main research method was created based on a literature review and a field survey. In this part, the 10 courtyard forms and 13 façade subsets were obtained via the organisation and summarisation of the courtyard types and façade elements of the “Three Lanes and Seven Alleys” buildings. In Step 2, according to the hierarchy and interrelationships between courtyard forms, the courtyards and façades, and the façades and façade elements, the combination rules of each façade shape element are defined. Step 3 involves the parameter value domain of the previously defined combination rules. In Step 4, the shape grammar rules of the architectural shapes and façades of “Three Lanes and Seven Alleys” historic district are defined. In Step 5, the parametric rule transformation of the automated generation method of architectural shapes and façades of “Three Lanes and Seven Alleys” historic district can be understood as selecting the required bases and reorganizing the mathematical relationship, placing them into courtyard types (with the required random factors) and configuring the plan base according to the bases. The three types of design thinking are as follows: building wall, window and door definition, and window and door details; plan base and pedestal; and plan base, roof base, and roof shape. After completing the method outlined above, the visualisation was rendered in Rhino through the visualisation feature of Grasshopper to achieve automated visualisation generation.

3.3. Research Subjects

The “Three Lanes and Seven Alleys” district is located in the heart of Fuzhou, a historic district first formed during the Jin and Tang dynasties, where scholarly and cultural classes were originally the primary residents. Twelve of these buildings are the most famous, and Figure 6 shows the plans and views of these buildings. A brief introduction to these 12 buildings is given to demonstrate why they were chosen.

The Shuixie Stage is an extremely prestigious building located at the east mouth of Yijinfang in the “Three Lanes and Seven Alleys” district. It was originally Zheng’s courtyard house, built during the Wanli period of the Ming Dynasty. The building occupies an area of 2746 square metres. Its special feature is the richly varied courtyard, which gives the entire building a sense of movement and progression. Ye’s Former Residence is centrally located on the west side of Nanhou Street. It was originally built during the Ming Dynasty and was renovated both during the Qing Dynasty and in modern times. The residence faces south and is surrounded by the main courtyard on the east side and two side courtyards on the west side. It covers an area of 2300 square metres. The Provincial Literature Museum is located in Anmin Lane. It was built during the Qing Dynasty and is situated in the northern part of the eastern section. The area of the building is 915 square metres. The wood carvings are exquisite, and the pavilions are elegant. Yan Fu’s Former Residence, built during the Qing Dynasty, is located in the northern part of the district and faces south. It has a total area of 620 square metres. The residence follows a typical courtyard design, with one house on the east side and one on the west side. The eastern courtyard is composed of a front and rear courtyard, a central seating area, and four surrounding walls. Suian Hall is located on Langguan Lane and is composed of two courtyards. It sits in a north-to-south-aligned position and covers a total area of 2040 square metres. Wang Lin’s Former Residence is located on Taxi Lane, facing south, with a total area of 2225 square metres. It is divided into the main courtyard and the side courtyard. The Yan Family Flower Hall was constructed during the Qianlong period of the Qing Dynasty and underwent repairs during the Guangxu period. It is situated in the southern part and faces north, occupying a substantial area of 2127 square metres. The hall is particularly spacious, featuring a grand central hall and additional compartments on either side. Lan Jianshu’s Former Residence is located on the east side of Nan Hou Street, at the intersection of Jibi Road and Nan Hou Street. It retains buildings from the Ming and Qing Dynasties and now serves as a showcase, covering a total area of 1870 square metres. Built during the Kangxi period of the Qing Dynasty, the Liu Family Compound is a large building with a north–south orientation and a total area of 4500 square metres. It is considered one of the finest structures in the “Three Lanes and Seven Alleys” historic district. The building is large in scale, and it has been well-preserved for a long time and is in good condition, with some of the courtyards reflecting the architectural style of the late Ming Dynasty. The site is also complete in terms of spatial types and elevation patterns. The front door of the Ermei Bookhouse opens onto Langguan Lane, while the back door opens onto Ta Lane. This unique house spans two lanes. The yard has a total area of over 2000 square metres and a history of more than 300 years. It was built during the Ming Dynasty and served as the old residence of Lin Xingzhang, the director of the Fengchi College during the Qing Dynasty. Lin Cong Yi’s Former Residence was built during the Ming Dynasty. During the Southern Ming Longwu regime, the Da Lisi Yamen was established here. In the Daoguang period, Lin Congyi purchased this property. It consists of three blocks on each side, with the main buildings in the front and back, totalling four entrances. The garden on the east side is larger, covering an area of nearly 3000 square metres. Because of its long history, the façade has a very rich shape and a more complete style. Xiaohuanglou is the most iconic building on Huang Lane, covering an area of 3640 square metres. It was constructed during the Daoguang period, along with the West Flower Hall Siu Wong Lau and the adjacent “East Garden” residential building [21,22,23].

3.4. Definition of the Courtyard Shape Grammar

Based on Zhou Li-Bin’s generalisation of courtyard plan forms, this study further expands on these forms, with the “” shape, the “T” shape, the “=” shape, the “” shape, the “” shape, the “” shape, the “” shape, the “U” shape, the “” shape, and the garden as the main types [24,25]. The details are shown in Figure 7.

3.5. Definition of Grammar Rules of Courtyard Shape

The traditional houses of the “Three Lanes and Seven Alleys” district are multi-entry types, with a courtyard as the basic element or basic unit, and after certain regular changes, they are expanded in the direction of the depth of the house to form a spatial sequence and plan layout with the “entrance” as the unit, with patios providing the transition [26]. In addition to the existing one-entrance courtyard, two-entrance, three-entrance, and four-entrance courtyards are common arrangements. The extension of the two-entrance and three-entrance courtyards can also result in a very rich form (Figure 8).

When the building consists of two-entrance courtyards and three-entrance courtyards, 194,238 architectural solutions can be obtained; when the building consists of two-entrance courtyards and four-entrance courtyards, 1,926,342 architectural solutions can be obtained; when the dwelling consists of three-entrance courtyards and four-entrance courtyards, 19,088,298 architectural solutions can be obtained.

3.6. “Three Lanes and Seven Alleys” Courtyard Façade form Definitions

According to the study of the literature and diagrams, the courtyard form can be divided into three parts, namely the entrance, patio, and interior, and its façade elements can be divided into the following subdivisions: saddle wall, grey plastic, carved flowers, grey tiles, wooden grill, wooden railing, wooden pattern, etc. The main styles are shown in Figure 9.

In the façade vocabulary, the roof, ridge, saddle wall, stone plinth, and corridor, as fixed factors, cannot be changed. The combination of doors can be changed according to the size of the openings; the wood pattern grille and grey sculptures can be changed in various ways; the details, such as carvings, can also be changed based on the first two features [27].

3.7. Parametric Program Conversion

After defining the shape grammar rules, the parametric rule conversion was performed. First, the rectangular plot was selected; second, the implanted courtyard was selected; third, the vertical courtyard was selected. The “” courtyard, “=” courtyard, and “U” courtyard are illustrated by A, B, and C, as shown in Figure 10.

Figure 10(i) to (xviii) illustrate three different generation processes of courtyard types A, B and C in three groups. Specifically, Figure 10(i)–(vi) show the first process, Figure 10(vii)–(xii) demonstrate the second process, and Figure 10(xiii)–(xviii) exhibit the third process. The 18 detailed figures are meticulously presented to compare the three processes producing the courtyard types. The side-by-side juxtaposition enables deeper analysis of each method’s workings and outputs. These visualizations enrich understanding of the developmental phases of the three courtyard types. In summary, the 18 figures—in threes—showcase the varying formation sequences of courtyard types A, B and C via three approaches.

In the AB combination, first, the courtyard division line L was determined, as shown in Figure 10(ii), which is usually automatically selected at the centre line of the plot, and the centre line can be adjusted later according to need; second, after determining the corresponding division lines in courtyards A and B, we determined the position of the LA1 line without coinciding with the boundary line and L (in accordance with Yan Fu’s Former Residence), determined the position of LB1 without coinciding with LB2 and L, and determined the position of LB2 without coinciding with the boundary line and LB1, as shown in Figure 10(iii). Then, we established the plane, as shown in Figure 10(iv). After establishing the plane position, we determined the beams and columns La1, La2, Lb1, and Lb2, as shown in Figure 10(v), and internally generated the required window and door proportions, as shown in Figure 10(vi), according to the relevant façade grammar rules mentioned above.

In the BA combination, the L position was also selected, as shown in Figure 10(viii), but since B and A are adjacent to each other as buildings, the LB2 and LA1 settings were removed after selection and replaced by the LB2 and LA1 non-overlap settings, as shown in Figure 10(ix). The plane was then established, as shown in Figure 10(x). The rest of the steps are the same as in AB, and are shown in Figure 10(xi,xii).

In the BC combination, the position of L is also selected, as seen in Figure 10(xiv). Then, after determining the corresponding division lines in the B and C courtyards, the position of the LB1 line was determined without coinciding with the sidelines and LB2 (in accordance with Yan Fu’s Former Residence), the position of LB2 was determined without coinciding with L, the position of LC1 was determined without coinciding with the sidelines and L, and the positions of LC2 and LC3 were determined on LC1. Due to the special nature of the area, it did not coincide with the sideline and was located symmetrically, as shown in Figure 10(xvi). The subsequent rules were the same as in AB, and are shown in Figure 10(xvii)–(xviii).

After constructing the relevant Grasshopper rules, it was possible to start generating the rules for automatic generation by converting them into cells.

4. Results and Conclusions

4.1. The Result of Workflows

With the relevant parametric conversion rules, this study elaborates on the organisation of the baselines in Figure 11. In addition to determining the courtyard demarcation lines and the planar baselines, it generates the exterior walls and defines the façade and roof battery groups based on the pedestals. In order to comply with the idea of automatic generation, the program was divided into three main parts, as shown in Figure 11. The first part is the processing of the input line frame. The second part is the placement of the courtyard and the generation of the façade according to the characteristics. The third part is when two courtyards are put together. The resulting buildings are close together and need to be combined into one building, and additional façade generation is performed; the rest of the architectural shapes and materials are utilised to facilitate program adjustments.

The Grasshopper rules for the architectural shapes and façades of the “Three Lanes and Seven Alleys” dwellings are established based on the rules of shape grammar. As seen in Figure 12, the imported plot is organized and the type of courtyard to be placed is selected. Moreover, within the limits of the specific width and depth of the plot, based on the foundation of the courtyard, the cell group responsible for the wall automatically generates the wall (including saddle wall elements). Based on the cell group for the wall, the windows and doors are generated according to their variables. The cell group responsible for the roof and the corridor automatically generates the roof and the corridor (including roof tiles and ridge).

4.2. Courtyard Data Analysis

This section explains the results generated by different random factors in Figure 12, focusing on the data structure of the courtyard form and parameter transformation.

In the parametric rule conversion definition, the courtyard types are defined as A, B, and C. However, this is not in line with the parametric data rule, because in the Grasshopper program rule, the data are in numerical form and the sequence starts from 0, so the three courtyard types correspond to three parameter values of 0, 1, and 2.

In

Table 1. Conversion values for courtyard types.

Courtyard Shape	Name of Courtyard Illustration	Conversion Parameter
“” shape	A	0
“=” shape	B	1
“U” shape	C	2

, “” shape courtyard, “=” shape courtyard, and “U” shape courtyard correspond to A, B, and C of the courtyard illustration name and Grasshopper data of 0, 1, 2.

In Table 1, the “” shape courtyard, the “=” shape courtyard, and the “U” shape courtyard correspond to A, B, and C of courtyard illustration labels and Grasshopper data of 0, 1, and 2.

In the first part of the workflow illustration (Figure 11), there are two inputs, represented by sliders. The upper part is the scale position of the line where L is located in Figure 10, which can be modified according to the size of different courtyards in the line frame. The data content of the lower slider is a random factor, and the data interval from 0 to 8 represents the original nine results. The “Random reduce” cell is used to disrupt the data structure so that the automatically generated results are more random.

To make the entrance courtyard type and exit courtyard type random, we injected random factors to make the entrance and exit courtyard types random. For specific random results, please refer to

Table 2. Courtyard parameters corresponding to random factors.

Courtyard Shape	Parameters Corresponding to Random Factors
Random factor	0	1	2	3	4	5	6	7	8
Entrance courtyard type	2	1	0	2	1	1	2	0	0
Exit courtyard type	2	2	1	1	0	1	1	1	0

. Figure 13 shows the results of random factors 0–8.

4.3. Courtyard Data Analysis

In addition to the random factor at the data level, the physical environment level and the subjective behaviour level can also be used as random factors to regulate the automatic production results.

For example, the specific results of the “Three Lanes and Seven Alleys” historical district were generated because Fuzhou is located in a subtropical region with short winters and long summers, so the district was designed with many patios to cope with the high temperatures and humidity in summer. From the basic courtyard forms given above, it can be seen that patios are an indispensable feature for reducing humidity, and the “Three Lanes and Seven Alleys” buildings have a good ventilation design, strong connectivity between the patio and the interior, and many doors and windows of large sizes. The depths of the main buildings are also larger than those of the northern Chinese dwellings, the eaves are deeper, and there are more external porches to reduce direct sunlight, which is different from the designs of the northern Chinese dwellings. In terms of roofs, the “Three Lanes and Seven Alleys” buildings have sloping roofs adapted to the rainy conditions in Fuzhou, while in the north of China, different forms, such as gable and hip roofs, are common. The “Three Lanes and Seven Alleys” has extensive guttering to facilitate the drainage of water from roofs. The wind speed is also a reason why the “Three Lanes and Seven Alleys” buildings have many courtyard combinations with 1–2 floors because a single floor is able to resist the threat of wind [24]. Through these studies, it can be seen that the depth of the patio, the number of windows and doors, the depth of the courtyard, the extension of the roof, etc., are all influenced by the physical environment, and the effect of the different values of the physical environment on the automatically generated results can be investigated in future research.

The “Three Lanes and Seven Alleys” historic district is known as the “Museum of Ming and Qing Dynasty Architecture”, which also reflects the integrity of its preservation, and we can investigate the effects of the continuous vertical façades, high walls, curving roads, and internal order and homogeneity on the observer. The relationship between human perception of the environment and architecture can also be further explored as an influencing factor.

Such factors can be added to the influence factors of architectural shape and façade design, which can be used in different areas to define the rules of the local historic district architecture, in order to produce buildings that fit local characteristics and restore the spirit of the place.

5. Discussion

The study shows that the automatic design solution generation for the architectural shapes and façades of the “Three Lanes and Seven Alleys” historic district can be achieved through parametric design based on shape grammar, and it also proves the following four points:

• Shape grammar can be used as a guiding method for historical style classification and the reconstruction of a historic district, which can preserve the local character and the spirit of a place.
• Although shape grammar has been widely researched in the field of architectural design, it can also be combined with parameterisation to achieve automated design solution generation for historic districts.
• The “Three Lanes and Seven Alleys” district has rich historical value, and its architectural shape and façade features are distinctive and can be applied to shape grammar. Its arrangement and combination rules are identifiable and are applicable to the rule-setting aspect of shape grammar and parametric design. Therefore, the deconstruction of the “Three Lanes and Seven Alleys” architectural shapes and façades in this paper fits the rules of shape grammar.
• Grasshopper visualisation and its programming features fit well with this study and can be deconstructed into steps to obtain the desired automatic generation of results.

Regarding shape grammar, the building shapes and façades of the “Three Lanes and Seven Alleys” historic district still need a more detailed definition in terms of the parameter domain values. Since there are many buildings in the “Three Lanes and Seven Alleys”, this paper proposes a methodology for analysing the vocabulary form of the shape grammar by studying only some of the buildings.

Although the feasibility of this study has been demonstrated, more discussion is needed regarding the definition of parameter thresholds in the shape grammar definition. The automatic generation of parametric design models requires very large-scale model data to be processed, which exceeds the abilities of parametric software tools due to certain limitations in data handling [28]. Given the more detailed requirements of architectural shape and façade, attempts to simplify the longer processing time would also be a pertinent future research direction.

To illustrate the main operations generated via the data, many of the diagrams in the text simplify the specific connections of the data as much as possible without compromising the interpretation of the final results. The future design does not consider the parametric conversion of special building materials and variations in the façade, such as saddle stucco, grey plastics, carvings, grey tiles, wooden grilles, wooden balustrades, wood graining, etc. Additionally, the generated results may differ from reality since the entire study is based on the vocabulary patterns and composition rules derived from the architectural patterns of the “Three Lanes and Seven Alleys” district. Based on vocabulary patterns and composition rules, building automation generates numerous scenarios that are different from existing architectural patterns. This is evident in the dimensions of the saddle walls, the height and width of the doors, the depth of the eaves, the height of the thresholds, the style of the courtyard, and the overall construction of the building. Shape grammar serves various functions in the field of architecture. It is anticipated that, in the future, the study of shape grammar will become more precise and comprehensive, allowing for its application in diverse building types, neighbourhoods, and even cities.

The parametric architectural design software is not popular in the mainstream market at present, but it is expected to be widely utilised in the architectural field in the future and the differences in its design methods from traditional architectural design will be tested. In the future, architects or people related to the architectural field will be expected to have the skills to operate parametric software to shorten the time and cost of a project, thus adapting to the fast-paced information age.