Village.
The comprehensibility, integration, connectivity, and depth values of Sigangpu Village, Gutuo Village, and Sijiji Village were calculated using the axial analysis method from Space Syntax. The comprehensibility parameter was used to describe the internal order and logicality of the villages. The integration parameter helped identify potential advantages or core spaces within the villages. The connectivity parameter was used to assess the possibility of internal permeability. The average depth value was employed to evaluate the accessibility of transportation. In the axial analysis, an axial map was used to represent the spatial layout, where the axial lines represented the collection of all tangents drawn based on the visible vertices of objects to each other. The parameter values were presented as a graded chromatic scale, with red (warm colors) indicating higher values and blue (cool colors) indicating lower values.
Intelligibility. Comprehensibility refers to the ease with which people can perceive the overall spatial system from local perceptions, and it reflects the recognizability of space at the network structure level. Understanding the overall length is based on the observer's association and construction of local perceptions; thus, this parameter reflects the degree of correlation between the local and the whole. The peak value of comprehensibility is 0.5, indicating that when the value is more significant than 0.5, there is a good correlation between the local and the whole, and the ease of understanding the spatial layout structure is higher. Conversely, a lower value indicates the opposite. Spaces with high comprehensibility often form local public areas with high social vitality and functional diversity, making it easy for people to create clear and distinguishable mental images. From the comprehensibility map (Fig. 2), Sigangpu Village, Gutuo Village, and Sijiji Village values are 0.2353, 0.0198, and 0.0987, respectively. This indicates that the comprehensibility of the layout structures in these three villages is relatively low, meaning weak recognizability. The scatter plot shows a specific correlation between the horizontal and vertical axes, and the goodness of fit of the trend line has a specific predictive ability, indicating that they possess both the correlation and ambiguity between the local and the whole.
The formation of this spatial characteristic can be attributed to two main factors. Firstly, traditional Yi culture emphasizes the harmonious coexistence between humans and nature. As a result, traditional Yi dwellings are often built in consideration of the natural terrain and landforms. For example, they are commonly constructed along the contours of the mountains or near water bodies. The dynamic and uncertain nature of mountains and water introduces a sense of ambiguity between the locals and the whole of the village. Secondly, the Yi people in Liangshan have a family lineage system known as "Jia zhi," naturally formed based on patrilineal blood relations. Traditional villages typically comprise several family lineages, each with its leader and rules. These family lineages also connect and interact, bringing about a sense of order between the locals and the whole village.
Table 1
Axis model parameters of Siganpu Village, Gutuo Village, and Sijiji Village
Content
|
Village
|
Min
|
Avg.
|
Max
|
Global integration
|
Siganpu Village
|
0.170595
|
0.350389
|
0.477953
|
Gutuo Village
|
0.107825
|
0.241029
|
1.09765
|
Sijiji Village
|
0.146586
|
0.246088
|
0.339588
|
Local integration
|
Siganpu Village
|
0.333333
|
1.12722
|
2.17712
|
Gutuo Village
|
0.333333
|
0.905173
|
1.89187
|
Sijiji Village
|
0.333333
|
0.974867
|
1.75729
|
Connectivity
|
Siganpu Village
|
1
|
2.51301
|
7
|
Gutuo Village
|
0
|
2.0687
|
5
|
Sijiji Village
|
0
|
2.16143
|
5
|
Mean depth
|
Siganpu Village
|
12.5522
|
17.3807
|
33.3657
|
Gutuo Village
|
2
|
27.738
|
49.6364
|
Sijiji Village
|
16.4615
|
22.7558
|
36.819
|
Integration. "Integration" is also known as "cohesion" and describes the degree of clustering within a village space. It can be divided into global integration and local integration. Integration reflects the level of connectivity between points in length and measures the accessibility of the village space. Points with higher integration in the system space have better spatial accessibility, exhibit higher vitality, and are relatively more attractive to people flow. Conversely, points with lower integration indicate lower spatial accessibility. The axis lines with higher values of global integration are referred to as the integrated core of the axis line system, representing the core area of the village. Generally, the worldwide integration value approaches 1, indicating a tighter spatial organizational structure and higher integration within the town. Conversely, as the global integration value comes 0, it suggests a more dispersed spatial organizational structure and lower integration within the village. Local integration represents the convenience of reaching a particular space within a limited depth radius. Areas with high regional integration can exert influence within a small range. In this study, the local integration was measured using a three-step depth radius, and the calculation method was consistent with that of global integration.
The average global integration values of Sigangpu Village, Guduo Village, and Sijiji Village were calculated using the Depthmap software and found to be 0.350389, 0.241029, and 0.246088, respectively, ranging from 0.107825 to 1.09765. The average local integration values were 1.12722, 1.12722, and 0.905173, ranging from 0.333333 to 2.17712 (Table 1). From the analysis of the global integration map (Fig. 3), it can be observed that the region with the highest global integration is located in the middle part of the village. This area has more residential buildings, a more intricate transportation network with many branching paths, and is considered the core space of the town with higher accessibility, centrality, and attractiveness. Spaces closer to the main roads become the peripheral spaces of the village. This is due to the significant influence of the traditional production mode on the village structure, as the Liangshan Yi people engage in semi-agricultural and semi-pastoral production, with a greater emphasis on animal husbandry than agriculture. The middle part of the village is situated in areas with moderate terrain. The selection of Yi ethnic houses follows the principle of "prefer pastureland on higher ground, prefer residential areas in the middle, and prefer farmland at the lower part," cleverly integrating the lifestyle, production mode, and natural conditions, forming a hierarchical relationship of production space-residential space-production space interaction [18]. The analysis of the local integration map (Fig. 4) reveals that areas with higher regional integration are also located in the middle part within a small range and have significant influence within this limited scope. Overall, the local integration levels of traditional villages are relatively similar, indicating similar power levels. This is because conventional Yi ethnic architecture mainly consists of residential buildings, lacking public buildings such as ancestral halls commonly found in Han ethnic architecture. This results in comparable levels of local integration.
Connectivity. Axis connectivity refers to the number of other axes directly intersecting a particular axis. It represents the sum of connected spaces to the i-th node, while the connectivity value indicates the degree of permeability in the system space. A higher connectivity value indicates more vital permeability, whereas a lower value indicates weaker permeability. By using the Depthmap software, the average connectivity values for Sigangpu Village, Guduo Village, and Sijiji Village were calculated as 2.51301, 2.0687, and 2.16143, respectively, ranging from 0 to 7 (Table 1). The connectivity analysis map (Fig. 5) shows that the interconnectivity between regions in the three villages is not high, and the permeability capabilities are nearly equal, indicating similar spatial independence. This is often due to the constraints imposed by the terrain and land use. The villages are located amidst steep mountains, with complex landscape and limited road access, resulting in less closely connected residential buildings. The areas with higher connectivity are primarily located in the middle parts of the villages, including newly constructed residential sections. These areas exhibit more vital permeability and tighter connections between residential buildings.
Depth. Depth refers to the number of spaces that must be traversed from one area to another. A higher depth value indicates weaker accessibility and greater spatial complexity, while a lower value indicates full accessibility. By using the Depthmap software, the average depth values for Sigangpu Village, Guduo Village, and Sijiji Village were calculated as 17.3807, 27.738, and 22.7558, respectively, ranging from 2 to 49.6364 (Table 1). This indicates that the overall spatial structure of the villages is relatively complex, with weaker accessibility. Furthermore, analyzing the depth values helps identify the areas in the towns that are easiest and most difficult to navigate. From the depth value analysis map (Fig. 6), it can be observed that the areas with the highest depth values in Sigangpu Village, Guduo Village, and Sijiji Village are located in the northwest, southwest, and northwest directions, respectively. These areas are the most difficult to orient oneself in, indicating weaker accessibility to residential buildings. The central parts of the villages have the lowest depth values, making them the easiest to navigate, with multiple pathways for accessibility. The accessibility in other areas gradually decreases outward from the central region. This is because of the Yi ethnic group's family system, conflicts between different family branches, and their historical need for defense. Most Yi villages are strategically located on mountains with rugged terrains, narrow passages, and cliffs, providing natural defensive advantages.
Dwelling.
Through the investigation of residential buildings in Sigangpu Village, Guduo Village, and Sijiji Village, it was found that the layout of their typical houses is similar. Here, we take the representative example of the Sepeiguoji Residence in Sigangpu Village, which is designated as a key-protected object. Based on the "topological model" and "convex space model" in spatial syntax, the quantitative analysis uses three quantitative indicators: connectivity, integration, and depth. The Sepeiguoji Residence consists of three main parts: the main building, the ancillary building, and the courtyard. From the perspective of the spatial enclosure, it has a "U"-shaped layout, presenting an inwardly converging spatial form. The internal space of the main functions (hall, bedrooms, dining room, kitchen, storage room, etc.) is partitioned by wooden panels, providing a flexible layout (Fig. 7). There is no clearly defined dining room or kitchen area on the ground floor. The dining area is in the middle of the hall and consists of a temporary wooden table, while cooking activities occur near the hearth. The mezzanine on the second-floor stores grain and is accessed via a movable wooden ladder (Fig. 8). The layout of ancillary functions (storage room, poultry farming room, etc.) is relatively regular.
Spatial topological relationships. The topological relationships in spatial syntax can reveal the spatial positioning and structure between different elements. Analyzing the spatial topological relationships of the Sepeiguoji Residence (Fig. 9), it can be observed that the bedrooms are arranged close to each other, and the bedrooms and storage rooms exhibit a parallel relationship. This layout characteristic is due to the Yi ethnic group's traditional emphasis on family harmony and unity. The children's bedrooms are located on either side of the main bedroom, with the position of the main bedroom symbolizing the center of the family. The proximity of the younger generation's bedrooms to the bedrooms of the elders signifies mutual reliance and support among family members. Additionally, the flexible spatial layout of the Sepeiguoji Residence can be observed from the plan forms and positional relationships of each bedroom. This flexibility is attributed to the abundant supply of lightweight local materials such as wood and bamboo in Yi ethnic areas.
The topological structure diagram reveals that the spatial structure of the Sepeiguoji Residence belongs to the primary-secondary core type (Fig. 10), with the central core space being the hall and the secondary core space being the courtyard. These two core spaces are interconnected with other auxiliary spaces, such as bedrooms, storage rooms, and livestock areas, forming a smooth functional spatial connection. From a practical perspective, this topological structure exhibits two branching centers, primarily influenced by the semi-agricultural and semi-pastoral production modes. Two branches are formed by dividing the functional spaces according to their intended service objects. The available rooms centered around the hall primarily serve people and crops, while the operating rooms centered around the courtyard serve crops and poultry.
Connectivity, Integration, and Mean Depth.
Table 2
Summary of the properties of spatial layout based on convex space analysis
Attribute
|
Granary、Son's bedroom、Inner bedroom、Daughter's bedroom
|
Hall
|
Outer corridor
|
Utility room、Breeding room
|
Inter
layer
|
Courtyard
|
Connectivity
|
1
|
7
|
2
|
1
|
1
|
4
|
Integration
|
0.9217
|
2.2384
|
1.7410
|
0.6812
|
0.9217
|
1.2053
|
Depth
|
2.5455
|
1.6364
|
1.8182
|
3.0910
|
2.5455
|
2.1818
|
Through the analysis of the residential floor plan using the convex space model in the Depthmap software, as shown in Table 2, the connectivity values of the Sepeiguoji Residence's hall and courtyard are 7 and 4, respectively, indicating a high level of connectivity and suggesting good permeability and a certain degree of publicness in its spatial layout. The hall occupies a central position within the entire residence and serves as the core of traditional Yi ethnic dwellings. It is the central public space where family and clan members gather, communicate, worship, and celebrate. The courtyard is a secondary public space in traditional dwellings adjacent to storage rooms, livestock areas, and exterior corridors. In addition to being a gathering and ceremonial opening for family members, the courtyard also functions as an area for drying crops and raising poultry.
The integration values of the hall, exterior corridor, and courtyard are 2.2384, 1.7410, and 1.2053, respectively, indicating a high level of integration and suggesting a compact spatial layout that facilitates the gathering and interaction of people. This is because the hall serves as the core of the residence, the exterior corridor acts as a transitional space connecting the lobby and courtyard, and the courtyard functions as the front yard of the dwelling, providing a place for family members to engage in activities and rest. Together, they form a unified whole and establish a continuous spatial order. The connections between these spaces are natural and seamless, blurring the boundaries between the interior and exterior of the dwelling and creating a harmonious living environment that reflects the Yi ethnic culture's respect for the natural surroundings.
The depth value of the side rooms (storage room, livestock room) in the main house with two side wings is 3.0910, the highest among the depth values, indicating the weakest accessibility. This is influenced by the "semi-agricultural and semi-pastoral" production mode and religious beliefs. On the one hand, the storage room and livestock room are typically used to store unclean items and animals and to prevent their odors and impacts from entering the main house. On the other hand, the main house is considered a sacred space, accessible only to family members and the souls of ancestors. Therefore, the side rooms are relatively independent of the main house and do not have direct passages leading to it.
Visibility. The spatial integration diagram of the main building (Fig. 11) shows that high perceptibility spaces form a continuous state between the outdoor and indoor areas. Significantly, the positioning of the hearth extends this perceptual state and becomes a visual focal point. The colors used in the figure represent the perceptibility of the building spaces, with warmer colors indicating higher perceptibility and more excellent colors meaning lower perceptibility. The hearth holds significant status and value in Yi ethnic traditional culture. There is a kind of worship for the home, an essential spatial node in Yi traditional dwellings, displaying high perceptibility in the spatial integration diagram. By analyzing the visual hierarchy of the hearth space (Fig. 12), it is found that the hearth space has a good line of sight. As the core space of Yi traditional dwellings, the hearth allows for observation of various rooms indoors, including the beds of children, the master, and the grain storage room, serving as the focal point of indoor visual attention. Furthermore, the spatial layout of the dwelling centers around the hearth, with functional areas such as the kitchen, living room, and bedrooms arranged around it. This layout facilitates communication and interaction among family members, serving as a gathering, communication, and ceremonial space, thus enhancing family cohesion. This layout is not only due to the Yi people's emphasis on family harmony and unity but also because the hearth holds sacred symbolism in Yi culture, representing family unity and happiness. The Yi people believe that the flames in the home can ward off diseases and negative energy, ensuring the health and safety of family members. During important festivals and ceremonies, the Yi people light bonfires in the hearth to worship ancestors and deities, praying for abundant harvests and peace.
Table 3. Spatial characteristics of villages and dwellings and their cultural causes
|
Spatial Characteristics
|
Cultural Factors
|
Village
|
Village Weak spatial legibility with a combination of local coherence and ambiguity
|
Ambiguity: Constraints of mountainous topography, Order: Family system
|
Village structure centered around the central area
|
Semi-agricultural and semi-pastoral production mode
|
Moderate independence in village spatial layout
|
Constraints of mountainous topography
|
Introverted and enclosed spatial form
|
Family system
|
Dwelling
|
Dwellings Arrangement of the younger generation's rooms around the elder's room
|
Emphasis on family harmony and unity
|
Divergent spatial layout centered around courtyards and halls
|
Semi-agricultural and semi-pastoral production mode
|
Flexible arrangement of functional rooms
|
Utilization of lightweight local materials
|
Strong public nature of halls and courtyards
|
Semi-agricultural and semi-pastoral production mode
|
Continuous spatial order of halls, external corridors, and courtyards
|
Respect for nature
|
Spatial layout of one main building and two side buildings
|
Semi-agricultural and semi-pastoral production mode, religious beliefs
|
Arrangement of functional rooms around the hearth in the main building
|
Emphasis on family harmony and unity, reverence for the hearth
|