2.2.1. Overall Idea

We begin by reviewing the literature and field research. We selected the historic town's protection area as our study location. Under the "Shaxi Historical and Cultural Town Conservation Plan", we also identified six old town building types by function. They are the Xingjiao Temple, the Patron God Monastery, the Ancient Theatre, the Essential Privileged Dwellings, the Generally Sheltered Dwellings, and the Stores. Second, we, local experts and craftsmen, discussed lucky on-site elements. They include the location (building components), symbolic significance, materials, and presentation methods. Then, we compiled a list of the lucky aspects found in each of the six buildings. Local experts are non-hereditary inheritors of traditional architecture and artisans have been building historic buildings for more than ten years. Finally, we calculate the auspicious element diversity index. It is to compare multicultural integration across architectural types. We also create a network model with propitious elements and get an index. It is to compare lucky culture compositions. Then, we compared and examined the calculations. It is to reveal the lucky cultural characteristics of classic old-town architecture. Next, the multicultural-indigenous culture link in the ancient town is investigated to exhibit the cultural perspective of the Bai people.

#### 2.2.2. Determination of the Diversity of Auspicious Elements

In this study, each building type is considered a "community" and each auspicious element is considered a "species". During the field research, the Xingjiao Temple, the Patron God Monastery, and the ancient theatre were the only building groups in the old town. Therefore, only a single sample was selected. In contrast, the quality of the other three types of buildings varies. We discussed it with local experts in ancient architecture. Then, we decided on 20 representative samples of these three types of buildings. Richness and evenness [23] exemplify the diversity of lucky aspects the most.

#### 1. Margalef index

This index reflects the richness of auspicious elements in each building type, which is calculated as follows.

$$\mathbf{D}\_{\text{ma}} = (\mathbf{S} - 1) / \ln \text{N} \tag{1}$$

S is the number of auspicious elements in each building type, and N is the number of all individuals of auspicious elements in the building type.

#### 2. Shannon–Wiener index

The Shannon–Wiener index describes the disorder and uncertainty in the occurrence of elements. A better Shannon–Wiener index score indicates a greater diversity of lucky elements. Its calculation formula is as follows.

$$\mathbf{H}' = -\sum\_{i=1}^{S} \mathbf{P\_i} \log\_2 \mathbf{P\_i} \tag{2}$$

S is the number of auspicious elements in each building type and Pi is the proportion of elements belonging to cultural category i in the total number of features N.

#### 3. Simpson's index

Simpson's index, also known as the dominance index, expresses how evenly the individuals in a community (buildings) are distributed among the different species (auspicious elements). The greater the value of Simpson's index, the greater the diversity of lucky elements. Moreover, its calculation formula is as follows.

$$D = 1 - \sum\_{i=1}^{S} \mathbf{n}\_i (\mathbf{n}\_i - 1) / \mathbf{N} (\mathbf{N} - 1) \tag{3}$$

N is the number of all individuals of auspicious elements in the building type and ni is the number of individuals of auspicious part i.

#### 2.2.3. Analysis of the Characteristics of the Co-Occurrence Network of Auspicious Elements

The social network analysis (SNA) method originated from the sociology of measurement. It is also used to study how different people in society interact with each other. The fundamental premise is to construct a "network", using actors as "points" and their relationships as "links" [24]. Auspicious element co-occurrence networks are modelled, calculated, and examined in three steps. First, each auspicious part is considered a "node". There are different lucky elements in building components of the same building type. Cooccurrence describes the relationship between common auspicious elements. If two nodes happen to occur together, it is written as "1", and if they do not, it is written as "0". Next, we made a co-occurrence matrix of lucky elements for each building type. Then, we built each building type's "auspicious element co-occurrence network model" using Ucinet analysis software. Lastly, different metrics are used to look at how a network works, including the network's density, K-core, absolute centrality, intermediate centrality, degree centrality, and intermediate centrality. They are chosen to study each building type's auspicious element co-occurrence network model. Specifically, co-occurrence networks in structural stability and network centrality. The selected indexes are as follows.
