# Hierarchical Structure of the Central Areas of Megacities Based on the Percolation Theory—The Example of Lujiazui, Shanghai

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## Abstract

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## 1. Introduction

#### Hierarchical Structure and Percolation Analysis

## 2. Method and Dataset

#### 2.1. Case Selection and Data Acquisition of Street Intersections

#### 2.2. The Percolation Algorithm

#### 2.3. Box Counting Method

## 3. Results

#### 3.1. Hierarchical Structure of Lujiazui City Center

#### 3.2. Fractal Properties of Lujiazui Urban Center

## 4. Discussion

#### Fractal Verification

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A demonstration of the main methods and workflow used in this study [21,22]. (Fractalyse 3.0: downloaded from http://fractalyse.org, accessed on 11 July 2021).

**Figure 2.**The definition of the central area of Lujiazui in Shanghai, and the acquisition of OSM data.

**Figure 4.**A 25 m buffer analysis of the road network was performed to export a TIFF image in monochrome threshold format with color mode 1.

**Figure 7.**Principles of percolation analysis in a finite range. Different colors represent different clusters.

**Figure 8.**Clustering features calculated by percolation analysis with 25 m as the radius step, 50 m as the minimum radius distance threshold, and 800 m as the maximum radius distance threshold.

**Figure 9.**Clustering features calculated by percolation analysis with 50 m as the radius step, 300 m as the minimum radius distance threshold, and 500 m as the maximum radius distance threshold.

**Figure 10.**Clustering features calculated by percolation analysis with 100 m as the radius step, 100 m as the minimum radius distance threshold, and 8000 m as the maximum radius distance threshold.

**Figure 15.**The hierarchical structure of the city when ${d}_{c}=450\mathrm{m},350\mathrm{m},325\mathrm{m},250\mathrm{m}$.

**Figure 18.**When the box size is about 450 m, the boxes with higher fractal dimension are roughly distributed around Century Avenue.

**Figure 19.**When the size of the box is about 900 m, take the Shanghai Pudong New Area People’s Government Area and the Shanghai International Convention Center Area as the two largest box dimensions.

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**MDPI and ACS Style**

Hu, X.; Wang, Y.; Wang, H.; Shi, Y.
Hierarchical Structure of the Central Areas of Megacities Based on the Percolation Theory—The Example of Lujiazui, Shanghai. *Sustainability* **2022**, *14*, 9981.
https://doi.org/10.3390/su14169981

**AMA Style**

Hu X, Wang Y, Wang H, Shi Y.
Hierarchical Structure of the Central Areas of Megacities Based on the Percolation Theory—The Example of Lujiazui, Shanghai. *Sustainability*. 2022; 14(16):9981.
https://doi.org/10.3390/su14169981

**Chicago/Turabian Style**

Hu, Xinyu, Yidian Wang, Hui Wang, and Yi Shi.
2022. "Hierarchical Structure of the Central Areas of Megacities Based on the Percolation Theory—The Example of Lujiazui, Shanghai" *Sustainability* 14, no. 16: 9981.
https://doi.org/10.3390/su14169981