都市地下鉄路線の最適化におけるフラクタル次元の応用

（中国メインランドの地下鉄がある27の省都を例に取ろう）

抄録

Fractal is a special kind of geometric shape characterized by features such as self-similarity and high complexity. Fractal has a fractal dimension that is different from the traditional topological dimension, which can be used to reveal the complexity of fractal. The metro is an important part of modern urban public transportation, but there is a lack of an intuitive and quantitative tool for optimizing it. We noticed that metro lines are rugged, complex and statistically self-similar. They can be regarded as fractal so that we can quantify their complexity. In this paper, we calculated fractal dimension (d) of metro lines for 27 provincial capital cities with metros in China mainland, and collected data on GDP (e), population (p), city area (s) and population density (ρ = p/s) of these cities to explore the relationship between fractal dimension and these variables. Correlation analysis shows that d has a significant linear positive correlation with e and p, with Pearson's correlation coefficients of 0.8578 and 0.8227 respectively. d has a non-significant linear correlation with s (r_sd = 0.0895), but a significant linear correlation with ρ (r_ρd = 0.6544). Based on the linear correlation of d with p, e and ρ, we performed a multiple linear regression to obtain this equation (d = 1.0436 + 3.2612 × 10⁻⁵e + 3.2767 × 10⁻⁵p + 8.6432 × 10⁻²(p/s) ). Substituting the e, p and s in the equation to calculate theoretical fractal dimension and comparing it with actual fractal dimension, we can evaluate the fitness of current metro lines, which can guide the optimization of metro lines.