Rybski Diego, García Cantú Ros Anselmo, Kropp Jürgen P
Potsdam Institute for Climate Impact Research-14412 Potsdam, Germany, EU.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042114. doi: 10.1103/PhysRevE.87.042114. Epub 2013 Apr 16.
Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e., a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of citylike structures which is solely based on the assumption that growth is more likely to take place close to inhabited space. The model involves one parameter which is an exponent determining how strongly the attraction decays with the distance. In addition, the model is run iteratively so that existing clusters can grow (together) and new ones can emerge. The model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster. Although the power-law distribution depends on both, the imposed exponent and the iteration, the fractality seems to be independent of the former and only depends on the latter. Analyzing land-cover data, we estimate the parameter-value γ≈2.5 for Paris and its surroundings.
城市群呈现出复杂的涌现特征，其中齐普夫定律（即幂律规模分布）和分形性可能被视为最显著的特征。我们提出了一个用于生成类似城市结构的简单模型，该模型仅基于这样一个假设：增长更有可能发生在靠近有人居住空间的地方。该模型涉及一个参数，即一个指数，它决定了吸引力随距离衰减的强度。此外，该模型通过迭代运行，以便现有的集群能够（一起）增长，新的集群能够出现。该模型能够再现最大集群边界的规模分布和分形性。尽管幂律分布取决于所施加的指数和迭代，但分形性似乎与前者无关，仅取决于后者。通过分析土地覆盖数据，我们估计巴黎及其周边地区的参数值γ≈2.5。
