Spatial structures of urban systems are best described as multifractals. To provide insight on a hidden mechanism responsible for such scaling we investigate the multiplicative random cascade (MRC) model of urban spatial structure. MRC is a multiplicative process capable of producing multifractal 2D patterns, which is expressed in a closed analytical form. We use street intersection points pattern (SIPP) data as a proxy of urban structure. Renyi’s generalized dimensions (RGD) spectra, probability distributions of intersections densities, and urban layouts generated by the MRC model are compared to the same descriptors extracted from SIPP data for six U.S. metropolitan statistical areas (MSAs). We found that the RGD spectrum of the best-fit MRC model closely matches the observed spectrum in all cases. We also found that CDF of models’ density distributions do not match closely observed density distributions, although, in some cases, differences are not large. Observed density distributions have forms that are close to the log-normal distribution which suggests that a hidden process is multiplicative. Finally, we found that the MRC model is broadly compatible with the observed urban layouts. Given our findings, we suggest that the hidden process of urban scaling is the preferential attachment dynamics — development is attracted to areas in proportion to the degree of their existing development.

最好将城市系统的空间结构描述为多重分形。为了提供负责这种缩放的隐藏机制的见解，我们研究了城市空间结构的乘法随机级联（MRC）模型。MRC是一个能够产生多重分形2D图案的乘法过程，它以封闭的分析形式表示。我们使用街道交叉点模式（SIPP）数据作为城市结构的代理。将Renyi的广义尺寸（RGD）光谱，路口密度的概率分布以及MRC模型生成的城市布局与从6个美国大都市统计区（MSA）的SIPP数据中提取的相同描述符进行比较。我们发现最适合的MRC模型的RGD光谱在所有情况下都与观察到的光谱非常匹配。我们还发现模型密度分布的CDF与紧密观察到的密度分布不​​匹配，尽管在某些情况下差异并不大。观察到的密度分布具有接近对数正态分布的形式，这表明隐藏过程是可乘的。最后，我们发现MRC模型与观察到的城市布局大致兼容。根据我们的发现，我们认为城市规模扩张的隐性过程是优先依恋动态-​​发展被吸引到的区域与它们现有发展的程度成比例。最后，我们发现MRC模型与观察到的城市布局大致兼容。根据我们的发现，我们认为城市规模扩张的隐性过程是优先依恋动态-​​发展被吸引到的区域与它们现有发展的程度成比例。最后，我们发现MRC模型与观察到的城市布局大致兼容。根据我们的发现，我们认为城市规模扩张的隐性过程是优先依恋动态-​​发展被吸引到的区域与它们现有发展的程度成比例。