The multi-scale structural complexity of urban morphology in China

The city is a living organism, of which the emergence and development is one of the most representative complex phenomena in the social system. By the traditional method of urban science, it has been assumed that the city grows uniformly in a way. Accordingly, its morphology can be described by the traditional Euclidean geometry. Recent studies have proposed that the complex spatial phenomena related to the existing urban system are more suitable to be explained by fractal geometry. Urban morphology is an approximate fractal structure rather than a regular one, because its morphology is affected by many factors, such as topography, history, economic and political environment. In this article, we measured the degree of urban morphology deviating from the fractal by the multi-scale structural complexity method. By this method, it can find the difference in whole complexity among different cities as well as comparison in the local complexity of a city among different spatial scales. It was found that the multi-scale structural complexity is not only related to the vitality of the urban socio-economic development but also affected by the typical statistical indicators (such as the urban infrastructure). Interestingly, by constructing the mutual information network among cities, we found that there is a strong correlation between the whole complexity of typical cities, such as Chongqing and Xi′an, and Beijing and Macao, that is to say, the construction or development of these cities may follow the same set of patterns. Moreover, there are also similarities (i.e., strong correlations) between the socioeconomic forms of the years, such as 2009 and 2013, which are either all stable or all depressed. Our research provides a new perspective for depicting the complexity of the urban system from different spatial scales.