分形城市研究进展:从几何形态到网络关联

The city is an accumulation of human civilization. It is also a highly complex system where a large number of agents interact, leading to a form and dynamics seemingly difficult to understand. Many studies in geography, ecology, sociology, economy and physics have been carried out to explore the general rules or regularities beneath the large number and the diverse agents operating in a city. It is widespread accepted that cities are an emergent phenomenon ruled by self-organization. As the language of nature and the fourth generation language of geography, fractal geometry has been a very powerful tool to capture the self-organized properties of cities. Most of the current studies are limited to the geometric fractal, i.e., based on fractal geometry: a shape made of parts similar to the whole in certain ways. Fractal geometry offers the significant advantages of capturing the spatial distribution, expansion, and filling properties of geographical objects in a city, and also describes the relationships between ranks and sizes of cities in an urban system. However, certain information-such as the efficiency of structural organization and the variance of levels of linkage-is ignored. As increasingly noticed by researchers, to better understand the ways a system of cities actually functions, we need to pay more attention to urban networks because current rapid developments of information and technology enable people to connect ever more easily and closely and in many new ways. This article reviews the advances of fractal cities from three aspects, which are geometric fractal, network fractal and evolutionary fractal. The significance and great potentials of fractal theory in urban studies are presented. The main research progress including fractal dimensions, fractal models, empirical studies and fractal cities and fractal urban systems are briefly reviewed, both for geometric and network fractals. As cities keep evolving, we also briefly review the evolutionary fractal cities, that is, the allometric scaling of cities. Based on current limitations on fractal cities, we propose a research agenda for fractal cities including (1) the development of measures and empirical studies on the third type of geographic fractals; (2) the spatial dependence and scale effects of fractal urban networks; (3) the coupling mechanics and influencing factors of fractal urban networks representing physical and non-physical urban spaces;(4) the DNA of a city from the perspective of fractals; and (5) the evolution simulation and policy intervention in fractal cities.