EXTERNAL AND INTERNAL COMPLEXITY OF URBAN SYSTEMS AND ITS STOMMEL DIAGRAM
将城市系统的空间复杂性分为外部和内部两类，基于指数律和幂律推导出斯托梅尔图，用于展示不同时空尺度的城市化过程。
Geographical systems of cities can be represented by a set of exponential laws,or equivalently,a series of power laws.The exponential laws consist of number law,size law,and area law.Both the exponential laws and the power laws compose the scaling laws of urban hierarchies and networks.The exponential laws indicate the spatial complexity of urban systems because that the exponentials can yield three mathematical marks of self—organized criticality(SOC),including the frequency—spectrum relationships indicative of 1/f noise,the negative power law distributions indicative of fractal structure,and Zipf's law indicative of rank—size rule.Based on the exponential laws,spatial complexity is divided into two types: external complexity and internal complexity.The former can be represented by the number law,while the latter can be represented with the size law and the area law.Starting from the exponential laws and power laws,a formula is derived for drawing the Stommel diagram showing urbanization process of different spatial and temporal extent.Stommel diagram is based directly on the internal complexity,but it has some information of external complexity of urban systems.