Rank-Size Construction of the Central Place Theory by Fractal Method and Its Application to the Yangtze River Delta in China

The central place theory is the classical theory in the urban geography field as well as the rank-size rule. The Zipf's law is the important practical formula to describe the rank-size rule, but there are still some problems when the Zipf's formula is used in urban system's size distribution, such as experiential discussions more than theoretical studies and the theoretical values far different from the practical values and so on. In order to offer a better theoretical explanation for the rank-size rule of regional urban system, a rank-size deep construction of city central place theory using fractal method is put forward. Given the fractal dimension of the sizes distribution as to one entire urban system, the reasonable rank-size distribution could be calculated by the model, and the model is called central ranksize rule. We can predict the future rank-size distribution of a region's urban system and estimate the value of "K" which is defined in Christaller center place model by our equation. At last, the case of the delta area of the Yangtze River in China is been taken to explain the application of the model.