Fractal Structure And Pattern Of Complex Urban Systems

Since city is one of the most important features of modern society, urbanization process is always of much concern in both theory and practice. Explanation for how urban patterns are shaped with the growth of economy will provide a basic support to the methods in urban planning. Due to its numerous factors and being unable to carry out experiments like researches in natural science, it is difficult to simulate urbanization process. A substantial number of efforts have been devoted to understanding and modeling urbanization and urban concentration. Traditional approaches to urban studies employ Euclidean geometry to describe the morphology of urban growth. However, new features of urban growth indicate that a better understanding of urban system and new framework for urban modeling is highly expected.Considering the new features of cities and urbanization process, based on progress of complex science, urban system is defined as a non-linear complex system far away from equilibrium in this paper. Theoretical paradigms transferred form modem physics have explored a new perspective to study urbanization process. To study the development of urban structure and urban pattern, urbanization is defined as the aggregating process of generalized urban flux here. With this point of view, a new theoretical model for urbanization is presented, which is based on statistical mechanics. It shows that a complex urban system far away from equilibrium is always seeking an optimized process to obtain maximum generalized urban flux under given prices. An ensemble of interacting micro urban agents is set up in this model, as well as the potential function of urban system. The basic functions of urban system are found, which control its dynamic behaviors. Moreover, renormalized equation for urban system is found and a fractal structure accordingly appears. Thus the dynamic mechanism of how micro non-linear interactions shape macro urban structure is presented through self-organized process. With two examples of Wuhan City and Hangzhou City, fractal growth of urban systems and their fractal dimensions are analyzed.A corresponding numerical simulation method is developed. Based on the framework of new statistical mechanics in the present model, the self-organizing map (SOM) is further explored. Fractal mechanism hidden in SOM is revealed and the weights of network gain new meanings that related to urban pattern. By unifying the pattern recognition process of SOM and the process of formation of urban pattern, an approach to quantitatively analyze urban pattern is found. Using urban statistic data of Bohai Rim Region, urban patterns are calculated and analyzed by the above method. Moreover, fractal structure is also found in urban pattern. An important conclusion is that certain urban pattern should be evaluated in an urban system. On this basis, a reasonable future plan for the core area of Bohai Rim Region is discussed. Finally, the advantages and disadvantages of this research are analyzed with suggestions for further study.