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Fractal dimension curves of urban growth can be modeled with sigmoidfunctions, including logistic function and quadratic logistic function.Different types of logistic functions indicate different spatial dynamics. Thefractal dimension curves of urban growth in western countries follows thecommon logistic function, while these curves of cities in northern Chinafollows quadratic logistic function. Now we want to know whether all Chinesecities follow the same rules of urban evolution. This paper is devoted toexploring the fractals and fractal dimension properties of the city of Shenzhenin southern China. The urban region is divided into four subareas, ArcGIStechnology, box-counting method is adopted to extract spatial datasets, and theleast squares regression is employed to estimate fractal parameters. Theresults show that: (1) The urban form of Shenzhen city has clear fractalstructure, but fractal dimension values of different subareas are different;(2) The fractal dimension growth curves of all the four study areas can only bemodeled by the common logistic function, and the goodness of fit increases overtime; (3) The peak of urban growth in Shenzhen had passed before 1986, thefractal dimension growth is approaching its maximum capacity. Conclusions canbe reached that the urban form of Shenzhen bears characteristics ofmultifractals, the fractal structure has been becoming better gradually throughself-organization, but its land resources are reaching the limits of growth.The fractal dimension curves of Shenzhen's urban growth are similar to those ofEuropean and American cities, but differ from those of the cities in northernChina. This suggests that there is subtle different dynamic mechanisms of citydevelopment between northern and southern China.

Fractal-based modeling and spatial analysis of urban form and growth: a case study of Shenzhen in China