  Fractal dimension curves of urban growth can be modeled with sigmoid
functions, including logistic function and quadratic logistic function.
Different types of logistic functions indicate different spatial dynamics. The
fractal dimension curves of urban growth in western countries follows the
common logistic function, while these curves of cities in northern China
follows quadratic logistic function. Now we want to know whether all Chinese
cities follow the same rules of urban evolution. This paper is devoted to
exploring the fractals and fractal dimension properties of the city of Shenzhen
in southern China. The urban region is divided into four subareas, ArcGIS
technology, box-counting method is adopted to extract spatial datasets, and the
least squares regression is employed to estimate fractal parameters. The
results show that: (1) The urban form of Shenzhen city has clear fractal
structure, but fractal dimension values of different subareas are different;
(2) The fractal dimension growth curves of all the four study areas can only be
modeled by the common logistic function, and the goodness of fit increases over
time; (3) The peak of urban growth in Shenzhen had passed before 1986, the
fractal dimension growth is approaching its maximum capacity. Conclusions can
be reached that the urban form of Shenzhen bears characteristics of
multifractals, the fractal structure has been becoming better gradually through
self-organization, but its land resources are reaching the limits of growth.
The fractal dimension curves of Shenzhen's urban growth are similar to those of
European and American cities, but differ from those of the cities in northern
China. This suggests that there is subtle different dynamic mechanisms of city
development between northern and southern China.
