A new model of urban population density indicating latent fractal structure

Fractal structure of a system suggests the optimal way in which parts are arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterise fractal cities, we need the measure of fractional dimension. However, if the fractal organisation is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalised gamma function may be used to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time.