Describing Urban Evolution with the Fractal Parameters Based on Area-Perimeter Allometry

The area-perimeter allometric scaling is an important approach for researching fractal cities, and the basic ideas and models have been researched for a long time. However, the fractal parameters based on this scaling relation have not been efficiently utilized in urban studies. This paper is devoted to developing a description method of urban evolution using the fractal parameter sets based on the area-perimeter measure relation. The novelty of this methodology is as follows: first, the form dimension and boundary dimension are integrated to characterize the urban structure and texture; second, the global and local parameters are combined to characterize an urban system and individual cities; third, an entire analytical process based on the area-perimeter scaling is illustrated. Two discoveries are made in this work: first, a dynamic proportionality factor can be employed to estimate the local boundary dimension; second, the average values of the local fractal parameters are approximately equal to the corresponding global fractal parameters of cities. By illustrating how to carry out the area-perimeter scaling analysis of Chinese cities in Yangtze River Delta in the case of remote sensing images with low resolution, we propose a possible new approach to exploring fractal systems of cities.