ABSTRACT
Introduction Dimension is a measurement of space, and measurement is the basic link between mathematical models and empirical research. So dimension is a necessary measurement for spatial analysis. Studying geographical spatial phenomena of scaling invariance such as
cities and systems of cities has highlighted the value of fractal dimension (Batty 2005; Batty and Longley 1994; Frankhauser 1994; Haag 1994; Mandelbrot 1983; White and Engelen 1994). However, there are two problems in practical work. On the one hand, sometimes it is diffi cult for us to determine the numerical value of fractal dimension for some realistic systems, but it is fairly easy to calculate the ratio of different fractal parameters; On the other hand, in many cases, it is enough to reveal the a system’s information by the fractaldimension ratios and it is unnecessary to compute fractal dimension further (Chen and Jiang 2009). The ratio of different dimensions of a fractal can constitute an allometric coeffi cient under certain conditions. As a parameter of scale-free systems, the allometric coeffi cient is in fact a scaling exponent, and the fractal-dimension ratio can be called allometric scaling exponent (ASE).
