  Central place systems have been demonstrated to possess self-similar patterns
in both the theoretical and empirical perspectives. A central place fractal can
be treated as a monofractal with a single scaling process. However, in the real
world, a system of human settlements is a complex network with multi-scaling
processes. The simple fractal central place models are not enough to interpret
the spatial patterns and evolutive processes of urban systems. It is necessary
to construct multi-scaling fractal models of urban places. Based on the
postulate of intermittent space filling, two typical multifractal models of
central places are proposed in this paper. One model is put forward to reflect
the process of spatial convergence (aggregation), and the generalized
correlation dimension varies from 0.7306 to 1.3181; the other model is
presented to describe the process of spatial divergence (diffusion), the
generalized correlation dimension ranges from 1.6523 to 1.7118. As a case
study, an analogy is drawn between the theoretical models and a system of
cities and towns of Central Plains, China. A finding is that urban systems take
on multifractal form, and can be modeled with multi-scaling fractals. This is a
preliminary attempt to develop the theory of fractal central places, and the
results are helpful for understanding the similarities and differences between
the geographical process of spatial aggregation and that of spatial diffusion.
