  The central place models are fundamentally important in theoretical geography
and city planning theory. The texture and structure of central place networks
have been demonstrated to be self-similar in both theoretical and empirical
studies. However, the underlying rationale of central place fractals in the
real world has not yet been revealed so far. This paper is devoted to
illustrating the mechanisms by which the fractal patterns can be generated from
central place systems. The structural dimension of the traditional central
place models is d=2 indicating no intermittency in the spatial distribution of
human settlements. This dimension value is inconsistent with empirical
observations. Substituting the complete space filling with the incomplete space
filling, we can obtain central place models with fractional dimension D<d=2
indicative of spatial intermittency. Thus the conventional central place models
are converted into fractal central place models. If we further integrate the
chance factors into the improved central place fractals, the theory will be
able to well explain the real patterns of urban places. As empirical analyses,
the US cities and towns are employed to verify the fractal-based models of
central places.
