  The attraction measure, scaling exponent, and impedance function of the
gravity model are redefined using the concepts from fractals and spatial
complexity. Firstly, the attraction measure of spatial interaction in human
systems is defined by the product of traffic inflow and outflow. Based on the
new definition, the gravity model originating from the Newtonian analogy is
differentiated from Wilson's spatial interaction model deriving from
entropy-maximizing principle. Secondly, the scaling exponent of the gravity
model based on the inverse distance relationship is revealed to be the ratio of
the fractal dimension of networks of cities to that of hierarchies of cities.
The value of the scaling exponent is then shown to approach to 2, which
corresponds to the value of the power exponent of the law of gravity in
classical physics. Thirdly, the inverse power function is demonstrated to be
more acceptable than the negative exponential function as an impedance function
of the gravity model. The limits of application of different gravity models
based on different impedance functions are brought to light. Applying the
expanded theory and models to China's interregional flows yields satisfying
results, which in turn lend further support to the expanded theory and models.
