关键词: 引力模型, 空间相互作用, 分维, 局域性, 长程作用, 对称, 复杂空间系统

Abstract: The spatial interaction models (SIMs) in geography are developed by using the ideas from fractals and spatial complexity, and three pending questions are answered. Firstly, based on the supposition that the distance cost exhibits a logarithmic growth instead of a linear growth, the impedance function of Wilson's spatial interaction model is converted from a negative exponential expression into an inverse power law. The contradiction of locality to action at a distance of SIM is thus avoided through this revision. Secondly, the inverse power law based gravity model is gotten out of the dimensional dilemma with the concept of fractal dimension. Geographical gravity measure is consequently made more understandable. Thirdly, the notion from symmetry based on the nonlinear dual programming of spatial interaction is employed to reveal the essence of entropy maximizing process of human geographical systems. The relationship between entropy maximization and structural optimization is brought to light for geographical analysis. The distinction and connection between the gravity model originating from the analogy with the law of universal gravitation and Wilson's spatial interaction model is discussed, and the similarities and differences are compared between the exponential function based and the power law based SIMs.

Key words: gravity model, spatial interaction, fractal dimension, locality, action at a distance, symmetry, complex spatial system