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

摘要： 借助空间复杂性观念和分形思想发展了地理学的空间相互作用模型，解决了长期以来悬而未决的3个问题。首先，通过修正距离成本假设，将Wilson的空间相互作用模型还原为负幂函数形式，从而回避了局域性与长程作用的矛盾。其次，利用分维概念解决了基于负幂律的空间相互作用模型的量纲问题，有助于更好地理解地理引力测度。其三，运用对称思想和对偶分析解析了人文地理系统熵最大化的本质含义，揭示了最大熵与最优化的理论关系。论证了源于万有引力类比的引力模型与Wilson空间相互作用模型的区别和联系，比较了负幂式空间相互作用模型与负指数式空间相互作用模型的共性和差异。

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