城市空间网络:标度、对称、复杂与优化--城市体系空间网络分形结构研究的理论总结报告

城市空间网络是学术界普遍关心的复杂性课题，这类课题的主要目标是借助后现代数学方法建立模型和设计模拟程序．发展城市空间网络的理论框架．本项研究以城市体系和交通网络为主要对象．借助网络结构与等级体系的数理转换关系．成功地实现了城市网络的数学抽象与模型建设．初步形成了关于城市地理系统的新的解释体系、主要理论成果包括地理空间层次的划分、城市系统标度定律的规范与变换、熵与效用最大化的对偶转换模型、自组织城市网络的发育机制、城市地理规律的对称与对称破缺等等．标度律及其对称性是城市系统的数理本质所在．复杂化为其外在演变特征．自组织优化为其内在发展趋势。

Self-organizing networks of cities:scaling laws,symmetry,complexity and optimization

Fractal network of cities is a pioneering study of the development and use of fractal geometry for understanding and planning the system of cities, showing how this geometry enables urban system to be modeled by postmodern mathematics and simulated through computer graphics. Self-organized network of cities and its spatial dynamics have been studied using fractal geometry and computer simulation. Transforming spatial network of cities into hierarchies through the process of spatial disaggregation, we can formulated fractal network of cities mathematically in an indirect way, and the form can be abstracted as equations, which make it possible to perform generalized spatial analysis.It shows how system of cities evolve and grow in ways that at first sigh appear irregular, but which, when understood in terms of fractals and self-organized network, illustrate an underlying order that reveals their complexity and diversity.