城乡路网的空间复杂性
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摘要
融汇系统科学、非线性科学和复杂科学相关理论和方法,构建城乡路网系统的空间复杂性理论体系和研究范式(关系),融入地计算思想和GIS技术,引入(或改进)系列复杂网络信息挖掘模型(映射),以武汉城市圈为主研究区,从形态、结构、功能等视角实证揭示出城乡路网系统的空间复杂性规律(反演)：
城乡路网系统是一开放而复杂的巨系统,具有自相似性、小世界性、无标度性和自组织性等某一或某些复杂性特征,表现为构成的多样性和高维性,形态架构的自相似性和自仿射性,结构关联的非线性和自组织性,功能组织的自主性和层次性,演化作用的协同性和突变性。
城乡路网系统形态的复杂性突出表现为整个城乡道路网以非整数维充填和渗渝空间,呈现局部一整体的自相似性和自仿射性特征。这种形态分形,一方面存在“尺度变换的标度不变性”,具有普遍性,分形发育性态不以时空变换而变化,标度变换具有良好环境包容性和阈值区间稳定性；另一方面,这种形态秩序不是一蹙即就,而是通过对称破缺一重建的矛盾运动逐步进化显现出来,需要通过一定的时空条件和尺度变换才可以“无中生有”地“突现”,从而表现出“标度变换的尺度约束性”,两个方面貌似对立,实为统一,不可须臾分离。
城乡路网系统结构的复杂性源于其构成要素的相互作用和耦合的非线性,这种结构的关联作用可以通过图论抽象成网,表现为一张微观杂乱纷陈、宏观井然有序的自组织网络。微观物理运动下城乡节点作用和分布遵循简单的规则(高斯与指数律分布),而宏观可观察的时空尺度下呈现某种结构和秩序(幂律分布)：路网拓扑性质的空间分布具有异质性、内在作用具有相关性及外在干扰具有稳定性或脆弱性,因此,整个系统整体“平均”来看具有较强随机性,局部“分割”却具有一定的无标度性或小世界性,出现在混沌的边缘,呈现随机一有序矛盾运动、自组织一他组织交互作用的动态临界相变过程。
城乡路网系统功能的复杂性主要通过通达性的层次性分异和层次性的通达性效应共同载现。其中,层次性涉及系统功能组织的复杂性,而通达性则是系统功能效应的空间展现,是系统内在的等级层次性机制长时间作用的结果,往往表现出宏观时空尺度上的分异性：
一方面,从时序演化来看,通达性的空间演化遵从层次性组织“路径依赖”,即初始形成的等级层次(对称性)不断被强化,表现出空间的稳定性和初值的依赖性；同时遵循能量最小化原理,表现出空间分布的趋同性——趋中性、多心化和向异性,新的等级层次(对称性重构)不断建立,整个系统处于集聚和分散、同一和异化、对称建立和对称破坏、渐变和突变的对立统一运动过程中。
另一方面,从空间分异来看,通达性的空间分布及效应的分异程度受制于观察尺度、计量方法和研究对象,表明系统具有认识意义上的复杂性；同时,与自然—人文地理格局保持某种同构,遵循“地质构造→自然地理→(→政治规划活动)→社会经济地理→城市地理→交通地理”的作用机理,通达性格局呈现环状—星状—带状形态和整体对称性架构—局部对称性破缺的空间交织及时序交替,表明系统功能复杂性是自然—人文地理对称性秩序(层次性结构)建立和破坏的涌现。
With the help of computing ideas, GIS technology, and a series of complex web mining models, this article uses the theories and methods of system science, nonlinear science and complexity science, builds a framework of spatial complex modeling of an urban and rural road network system. Then this article takes Wuhan Metropolitan area as an example and reveals the laws of the spatial complex theory of urban-rural road network systems, from the perspective of shape, structure, function and so forth.
The urban and rural road network system is a giant open complex system, which has the characteristics such as self-similar, small world, scale-free and self-organized. As a diverse and high dimensional system, the urban and rural road network system is found to be morphologic self-similar, nonlinear, hierarchical, self-organized, functional autonomous, evolutionary collaboration and mutability.
The complexity of an urban and rural road network prominently manifests the non-integer dimensions, showing a local and overall self-similarity and self-affinity. On one hand, this form is universal. That is because it owns the scale invariance of transformation, the fractal evolutionary state does not change on the basis of space-time transformation, and the scale transformation has a good environment inclusiveness and threshold stability. On the other hand, the order of this form does not take place at once. It originates from a paradoxical movement of the symmetrical incompletion and reconstruction. This requires certain space-time conditions and scale transformations.The above two aspects seem to be opposite but relevant to each other.
The complexity of an urban and rural road network is caused by the interactions between the elements and the coupling nonlinear interactions of the road network, which can be represented as an abstract graph. The road network is in fact a micro-clutter divergent and macro-organized self-organizing entity. At the level of microscopic physical movement, the function of the road network follows a simple rule (Gaussian and Exponential distribution), while at the level of macro-observation, certain structural properties of the road network follow power-law distribution. The spatial distribution of the network topology is heterogeneous and correlated for its internal function but is stable and vulnerable for external interferences. For this reason, the entire network demonstrates significant randomness on average and partial "split", i.e., scale-free or small world. Such an order emerged from random means that the road network is self-organized and dynamic evolution system especially for the interactions of the critical phase transition.
The complexity of the function of the urban-rural road network can be understood from two aspects, that is, the hierarchical differentiation and the accessibility. The former is closely related to the function and operation of the road network, the latter is the result of long-term interaction between the hierarchical parts of the system. In addition, there are macro spatial-temporal differentiations for the accessibilities of roads.
On the one hand, from the perspective of time evolution, the spatial evolution of road accessibility follows the organizational "path dependence". The hierarchical structure in initial road networks keeps enhancing at different development phases. It demonstrates spatial stability and initial dependence; at the same time, the evolution of the road network also follows the principles of energy minimization and reveals a convergence-center trending including centrotaxis、multicenters and anisotropy. With the evolution of the road network, new hierarchies emerge and the entire system lies in between aggregation and dispersion, universality and disparity, symmetry and dissymmetry and graduation and mutation.
On the other hand, from the perspective of spatial differentiation, limited by the observation scale, measurement methods and research objects, the spatial distribution of accessibility and the effect of fractionation is complex in cognition. Meanwhile, it maintains a homogeneous structure with the nature-human geographical pattern, and follows the mechanism of "geological structure geography→(political planning activities)→socio-economic geography urban geography→traffic (accessibility) geography". The pattern of accessibility looks like a ring, star or strip, overall symmetrical but local dissymmetrical breaking intertwined space and timing alternate, which further supports the idea that the complexity of the system function is the manifestation of the establishment and destruction of the natural-human geographical symmetry sequence (hierarchical structure).
城乡路网系统是一开放而复杂的巨系统,具有自相似性、小世界性、无标度性和自组织性等某一或某些复杂性特征,表现为构成的多样性和高维性,形态架构的自相似性和自仿射性,结构关联的非线性和自组织性,功能组织的自主性和层次性,演化作用的协同性和突变性。
城乡路网系统形态的复杂性突出表现为整个城乡道路网以非整数维充填和渗渝空间,呈现局部一整体的自相似性和自仿射性特征。这种形态分形,一方面存在“尺度变换的标度不变性”,具有普遍性,分形发育性态不以时空变换而变化,标度变换具有良好环境包容性和阈值区间稳定性；另一方面,这种形态秩序不是一蹙即就,而是通过对称破缺一重建的矛盾运动逐步进化显现出来,需要通过一定的时空条件和尺度变换才可以“无中生有”地“突现”,从而表现出“标度变换的尺度约束性”,两个方面貌似对立,实为统一,不可须臾分离。
城乡路网系统结构的复杂性源于其构成要素的相互作用和耦合的非线性,这种结构的关联作用可以通过图论抽象成网,表现为一张微观杂乱纷陈、宏观井然有序的自组织网络。微观物理运动下城乡节点作用和分布遵循简单的规则(高斯与指数律分布),而宏观可观察的时空尺度下呈现某种结构和秩序(幂律分布)：路网拓扑性质的空间分布具有异质性、内在作用具有相关性及外在干扰具有稳定性或脆弱性,因此,整个系统整体“平均”来看具有较强随机性,局部“分割”却具有一定的无标度性或小世界性,出现在混沌的边缘,呈现随机一有序矛盾运动、自组织一他组织交互作用的动态临界相变过程。
城乡路网系统功能的复杂性主要通过通达性的层次性分异和层次性的通达性效应共同载现。其中,层次性涉及系统功能组织的复杂性,而通达性则是系统功能效应的空间展现,是系统内在的等级层次性机制长时间作用的结果,往往表现出宏观时空尺度上的分异性：
一方面,从时序演化来看,通达性的空间演化遵从层次性组织“路径依赖”,即初始形成的等级层次(对称性)不断被强化,表现出空间的稳定性和初值的依赖性；同时遵循能量最小化原理,表现出空间分布的趋同性——趋中性、多心化和向异性,新的等级层次(对称性重构)不断建立,整个系统处于集聚和分散、同一和异化、对称建立和对称破坏、渐变和突变的对立统一运动过程中。
另一方面,从空间分异来看,通达性的空间分布及效应的分异程度受制于观察尺度、计量方法和研究对象,表明系统具有认识意义上的复杂性；同时,与自然—人文地理格局保持某种同构,遵循“地质构造→自然地理→(→政治规划活动)→社会经济地理→城市地理→交通地理”的作用机理,通达性格局呈现环状—星状—带状形态和整体对称性架构—局部对称性破缺的空间交织及时序交替,表明系统功能复杂性是自然—人文地理对称性秩序(层次性结构)建立和破坏的涌现。
With the help of computing ideas, GIS technology, and a series of complex web mining models, this article uses the theories and methods of system science, nonlinear science and complexity science, builds a framework of spatial complex modeling of an urban and rural road network system. Then this article takes Wuhan Metropolitan area as an example and reveals the laws of the spatial complex theory of urban-rural road network systems, from the perspective of shape, structure, function and so forth.
The urban and rural road network system is a giant open complex system, which has the characteristics such as self-similar, small world, scale-free and self-organized. As a diverse and high dimensional system, the urban and rural road network system is found to be morphologic self-similar, nonlinear, hierarchical, self-organized, functional autonomous, evolutionary collaboration and mutability.
The complexity of an urban and rural road network prominently manifests the non-integer dimensions, showing a local and overall self-similarity and self-affinity. On one hand, this form is universal. That is because it owns the scale invariance of transformation, the fractal evolutionary state does not change on the basis of space-time transformation, and the scale transformation has a good environment inclusiveness and threshold stability. On the other hand, the order of this form does not take place at once. It originates from a paradoxical movement of the symmetrical incompletion and reconstruction. This requires certain space-time conditions and scale transformations.The above two aspects seem to be opposite but relevant to each other.
The complexity of an urban and rural road network is caused by the interactions between the elements and the coupling nonlinear interactions of the road network, which can be represented as an abstract graph. The road network is in fact a micro-clutter divergent and macro-organized self-organizing entity. At the level of microscopic physical movement, the function of the road network follows a simple rule (Gaussian and Exponential distribution), while at the level of macro-observation, certain structural properties of the road network follow power-law distribution. The spatial distribution of the network topology is heterogeneous and correlated for its internal function but is stable and vulnerable for external interferences. For this reason, the entire network demonstrates significant randomness on average and partial "split", i.e., scale-free or small world. Such an order emerged from random means that the road network is self-organized and dynamic evolution system especially for the interactions of the critical phase transition.
The complexity of the function of the urban-rural road network can be understood from two aspects, that is, the hierarchical differentiation and the accessibility. The former is closely related to the function and operation of the road network, the latter is the result of long-term interaction between the hierarchical parts of the system. In addition, there are macro spatial-temporal differentiations for the accessibilities of roads.
On the one hand, from the perspective of time evolution, the spatial evolution of road accessibility follows the organizational "path dependence". The hierarchical structure in initial road networks keeps enhancing at different development phases. It demonstrates spatial stability and initial dependence; at the same time, the evolution of the road network also follows the principles of energy minimization and reveals a convergence-center trending including centrotaxis、multicenters and anisotropy. With the evolution of the road network, new hierarchies emerge and the entire system lies in between aggregation and dispersion, universality and disparity, symmetry and dissymmetry and graduation and mutation.
On the other hand, from the perspective of spatial differentiation, limited by the observation scale, measurement methods and research objects, the spatial distribution of accessibility and the effect of fractionation is complex in cognition. Meanwhile, it maintains a homogeneous structure with the nature-human geographical pattern, and follows the mechanism of "geological structure geography→(political planning activities)→socio-economic geography urban geography→traffic (accessibility) geography". The pattern of accessibility looks like a ring, star or strip, overall symmetrical but local dissymmetrical breaking intertwined space and timing alternate, which further supports the idea that the complexity of the system function is the manifestation of the establishment and destruction of the natural-human geographical symmetry sequence (hierarchical structure).
引文
① 数据来源：刘力,之江仁,等.中国高速公路及城乡公路网地图集(超大详查版)[M].济南：山东省地图出版社,2010.
① 根据刘式达,刘式适(2004)和陈彦光(2008)研究表明,对于非临界的自组织自组织网络理论,关联函数服从指数律而非幂律,只有接近临界状态,幂律才会显现出来。具体参见：刘式达,刘式适.孤波和湍流[Ml.上海：上海科技教育出版社,1994.和陈彦光.分形城市系统：标度·对称·空间复杂性[Ml.北京：科学出版社.2008：222.
① 学者普遍认为幂次分布、负指数分布、高斯分布(或泊松分布)在表征复杂性程度方面遵循“依次递减”规律,即相对于高斯(Gauss)分布,指数分布是复杂系统的分布特征；相对于幂次分布,指数分布又是简单系统的行为标志。具体见文献：刘继生,陈彦光.城市密度分布与异速生长定律的空间复杂性探讨[J].东北师大学报(自然科学版),2004,36(4)：136-148.
① 许多学者认为“鲁棒而脆弱”的对立统一是复杂系统的最基本特性之。,详见：汪小帆,李翔,陈关荣,等.复杂网络理论及其就用[M].北京：清华大学出版社,2006：15.
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