Spatial Complexity Of Urban-rural Road Network

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).