基于复杂性科学的虚拟城市建模研究
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摘要
城市是一个复杂系统。虽然目前科学界对复杂系统没有严格的定义,但复杂系统所具有的特征是明确的,包括分形结构、自组织临界性、复杂网络等基本特征。本文将运用复杂性科学理论和复杂系统建模工具,研究城市系统的复杂性特征,包括城市的分形结构,城市的自组织及自组织临界性,以及城市系统中的复杂网络等。论文的主要研究内容包括以下几个部分:
1.城市分形结构研究
分形结构具有层次性和自相似性,具有空间利用率高,可扩展性强等优点,广泛存在于自然界中。人类的活动空间自觉或不自觉地形成了空间的分形结构,从建筑到居住环境,从社区到整个城市,从城市到城市体系,人类的活动空间具有层次性和自相似性。不仅城市的空间结构具有分形特征,城市中几乎一切具有整体分布性质的事物都具有分形特征,如交通、通信、能源传输等硬件设施,以及公安、银行、医院、学校等服务设施,都相应地具有分形特征。研究城市分形特征中的层次性和自相似模式,有助于在城市规划过程中优化空间结构,在城市管理过程中优化资源配置。
本文在分析城市分形特征的基础上,利用这些分形特征建立了分形城市模型。模型运用分形机制规划城市空间,其中包含一个迭代过程和一个分形过程,迭代过程是一个空间布局的规划过程,同一个层次上的规划过程具有相似性;而分形过程是递归的迭代过程,该过程实现了空间结构的层次性。在两个过程的相互作用下,城市的区域不断被划分和分形,最终可以形成在各种大小尺度上具有自相似结构—即所谓无标度性—的分形城市。论文进一步比较了虚拟分形城市与中心地景观的异同,并验证了虚拟分形城市的空间分布满足Zipf律。分形城市模型为城市建模提供了一个新的方法,对于城市现象研究和城市规划具有一定的理论和实践意义。
2.城市自组织和自组织临界性研究
复杂系统的另一个特征的是系统的自组织性。城市作为一个复杂系统,也是一个自组织系统。在一个城市系统中存在大量的自组织机制,而使这些机制发挥作用的影响因素极其复杂,本文仅就基于博弈的空间实体的选址作为城市形成和演化的自组织机制,结合Hoteling模型和DLA模型,通过该机制建立了基于自组织的城市形成和演化模型。与分形规划过程相反,自组织过程是一个自下而上的过程。分形规划过程和自组织过程虽然是两个完全相反的过程,但得到的结果是一致的,即在模拟城市现象方面两个过程是异曲同工、殊途同归的。
具体过程是将个体(居民点和商业点)的选址博弈行为作为城市空间布局演化的基本机制,个体根据局部环境的供需均衡情况决定其行为(转变、迁移、维持等)。虚拟城市系统的空间格局是群体博弈的结果,当系统演化到相对稳定的程度,系统状态是一个博弈均衡状态。运用多Agent技术建立计算机模型,对计算机模型的模拟演化结果进行统计分析,通过与真实城市系统的空间分布特征的对比分析,对模型进行定性与定量相结合的研究。该模型对于研究宏观城市系统的长期演化趋势具有理论价值。
通过对模型的理论分析,得到有关商业、交通、信息技术等环境因素影响城市发展的一些结论,如“当系统演化到接近均衡状态时,会出现居民点和商业点的聚集现象。商业点的聚集程度会大大高于居民点的聚集程度”;“在城市发展进入均衡状态时,商业繁荣程度越高,城市的稳定性越弱,反之则越强”;“空间个体密集区域的稳定性较高”等等。通过模拟实验分析,验证了理论分析的正确性,同时也验证了所生成的虚拟城市模型处于自组织临界状态。
3.城市道路网络的自然形成与演化研究
复杂网络是复杂性科学研究的重要领域,复杂网络具有小世界,集群(集聚程度),幂律的度分布等重要特征。动物身体内的血管、神经系统,植物的枝杆、叶脉,大地的江河水系等都是复杂网络,城市的交通系统也是一个复杂网络。本文在借鉴J. Sun模型的基于L-系统的道路网络分形模型的基础上,提出了一个基于自组织的道路网络模型,它根据局部的交通需求分布式地自动生成交通系统。生成规则十分简单,就是根据交通需求率的大小生成不同等级的道路,交通需求率越高,生成的道路等级越高。局部地域的交通需求率与人口分布密度成正比,人口分布越密集则交通需求率越高。另一方面,已有的交通系统会影响人口的分布,为了获得交通的便利,人们有向交通干线迁移的趋势。由于存在这一互为因果的互动因素,系统始终处于动态演化过程中。通过模型可以研究在自然状态下城市道路网络的形成与演化规律,对于研究自然形成的交通系统的模式特征具有理论意义,对城市道路网络的规划具有指导意义。
本文通过与复杂网络5个基本特征的比较,从理论上论证了所形成的虚拟道路网络是一个复杂网络。模型给道路网络规划的启示是:①现有的道路网络具有内在的合理性,应尽可能在现有道路网络的基础上,运用复杂网络模型模拟和分析道路网络的负载能力、流量和时间波动,对道路网络中的个别路段进行拓宽和改造;②寻求人口分布与道路网络分布之间的均衡关系;③道路网络中的等级体系体现了资源利用和效率的平衡关系;④物流运输规划可以借鉴植物叶脉或动物血管等仿生学模型。
4.城市生态系统研究
本文将城市隐喻为生命体,城市之间的竞争与合作机制构成了由城市群组成的生态系统;引入“生态位”的概念分析城市的发展和演化策略,包括城市发展规模的选择和特色的定位。城市生态位是城市系统长期演化的结果,各个生态位形成了一个相互依赖的服务链条,在这个链条上传递着物质、能量和信息。城市规划者需要描绘出区域城市系统中的生态位图景,并确定自己所占据的生态位制定出适宜的生存策略。每个城市都应该拥有自己的生态位,即自己生存发展的空间。如果偏离了生态位,就会导致城市之间的恶性竞争和畸形发展。
运用复杂性科学研究城市空间结构和城市管理问题是一个兴起了多年的热点问题,目前仍然具有重要的研究意义,因为我国的城市一直处在一个动态的发展过程中,各大中小城市对自身的定位还远远没有完成,城市的空间布局也在平衡资源的矛盾中不断发展变化,因此城市演化规律的研究对于城市规划和城市管理具有重要的现实意义。
Cities are viewed as complex systems. There hasn’t a clear definition of complex system in science, but characteristics of complex system are tangible, which consist of fractal structure, self-organized critical, complex network. Based on the theory of complex science and modeling tool of complex system, the paper has studied city system’s complex characteristics, including city’s fractal, city’s self-organized and self-organized criticality, and city’s complex network. The paper has concentrated on the following subjects:
1. Study on City Fractal Structure
Fractals are hierarchically ordered structures revealing self-similarity across scales, which widely exist in the nature, and besides, they have advantages of high space utilization as well as better expansibility. Fractal structures come into being consciously or unconsciously in designing human activity space from architecture to inhabitant environment, community to city, and city to city system. Not only does city’s apace have fractal structure, but also all integer things in a city have fractal structures, both in hardware infrastructures such as traffic, communications, energy source transport etc., and service establishments such as police, bank, school, and hospital etc. To do research on hierarchy and self-similarity in city fractal characteristics can help to better space utilization in city planning and optimize resource allocation in city management.
The paper has offered a city fractal planning model, in which fractal mechanism is applied. The planning process includes an iterative process and a fractal process. Iterative process is a planning process of space layout with the characteristics of similarity on the same hierarchy, whereas fractal process is a recursive iterative process, which realizes hierarchies of fractal structure. With the interaction of two processes, city space is continuously plotted and fractal, it finally forms a fractal city with self-similarity across scales. The paper has further compared similarities and differences between virtual fractal city model and central place system, and validated that the virtual fractal city obeys Zipf’s law. Virtual fractal city model has put forward a creative method for city modeling and offers both theoretical and practical significance to study of city phenomena and city planning.
2. Study on Self-Organized City and City’s Self-Organized Criticality
Since another characteristic of complexity is self-organized, city is considered to be a complex system, and meanwhile it is also called a Self-organized system. There are many self-organized mechanism in a city system, and relationship among these mechanism is very complex. The paper combines Hoteling model and DLA model to construct city’s forming and evolving model based on self-organized mechanism of space entities’site-selection. Contrary to fractal planning process, self-organized process is a bottom-up process. In spite of the fact that the two processes are distinctly different, they achieve the same result in simulating cities’phenomenon.
The self-organized process in our model has used an evolvement mechanism of city space layout which is based on actions of individual’s site-selection. Individuals choose their behaviors (transition, migration, or stand) according to their circumstances. Virtual city’s space layout is a result of all individual’s decisions. With the aid of multi-agent technology, we can build corresponding computer model to simulate the process, and analyze the simulating results. Comparing with space layout features of real city, we can study long-term developing trend of city system.
Through the analysis of results, we can draw many conclusions about circumstance factors influencing city’s development. For instance, when system develops to a balanced state, we can observe habitant-site and commerce-site are assembling together, and assembling degree of commerce-site is greater than that of habitant-site. Furthermore, the more prosperous city’s commerce is, the weaker city’s stability is, and vice versa. The paper has validated the theoretical analysis through analysis of results of simulating experiments. In the mean time, it has also validated that virtual city model is in the self-organized critical state.
3. Study on Formation and Evolvement of Road Network
Complex network is an important field in the complex science. The characteristic of complex network includes small world, cluster, and power-law of degree distribution. Animal’s blood vessel, neural system, plant’s twig and vein, water system of rivers are all complex network. City traffic system can also be treated as a complex network. Based on J. Sun model, this paper has put forward a traffic auto-generation system model. The model can automatically generate new road system according to local traffic situation. The demand for traffic determines the magnitude of road network. The demand for local roads is positively correlated with population density, while the existing road layout has an impact on the distribution of population since people will move towards main lines of communication. The interaction between road layout and population density causes the traffic system to be in a dynamic evolving state. The forming and evolving law of cities’road networks can be studies with the help of model.
Comparing with 5 features of complex network, the paper has got some revelations about city road network programming:①Current road system has its own inner rationality. City road network planner should make the most of current road system to open up or rebuild road sections based on old road. One can use complex network model to simulate traffic and analyze load ability, flux, undulation of road system to get more knowledge of current road system.;②It needs to find the balanced relations between population distribution and road network layout;③Hierarchy in road system embodies the balance between resource utility and efficiency.;④Bionic model of Animal’s blood vessel or plant vein can be employed in planning logistics.
4. Study on City Ecosystem
The paper use a metaphor that city is a kind of life-form. City system is a city ecosystem in which there exist mechanisms of competition and cooperation among cities. The concept of ecological niche can help us to analyze strategy of city development and evolvement, such strategy as city development scale and city feature orientation. Cities’ecological niche is a result of a long evolvement and each ecological niche has formed an interdependent service chain, by which substance, energy and information are passed. City planner should describe the city system’s ecological niche map and determine the position in which he is, in order to figure out strategy of city development. Every city should have its own ecological niche, namely survival room. If development of a city deviates from its ecological niche, malignant competitions among cities and cities’abnormal development will yield.
It has been a hot topic for many years to apply complex science to the study of city space structure and city management. The topic still remains great significant at present, since many cities in our country are all the while in a dynamic state. These cities’developing orientations are not clear and city space structures keep changing to balance the confliction of utility of all kinds of resource. Therefore, study on law of city development is of great importance to planning and management of cities.
1.城市分形结构研究
分形结构具有层次性和自相似性,具有空间利用率高,可扩展性强等优点,广泛存在于自然界中。人类的活动空间自觉或不自觉地形成了空间的分形结构,从建筑到居住环境,从社区到整个城市,从城市到城市体系,人类的活动空间具有层次性和自相似性。不仅城市的空间结构具有分形特征,城市中几乎一切具有整体分布性质的事物都具有分形特征,如交通、通信、能源传输等硬件设施,以及公安、银行、医院、学校等服务设施,都相应地具有分形特征。研究城市分形特征中的层次性和自相似模式,有助于在城市规划过程中优化空间结构,在城市管理过程中优化资源配置。
本文在分析城市分形特征的基础上,利用这些分形特征建立了分形城市模型。模型运用分形机制规划城市空间,其中包含一个迭代过程和一个分形过程,迭代过程是一个空间布局的规划过程,同一个层次上的规划过程具有相似性;而分形过程是递归的迭代过程,该过程实现了空间结构的层次性。在两个过程的相互作用下,城市的区域不断被划分和分形,最终可以形成在各种大小尺度上具有自相似结构—即所谓无标度性—的分形城市。论文进一步比较了虚拟分形城市与中心地景观的异同,并验证了虚拟分形城市的空间分布满足Zipf律。分形城市模型为城市建模提供了一个新的方法,对于城市现象研究和城市规划具有一定的理论和实践意义。
2.城市自组织和自组织临界性研究
复杂系统的另一个特征的是系统的自组织性。城市作为一个复杂系统,也是一个自组织系统。在一个城市系统中存在大量的自组织机制,而使这些机制发挥作用的影响因素极其复杂,本文仅就基于博弈的空间实体的选址作为城市形成和演化的自组织机制,结合Hoteling模型和DLA模型,通过该机制建立了基于自组织的城市形成和演化模型。与分形规划过程相反,自组织过程是一个自下而上的过程。分形规划过程和自组织过程虽然是两个完全相反的过程,但得到的结果是一致的,即在模拟城市现象方面两个过程是异曲同工、殊途同归的。
具体过程是将个体(居民点和商业点)的选址博弈行为作为城市空间布局演化的基本机制,个体根据局部环境的供需均衡情况决定其行为(转变、迁移、维持等)。虚拟城市系统的空间格局是群体博弈的结果,当系统演化到相对稳定的程度,系统状态是一个博弈均衡状态。运用多Agent技术建立计算机模型,对计算机模型的模拟演化结果进行统计分析,通过与真实城市系统的空间分布特征的对比分析,对模型进行定性与定量相结合的研究。该模型对于研究宏观城市系统的长期演化趋势具有理论价值。
通过对模型的理论分析,得到有关商业、交通、信息技术等环境因素影响城市发展的一些结论,如“当系统演化到接近均衡状态时,会出现居民点和商业点的聚集现象。商业点的聚集程度会大大高于居民点的聚集程度”;“在城市发展进入均衡状态时,商业繁荣程度越高,城市的稳定性越弱,反之则越强”;“空间个体密集区域的稳定性较高”等等。通过模拟实验分析,验证了理论分析的正确性,同时也验证了所生成的虚拟城市模型处于自组织临界状态。
3.城市道路网络的自然形成与演化研究
复杂网络是复杂性科学研究的重要领域,复杂网络具有小世界,集群(集聚程度),幂律的度分布等重要特征。动物身体内的血管、神经系统,植物的枝杆、叶脉,大地的江河水系等都是复杂网络,城市的交通系统也是一个复杂网络。本文在借鉴J. Sun模型的基于L-系统的道路网络分形模型的基础上,提出了一个基于自组织的道路网络模型,它根据局部的交通需求分布式地自动生成交通系统。生成规则十分简单,就是根据交通需求率的大小生成不同等级的道路,交通需求率越高,生成的道路等级越高。局部地域的交通需求率与人口分布密度成正比,人口分布越密集则交通需求率越高。另一方面,已有的交通系统会影响人口的分布,为了获得交通的便利,人们有向交通干线迁移的趋势。由于存在这一互为因果的互动因素,系统始终处于动态演化过程中。通过模型可以研究在自然状态下城市道路网络的形成与演化规律,对于研究自然形成的交通系统的模式特征具有理论意义,对城市道路网络的规划具有指导意义。
本文通过与复杂网络5个基本特征的比较,从理论上论证了所形成的虚拟道路网络是一个复杂网络。模型给道路网络规划的启示是:①现有的道路网络具有内在的合理性,应尽可能在现有道路网络的基础上,运用复杂网络模型模拟和分析道路网络的负载能力、流量和时间波动,对道路网络中的个别路段进行拓宽和改造;②寻求人口分布与道路网络分布之间的均衡关系;③道路网络中的等级体系体现了资源利用和效率的平衡关系;④物流运输规划可以借鉴植物叶脉或动物血管等仿生学模型。
4.城市生态系统研究
本文将城市隐喻为生命体,城市之间的竞争与合作机制构成了由城市群组成的生态系统;引入“生态位”的概念分析城市的发展和演化策略,包括城市发展规模的选择和特色的定位。城市生态位是城市系统长期演化的结果,各个生态位形成了一个相互依赖的服务链条,在这个链条上传递着物质、能量和信息。城市规划者需要描绘出区域城市系统中的生态位图景,并确定自己所占据的生态位制定出适宜的生存策略。每个城市都应该拥有自己的生态位,即自己生存发展的空间。如果偏离了生态位,就会导致城市之间的恶性竞争和畸形发展。
运用复杂性科学研究城市空间结构和城市管理问题是一个兴起了多年的热点问题,目前仍然具有重要的研究意义,因为我国的城市一直处在一个动态的发展过程中,各大中小城市对自身的定位还远远没有完成,城市的空间布局也在平衡资源的矛盾中不断发展变化,因此城市演化规律的研究对于城市规划和城市管理具有重要的现实意义。
Cities are viewed as complex systems. There hasn’t a clear definition of complex system in science, but characteristics of complex system are tangible, which consist of fractal structure, self-organized critical, complex network. Based on the theory of complex science and modeling tool of complex system, the paper has studied city system’s complex characteristics, including city’s fractal, city’s self-organized and self-organized criticality, and city’s complex network. The paper has concentrated on the following subjects:
1. Study on City Fractal Structure
Fractals are hierarchically ordered structures revealing self-similarity across scales, which widely exist in the nature, and besides, they have advantages of high space utilization as well as better expansibility. Fractal structures come into being consciously or unconsciously in designing human activity space from architecture to inhabitant environment, community to city, and city to city system. Not only does city’s apace have fractal structure, but also all integer things in a city have fractal structures, both in hardware infrastructures such as traffic, communications, energy source transport etc., and service establishments such as police, bank, school, and hospital etc. To do research on hierarchy and self-similarity in city fractal characteristics can help to better space utilization in city planning and optimize resource allocation in city management.
The paper has offered a city fractal planning model, in which fractal mechanism is applied. The planning process includes an iterative process and a fractal process. Iterative process is a planning process of space layout with the characteristics of similarity on the same hierarchy, whereas fractal process is a recursive iterative process, which realizes hierarchies of fractal structure. With the interaction of two processes, city space is continuously plotted and fractal, it finally forms a fractal city with self-similarity across scales. The paper has further compared similarities and differences between virtual fractal city model and central place system, and validated that the virtual fractal city obeys Zipf’s law. Virtual fractal city model has put forward a creative method for city modeling and offers both theoretical and practical significance to study of city phenomena and city planning.
2. Study on Self-Organized City and City’s Self-Organized Criticality
Since another characteristic of complexity is self-organized, city is considered to be a complex system, and meanwhile it is also called a Self-organized system. There are many self-organized mechanism in a city system, and relationship among these mechanism is very complex. The paper combines Hoteling model and DLA model to construct city’s forming and evolving model based on self-organized mechanism of space entities’site-selection. Contrary to fractal planning process, self-organized process is a bottom-up process. In spite of the fact that the two processes are distinctly different, they achieve the same result in simulating cities’phenomenon.
The self-organized process in our model has used an evolvement mechanism of city space layout which is based on actions of individual’s site-selection. Individuals choose their behaviors (transition, migration, or stand) according to their circumstances. Virtual city’s space layout is a result of all individual’s decisions. With the aid of multi-agent technology, we can build corresponding computer model to simulate the process, and analyze the simulating results. Comparing with space layout features of real city, we can study long-term developing trend of city system.
Through the analysis of results, we can draw many conclusions about circumstance factors influencing city’s development. For instance, when system develops to a balanced state, we can observe habitant-site and commerce-site are assembling together, and assembling degree of commerce-site is greater than that of habitant-site. Furthermore, the more prosperous city’s commerce is, the weaker city’s stability is, and vice versa. The paper has validated the theoretical analysis through analysis of results of simulating experiments. In the mean time, it has also validated that virtual city model is in the self-organized critical state.
3. Study on Formation and Evolvement of Road Network
Complex network is an important field in the complex science. The characteristic of complex network includes small world, cluster, and power-law of degree distribution. Animal’s blood vessel, neural system, plant’s twig and vein, water system of rivers are all complex network. City traffic system can also be treated as a complex network. Based on J. Sun model, this paper has put forward a traffic auto-generation system model. The model can automatically generate new road system according to local traffic situation. The demand for traffic determines the magnitude of road network. The demand for local roads is positively correlated with population density, while the existing road layout has an impact on the distribution of population since people will move towards main lines of communication. The interaction between road layout and population density causes the traffic system to be in a dynamic evolving state. The forming and evolving law of cities’road networks can be studies with the help of model.
Comparing with 5 features of complex network, the paper has got some revelations about city road network programming:①Current road system has its own inner rationality. City road network planner should make the most of current road system to open up or rebuild road sections based on old road. One can use complex network model to simulate traffic and analyze load ability, flux, undulation of road system to get more knowledge of current road system.;②It needs to find the balanced relations between population distribution and road network layout;③Hierarchy in road system embodies the balance between resource utility and efficiency.;④Bionic model of Animal’s blood vessel or plant vein can be employed in planning logistics.
4. Study on City Ecosystem
The paper use a metaphor that city is a kind of life-form. City system is a city ecosystem in which there exist mechanisms of competition and cooperation among cities. The concept of ecological niche can help us to analyze strategy of city development and evolvement, such strategy as city development scale and city feature orientation. Cities’ecological niche is a result of a long evolvement and each ecological niche has formed an interdependent service chain, by which substance, energy and information are passed. City planner should describe the city system’s ecological niche map and determine the position in which he is, in order to figure out strategy of city development. Every city should have its own ecological niche, namely survival room. If development of a city deviates from its ecological niche, malignant competitions among cities and cities’abnormal development will yield.
It has been a hot topic for many years to apply complex science to the study of city space structure and city management. The topic still remains great significant at present, since many cities in our country are all the while in a dynamic state. These cities’developing orientations are not clear and city space structures keep changing to balance the confliction of utility of all kinds of resource. Therefore, study on law of city development is of great importance to planning and management of cities.
引文
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