Wholeness as a hierarchical graph to capture the nature of space

According to Christopher Alexander’s theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks, can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented, which enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating built and natural environments of beauty or with a high degree of wholeness.     

Geographic space as a living structure for predicting human activities using big data

Inspired by Christopher Alexander’s conception of the world – space is not lifeless or neutral, but a living structure involving far more small things than large ones – a topological representation has been previously developed to characterize the living structure or the wholeness of geographic space. This paper further develops the topological representation and living structure for predicting human activities in geographic space. Based on millions of street nodes of the United Kingdom extracted from OpenStreetMap, we established living structures at different levels of scale in a nested manner. We found that tweet locations at different levels of scale, such as country and city, can be well predicted by the underlying living structure. The high predictability demonstrates that the living structure and the topological representation are efficient and effective for better understanding geographic forms. Based on this major finding, we argue that the topological representation is a truly multiscale representation, and point out that existing geographic representations are essentially single scale, so they bear many scale problems such as modifiable areal unit problem, the conundrum of length and the ecological fallacy. We further discuss on why the living structure is an efficient and effective instrument for structuring geospatial big data, and why Alexander’s organic worldview constitutes the third view of space.     

Street‐based topological representations and analyses for predicting traffic flow in GIS

It is well received in the space syntax community that traffic flow is significantly correlated to a morphological property of streets, which are represented by axial lines, forming a so called axial map. The correlation co‐efficient (R ²) approaches 0.8 and even a higher value according to the space syntax literature. In this paper, we study the same issue using the Hong Kong street network and the Hong Kong Annual Average Daily Traffic datasets, and find surprisingly that street‐based topological representations (or street–street topologies) tend to be better representations than the axial map. In other words, vehicle flow is correlated to a morphological property of streets better than that of axial lines. Based on the finding, we suggest the street‐based topological representations as an alternative GIS representation, and the topological analyses as a new analytical means for geographic knowledge discovery.     

家的解码:空间句法对家空间研究的内容与方法

家是地理学透视社会现象的窗口,家空间是地理学关注人地关系的微观尺度。作为住宅建筑与其居住主体发生联系的空间系统,家空间内部的组构差异可以反映不同的社会文化逻辑。空间句法作为一种定量分析城市形态的理论方法,在研究家空间形态与其社会文化逻辑关系时兼具定量和定性分析的优势。国外运用空间句法对家（family、home、house）空间的研究已日益成熟,而国内的相关工作却尚未涉及。首先阐述空间句法对家研究的基本过程与思路;其次,基于对国外相关研究的梳理、分析后,从家的“基因型”、家的“恒定”与“转换” 、家的“二元性”3个方面进行了归纳和总结,发现空间句法中的“空间”与传统地理学中的“空间”既不同又互补;不同民族文化、生活方式与其家空间之间存在组构关系;相同文化背景下家空间的组构具有时代性。地理学对家空间的关注一直比较薄弱,空间句法对家空间的研究为探究人与其居住空间之关系提供了新的视角。     

基于空间句法耦合SLEUTH模型的新老城区扩展模拟研究——以开封市为例

在快速城镇化背景下,历史文化名城常扩建新区并形成新老城区联动发展格局,新建城区以“飞地”形式扩张,不易被传统的元胞自动机方法准确模拟。空间句法是基于空间拓扑的整体性交通网络研究方法,其自上而下的建模策略与元胞自动机自下而上的邻域转换规则起到了互补,两种模型相结合提供了解决上述问题的途径。本文在验证交通土地空间关联的基础上,将句法变量融入SLEUTH模型的排除图层,对开封城市扩张进行了综合模拟。研究结果表明：① 交通增量与用地扩张具有显著的正相关,其关联度随研究单元粒度的扩大而提升。② 在城市从飞地新区扩建到后续填补开发的过程中,与用地扩张关联最高的交通类型由穿行性交通转向到达性交通,且遍历全局的计算结果方位指向性特征更加明显,遍历局部的计算结果片区集聚性特征更加明显。③ 将空间句法与SLEUTH模型松散耦合,可以有效捕捉飞地型城市新增团块,开封市中心城区空间扩张类型可被解读为老城区边缘型增长和新城区飞地型增长并存的模式。④ 空间句法模型不仅能够反演城市交通流,而且对城市产业布局、规划现状与演化轨迹具有间接指向性,这对城市增长模拟十分重要。     

基于空间句法的武汉城区“两抢一盗”犯罪分布环境

结合空间组构与环境犯罪学,初步建构基于空间句法的犯罪分布环境阐释理论。以武汉市中心城区为案例区域,以立案判决的2013年盗窃罪、抢劫罪和抢夺罪案件分布地点为数据源,以典型犯罪空间为实证研究对象,解读城市“两抢一盗”犯罪现象的分布环境。宏观尺度下,空间组构自发涌现的城市节点容易成为犯罪吸引场,与犯罪热点区分布形成密切关系;节点可达性衔接宏微观空间,影响犯罪人到达、逃逸犯罪地点成本的大小以及犯罪失败风险的高低;微观尺度上,局部空间与整体空间割裂形成的“空间缝隙”为犯罪人的空间探索创造了可能,空间的高集成度与空间使用者的单一化强化了犯罪集聚;空间拓扑深度则通过塑造社区人流的社会结构与领域感影响犯罪的空间防卫。空间句法为分析犯罪人的滋生环境、犯罪动机的刺激环境、犯罪人“到达”、“实施”、“逃逸”的活动环境以及防卫犯罪活动的约束环境提供了有力支撑。     

Fluvial architecture in actively deforming salt basins: Chinle Formation,Paradox Basin,Utah

Determining the response of fluvial systems to syn‐sedimentary halokinesis is important for reconstructing the palaeogeography of salt basins, determining the history of salt movement and predicting development and architecture of sandstone bodies for subsurface fluid extraction. To assess both the influence of salt movement on fluvial system development and the use of lithostratigraphic correlation schemes in salt basins we have analysed the Triassic Chinle Formation in the Paradox Basin, Utah. Results indicate that sandstone body development proximal to salt bodies should be considered at two scales: intra‐ (local) and inter‐ (regional) mini‐basin scale. At the intra‐mini basin or local scale, conformable packages of up to 12 m deep meandering fluvial channel deposits and associated overbank deposits are developed, which may thin, pinch‐out or become truncated towards salt highs. When traced down the axis of a mini‐basin, individual stories extend for a few hundred metres, and form part of amalgamated channel‐belt packages up to 60 m thick that can be traced for at least 25 km parallel to palaeoflow. Where salt movement outpaces sediment accumulation, progressive low angle unconformities are developed along the flanks of salt highs. Significantly, in mini‐basins with high sand supply, sandstone bodies are present across salt highs where they show increased amalgamation, decrease in thickness due to truncation and no change in internal sandstone body character. At inter mini‐basin or regional scale, spatial and temporal variations in accommodation space generated by differential salt movement strongly influence facies distributions and facies correlation lengths. Broad lithostratigraphic packages (5–50 m thick) can be correlated within mini‐basins, but correlation of these units between adjacent mini‐basins is problematic. Knowledge of fluvial system development at a regional scale is critical as, fluvial sediment distribution is focussed by topography generated by growing salt bodies, such that adjacent mini‐basins can have significant differences in sandstone body thickness, distribution and lateral extent. The observations from the Chinle Formation indicate that lithostratigraphic‐based correlation schemes can only be applied within mini‐basins and cannot be used to correlate between adjacent mini‐basins or across a salt mini‐basin province. The key to predicting sandstone body development is an understanding of the timing of salt movement and reconstructing fluvial drainage system development.     

旅游型城市公共空间特征及场所营造指向研究——以甘南藏族自治州夏河县为例

近年来，随着城镇化和旅游业的快速发展，加速了夏河县城市公共空间的更新建设，但也带来场所精神蜕变、识别性降低等一系列问题。在对夏河县进行社会调查、路网拓扑建模的基础上，采用模糊综合评价法、空间句法、核密度分析等方法对场所空间品质、空间活力进行系统地探析，进而对场所单元、丛拉商业文化场所等5处公共场所组团提出了具体的营建策略，并提出场所系统的营造应从构筑系统化的场所、坚持多组团多策略的营造原则、从多主体进行场所营造、营造高通达性的场所、以热点场所单元策动场所组团和场所系统的营造等视角出发营造一个高品质、高活力的场所系统。同时，期望能够为旅游型城市公共空间的场所营造提供一套可借鉴的公共空间评价方法和营造策略     

Developing open space networks in shrinking cities

Urban green spaces provide essential ecosystem services and improve resident quality of life, but open space networks are often fragmented by urban development, and it is difficult to reclaim natural lands after they have been built up. Shrinking cities (i.e., cities experiencing population decline) typically contain an abundance of vacant and abandoned residential buildings that are demolished for safety and maintenance reasons. The resulting empty lots can potentially be reclaimed as natural areas to defragment the green network and increase open space connectivity. To date however, planning efforts have largely ignored post-demolition land uses for these lots, allowing many to become empty wastelands. This research approaches this gap by presenting an alternative plan for residential demolition sites using landscape ecology principles and methods to incorporate them into the open space network. Using Buffalo, NY – a typical rustbelt shrinking city – as a case study, areas most at risk for experiencing demolitions are identified using a clustering technique, and each building within the cluster is assigned a likelihood it will be demolished using a logit model. Properties with the highest risk for demolition are then prioritized based on their ability to contribute to and connect the open space network using landscape connectivity metrics. Results indicate the approach can foster large increases in green network connectivity using small parcels (a 356% increase in total open space area was observed in this study after three years of purposeful selection), allowing cities to reclaim unused urban areas and defragment the open space network.     

珠江三角洲城市群区域绿道与生态游憩空间的连接度与分布模式

绿道对城市群构建连续的生态开放空间网络具有重要作用。基于珠三角城市群现有区域绿道网络,采用拓扑网络和社会网络分析评估生态游憩空间的连接度,揭示生态游憩空间联系的空间分布模式,结果表明：“生态游憩空间-区域绿道”拓扑网络的α、β、γ指数分别为0、0.386、0.129,说明网络中点和边较少,网络为树状形,环通性不高,总体连接度较低;绿道对生态游憩空间的连接度呈集群式分布,且处在边缘的凝聚子群连接度高于中心地区的子群;各集群之间的连接度呈现出东部-北部区域大于西部、东西部之间空间分割性比较明显的格局;连接度分布模式的形成主要受绿道政策与布局、绿道建设机制、生态游憩空间规模集聚格局、地理阻隔与空间邻近性的影响。最后,论文提出了优化“生态游憩空间-绿道”分布模式、构建连接度更高的生态开放空间系统的路径,给中国城市群规划和发展提供参考。     

后结构主义背景下关系地理学的研究进展

随着后结构主义思潮和“关系转向”的兴起,关系地理学（relational geography）应运而生。关系地理学把世界理解为流动的拓扑结构以及相互关联的产物,主张关系思维,强调事物在发展过程中相互影响与依存的动态关系。通过对关系地理学相关著作和期刊论文的分析发现,关系地理学的产生受到社会网络分析理论与非表征理论的深刻影响,其重构了空间、地方、尺度与主体性的内涵,提出关系空间、地方关系、多尺度或尺度终结,以及主体间性的地理学概念,建构了新的关于网络、关系和流的拓扑地理。关系地理学现有的实证研究主要聚焦于空间扩散与空间发展、主体发展与社会文化问题、身体与健康旅游/地理等内容。此外,基于“人”与“超越人类”,“物”与“重返物质”4个方面的内容提出关系地理学可能的研究展望,并对“关系”的内涵与外延进行了延伸讨论,以期为中国人文地理学研究提供新的学术视角。     

Exploring space–time paths in physical and social closeness spaces: a space–time GIS approach

Exploring the evolution of people’s social interactions along with their changing physical locations can help to achieve a better understanding of the processes that generate the relationships between physical distance and social interactions, which can benefit broad fields of study related to social networks. However, few studies have examined the evolving relationships between physical movements and social closeness evolution. This is partially related to the shortage of longitudinal data in both physical locations and social interactions and the lack of an exploratory analysis environment capable of effectively investigating such a process over space and time. With the increasing availability of sociospatiotemporal data in recent years, it is now feasible to examine the relationships between physical separation and social interactions at the individual level in a space–time context. This research was intended to offer a spatiotemporal exploratory analysis approach to address this challenge. The first step was to propose the concept of a social closeness space–time path, which is an extension of the space–time path concept in time geography, to represent evolving human relationships in a social closeness space. A space–time geographical information system (GIS) prototype was then designed to support the representation and analysis of space–time paths in both physical and social closeness spaces. Finally, the effectiveness of the proposed concept and design in gaining insight into the impact of physical migration on online social closeness was demonstrated through an empirical study. The contributions of this study include an extension of the time–geographic framework from physical space to social closeness space, the development of a multirepresentation approach in a GIS to integrate an individual’s space–time paths in both physical and social closeness spaces, and an exploratory analysis of the evolving relationships between physical separation and social closeness over time.     

Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the α‐cut induced fuzzy topology, which are (A_α∧?A)(x)<1?α and ((A^c)_α∧?A)(x)<1?α. In other words, the intersection of the interior and boundary or boundary and exterior are always bounded by 1?α, where α is a value of a level cutting. Specifically, the following areas are covered: (a) the homeomorphic invariants of the fuzzy topology; (b) a definition of the connectivity of the newly developed fuzzy topology; (c) a model of the fuzzy topological relations between simple fuzzy regions in GIS; and (d) the quantitative values of topological relations can be calculated.     

Comparison of conceptual landscape metrics to define hillslope-scale sediment delivery ratio

The aim of this study was to evaluate four metrics to define the spatially variable (regionalised) hillslope sediment delivery ratio (HSDR). A catchment model that accounted for gully and streambank erosion and floodplain deposition was used to isolate the effects of hillslope gross erosion and hillslope delivery from other landscape processes. The analysis was carried out at the subcatchment (~ 40 km²) and the cell scale (400 m²) in the Avon-Richardson catchment (3300 km²), south-east Australia. The four landscape metrics selected for the study were based on sediment travel time, sediment transport capacity, flux connectivity, and residence time. Model configurations with spatially-constant or regionalised HSDR were calibrated against sediment yield measured at five gauging stations. The impact of using regionalised HSDR was evaluated in terms of improved model performance against measured sediment yields in a nested monitoring network, the complexity and data requirements of the metric, and the resulting spatial relationship between hillslope erosion and landscape factors in the catchment and along hillslope transects. The introduction of a regionalised HSDR generally improved model predictions of specific sediment yields at the subcatchment scale, increasing model efficiency from 0.48 to > 0.6 in the best cases. However, the introduction of regionalised HSDR metrics at the cell scale did not improve model performance. The flux connectivity was the most promising metric because it showed the largest improvement in predicting specific sediment yields, was easy to implement, was scale-independent and its formulation was consistent with sedimentological connectivity concepts. These properties make the flux connectivity metric preferable for applications to catchments where climatic conditions can be considered homogeneous, i.e. in small-medium sized basins (up to approximately 3000 km² for Australian conditions, with the Avon-Richardson catchment being at the upper boundary). The residence time metric improved model assessment of sediment yields and enabled accounting for climatic variability on sediment delivery, but at the cost of greater complexity and data requirements; this metric might be more suitable for application in catchments with important climatic gradients, i.e. large basins and at the regional scale. The application of a regionalised HSDR metric did not increase data or computational requirements substantially, and is recommended to improve assessment of hillslope erosion in empirical, semi-lumped erosion modelling applications. However, more research is needed to assess the quality of spatial patterns of erosion depicted by the different landscape metrics.     

Spatial chromatic model in high-dimensional spaces and the uniqueness of chromatic code: a new perspective of geographic entity–space relationship

The abstraction, representation, and computation of entity–space relationship are keystones of geographic information science (GIS). The newly proposed spatial chromatic tessellation (SCT) provides a novel model to explore this relationship. SCT has demonstrated a variety of potential applications in GIS, such as reasoning spatial topology, point pattern analysis, and Voronoi diagrams. This study aims to theoretically investigate SCT by focusing on two aspects: (1) extending SCT to higher dimensional spaces. Results show that cells missing in lower dimensional spaces are hidden in higher dimensional spaces; (2) exploring the uniqueness of chromatic codes, particularly the chromatic codes of 2-cell and 3-cell clusters: their codes are proved to be unique. In a mathematical perspective, the observed phenomena from the above two aspects bring some new thoughts into the first law of geography and spatial heterogeneity. Based on these new understandings of entity–space relationship, SCT is replaced by spatial chromatic model (SCM) in which spaces are created by entities themselves rather than by partitioning the space preexisted. This makes a change from an absolute geographic space to a relative geographic space.     

Defining and generating axial lines from street center lines for better understanding of urban morphologies

Axial lines are defined as the longest visibility lines for representing individual linear spaces in urban environments. The least set of axial lines that cover the free space of an urban environment or the space between buildings constitute what is often called an axial map. This is a fundamental tool in space syntax, a theory developed by Bill Hillier and his colleagues for characterizing the underlying urban morphologies. For a long time, generating axial lines with the help of some graphic software has been a tedious manual process that is criticized for being time consuming, subjective, or even arbitrary. In this article, we redefine axial lines as the least set of individual straight line segments mutually intersected along natural streets that are generated from street center lines using the Gestalt principle of good continuity. Based on this new definition, we develop an automatic solution for generating the newly defined axial lines from street center lines. We apply this solution to six typical street networks (three from North America and three from Europe) and generate a new set of axial lines for analyzing the urban morphologies. Through a comparison study between the new axial lines and the conventional or old axial lines and between the new axial lines and natural streets, we demonstrate with empirical evidence that the newly defined axial lines are a better alternative for capturing the underlying urban structure.     

A space-time varying graph for modelling places and events in a network

Modelling topological relationships between places and events is challenging especially because these relationships are dynamic, and their evolutionary analysis relies on the explanatory power of representing their interactions across different temporal resolutions. In this paper, we introduce the Space-Time Varying Graph (STVG) based on the whole graph approach that combines directed and bipartite subgraphs with a time-tree for representing the complex interaction between places and events across time. We demonstrate how the proposed STVG can be exploited to identify and extract evolutionary patterns of traffic accidents using graph metrics, ad-hoc graph queries and clustering algorithms. The results reveal evolutionary patterns that uncover the places with high incidence of accidents over different time resolutions, reveal the main reasons why the traffic accidents have occurred, and disclose evolving communities of densely connected traffic accidents over time.     

服务业区位选择的交通网络指向研究——以北京城市中心区为例

基于空间句法、核密度估计和皮尔森相关分析等方法,以北京城市中心区为例,结合空间句法轴线模型与百度POI（Points of Interest）数据,探讨服务业区位选择的交通网络指向规律。结果表明：①北京城市中心区的交通网络总体呈现“东优西劣、北优南劣、西南最劣”的空间格局,高层级网络则呈现“中心环状集聚—外围多极分布”的分布模式。②与高穿行度交通网络相比,高整合度交通网络的区位指向性更强,在不同尺度均更易诱发服务业的集聚。③总体而言,服务业区位选择的交通网络指向性明显,但不同类型服务业的区位指向程度依据研究尺度的不同具有显著差异,并据此将25类主要服务业划分为街区指向型、街道指向型、双重指向型和无指向型四类。本文对探索服务业集聚发展规律、提高服务业和交通网络规划的科学性具有参考意义,并可为北京城市中心区服务业存量优化提供决策依据。     

Functional analysis of landscape connectivity at the landscape,component, and patch levels: A case study of Minqing County,Fuzhou City,China

Maintaining forest landscape connectivity is one of the most effective ways to alleviate natural forest fragmentation and biodiversity loss problems. Recently, graph theory based metrics have been used as powerful tools in the assessment of landscape connectivity. However, the functional features of landscape units at different structure levels, based on which outcomes can be enriched and advice can be given for practical applications, have been overlooked. In this study, a series of graph-based connectivity indices was calculated to 1) evaluate the optimal threshold distance, 2) identify the key landscape units at the component and patch levels, and 3) classify the functional types of components and patches and analyze functional patterns at different structural levels. The relationship between patch size and patch functional performance in maintaining landscape connectivity was discussed. With a natural forest area in Minqing County of China as the study area, recommendations regarding forest conservation and connectivity enhancement were provided based on the research conclusions. This study provides a way to comprehensively analyze habitat fragmentation and functional patterns for local forest conservation.