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.

Capturing and characterizing collective human activities in a geographic space have become much easier than ever before in the big era. In the past few decades it has been difficult to acquire the spatiotemporal information of human beings. Thanks to the boom in the use of mobile devices integrated with positioning systems and location-based social media data, we can easily acquire the spatial and temporal information of social media users. Previous studies have successfully used street nodes and geo-tagged social media such as Twitter to predict users’ activities. However, whether human activities can be well represented by social media data remains uncertain. On the other hand, buildings or architectures are permanent and reliable representations of human activities collectively through historical footprints. This study aims to use the big data of US building footprints to investigate the reliability of social media users for human activity prediction. We created spatial clusters from 125 million buildings and 1.48 million Twitter points in the US. We further examined and compared the spatial and statistical distribution of clusters at both country and city levels. The result of this study shows that both building and Twitter data spatial clusters show the scaling pattern measured by the scale of spatial clusters, respectively, characterized by the number points inside clusters and the area of clusters. More specifically, at the country level, the statistical distribution of the building spatial clusters fits power law distribution. Inside the four largest cities, the hotspots are power-law-distributed with the power law exponent around 2.0, meaning that they also follow the Zipf’s law. The correlations between the number of buildings and the number of tweets are very plausible, with the r square ranging from 0.53 to 0.74. The high correlation and the similarity of two datasets in terms of spatial and statistical distribution suggest that, although social media users are only a proportion of the entire population, the spatial clusters from geographical big data is a good and accurate representation of overall human activities. This study also indicates that using an improved method for spatial clustering is more suitable for big data analysis than the conventional clustering methods based on Euclidean geometry.

Urban structure can be better comprehended through analyzing its cores. Geospatial big data facilitate the identification of urban centers in terms of high accuracy and accessibility. However, previous studies seldom leverage multi-source geospatial big data to identify urban centers from a topological perspective. This study attempts to identify urban centers through the spatial integration of multi-source geospatial big data, including nighttime light imagery (NTL), building footprints (BFP) and street nodes of OpenStreetMap (OSM). We use a novel topological approach to construct complex networks from intra-urban hotspots based on the theory of centers by Christopher Alexander. We compute the degree of wholeness value for each hotspot as the centric index. The overlapped hotspots with the highest centric indices are regarded as urban centers. The identified urban centers in New York, Los Angeles, and Houston are consistent with their downtown areas, with overall accuracy of 90.23%. In Chicago, a new urban center is identified considering a larger spatial extent. The proposed approach can effectively and objectively prevent counting those hotspots with high intensity values but few neighbors into the result. This study proposes a topological approach for urban center identification and a bottom-up perspective for sustainable urban design.

The hierarchical structure of geographic or urban space can be well-characterized by the concept of living structure, a term coined by Christopher Alexander. All spaces, regardless of their size, possess certain degrees of livingness that can be mathematically quantified. While previous studies have successfully quantified the livingness of small spaces such as images or artworks, the livingness of geographic space has not yet been characterized in a recursive manner. Zipf’s law has been observed in urban systems and intra-urban structures. However, whether Zipf’s law is applicable to the hierarchical substructures of geographic space has rarely been investigated. In this study, we recursively extract the substructures of geographic space using global nighttime light imagery. We quantify the livingness of global cities considering the number of substructures (S) and their inherent hierarchy (H). We further investigate the scaling properties of the extracted substructures across scales and the relationships between livingness and population for global cities. The results demonstrate that all substructures of global cities form a living structure that conforms to Zipf’s law. The degree of livingness better captures population distribution than nighttime light intensity values for the global cities. This study contributes in three aspects: First, it considers global cities as a whole to quantify spatial livingness. Second, it applies the concept of livingness to cities to better capture the spatial structure of the population using nighttime light data. Third, it introduces a novel method to recursively extract substructures from nighttime images, offering a valuable tool to investigate urban structures across multiple spatial scales.

The intra-urban space is essentially an organized structure of complexity that consists of centers at different hierarchical levels or scales. This kind of complexity can be measured from the perspective of living structure inspired by Christopher Alexander's organic view of space. Previous studies have revealed that the living structure can be used to characterize the structural complexity of photos, satellite images and urban systems. However, its potential to measure intra-urban complexity using massive point-based datasets remains underexplored. This study introduces a recursive method to analyze intra-urban complexity using massive point-of-interest (POI) data. By recursively decomposing urban substructures, we quantified structural complexity based on the livingness of substructures using a unified criterion. Our findings indicate that cities or intra-urban areas with higher livingness exhibit greater structural complexity. The resulting substructures exhibit power-law distributions and align closely with human activity patterns across multiple spatial scales in four large cities in China. Remarkably, intra-urban structures can be effectively understood with no more than four levels of recursive decomposition. Furthermore, we found that the urban centers or core areas can be effectively located using the proposed method. These insights underscore the potential of living structure as a framework for understanding and measuring the organized complexity of intra-urban spaces.