Human actions and interactions are shaped in part by our direct environment. The studies of Christopher Alexander show that objects and structures can inhibit natural properties and characteristics; this is measured in living structure. He also found that we have better connection and feeling with more natural structures, as they more closely resemble ourselves. These theories are applied in this study to analyze and compare the urban morphology within different cities. The main aim of the study is to measure the living structure in cities. By identifying the living structure within cities, comparisons can be made between different types of cities, artificial and historical, and an estimation of what kind of effect this has on our wellbeing can be made. To do this, natural cities and natural streets are identified following a bottom-up data-driven methodology based on the underlying structures present in OpenStreetMap (OSM) road data. The naturally defined city edges (natural cities) based on intersection density and naturally occurring connected roads (natural streets) based on good continuity between road segments in the road data are extracted and then analyzed together. Thereafter, historical cities are compared with artificial cities to investigate the differences in living structure; it is found that historical cities generally consist of far more living structure than artificial cities. This research finds that the current usage of concrete, steel, and glass combined with very fast development speeds is detrimental to the living structure within cities. Newer city developments should be performed in symbiosis with older city structures as a whole, and the structure of the development should inhibit scaling as well as the buildings themselves.

I have advocated and argued for a paradigm shift from Tobler’s law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and – more importantly – from Descartes’ mechanistic thinking to Alexander’s organic thinking. Fractal geometry falls under the third definition of fractal given by Bin Jiang – that is, a set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times – rather than under the second definition of fractal by Benoit Mandelbrot, which requires a power law between scales and details. The new fractal geometry is more towards Christopher Alexander’s living geometry, not only for understanding complexity, but also for creating complex or living structure. This short paper attempts to clarify why the paradigm shift is essential and to elaborate on several concepts, including spatial heterogeneity (scaling law), scale (or the fourth meaning of scale), data character (in contrast to data quality), and sustainable transport in the big data era.

The Earth’s surface or any territory is a coherent whole or subwhole, in which the notion of “far more small things than large ones” recurs at different levels of scale ranging from the smallest of a couple of meters to the largest of the Earth’s surface or that of the territory. The coherent whole has the underlying character called wholeness or living structure, which is a physical phenomenon pervasively existing in our environment and can be defined mathematically under the new third view of space conceived and advocated by Christopher Alexander: space is neither lifeless nor neutral, but a living structure capable of being more alive or less alive. This paper argues that both the map and the territory are a living structure, and that it is the inherent hierarchy of “far more smalls than larges” that constitutes the foundation of maps and mapping. It is the underlying living structure of geographic space or geographic features that makes maps or mapping possible, i.e., larges to be retained, while smalls to be omitted in a recursive manner (Note: larges and smalls should be understood broadly and wisely, in terms of not only sizes, but also topological connectivity and semantic meaning). Thus, map making is largely an objective undertaking governed by the underlying living structure, and maps portray the truth of the living structure. Based on the notion of living structure, a map can be considered to be an iterative system, which means that the map is the map of the map of the map, and so on endlessly. The word endlessly means continuous map scales between two discrete ones, just as there are endless real numbers between 1 and 2. The iterated map system implies that each of the subsequent small-scale maps is a subset of the single large-scale map, not a simple subset but with various constraints to make all geographic features topologically correct.

A new method for selecting optimal scales when mapping topographic or hydrographic features is introduced. The method employs rank-size partition of heavy-tailed distributions to detect nodes of rescaling invariance in the underlying hierarchy of the dataset. These nodes, known as head/tail breaks, can be used to indicate optimal scales. Then, the Fractal Net Evolution Assessment (FNEA) segmentation algorithm is applied with the topographic or hydrographic surfaces to produce optimally scaled objects. A topological transformation allows linking the two processes (partition and segmentation), while fractal dimension of the rescaling process is employed as an optimality metric. The new method is experimented with the two biggest river basins in Greece, namely Pinios and Acheloos river basins, using a digital elevation model as the only input dataset. The method proved successful in identifying a set of optimal scales for mapping elevation, slope, and flow accumulation. Deviation from the ideal conditions for implementing head/tail breaks are discussed. Implementation of the method requires an object-based analysis program and few common geospatial functions embedded in most GIS programs. The new method will assist in revealing underlying environmental processes in a variety of earth science fields and, thus, assist in land management decision-making and mapping generalization. 

Comprehensive user evaluations of outdoor augmented reality (AR) applications in the architecture, engineering, construction and facilities management (AEC/FM) industry are rarely reported in the literature. This paper presents an AR prototype system for infrared thermographic façade inspection and its evaluation. The system employs markerless tracking based on image registration using natural features and a third person perspective (TPP) augmented view displayed on a hand-held smart device. We focus on evaluating the system in user experiments with the task of designating positions of heat spots on an actual façade as if acquired through thermographic inspection. User and system performance were both assessed with respect to target designation errors. The main findings of this study show that positioning accuracy using this system is adequate for objects of the size of one decimeter. After ruling out the system inherent errors, which mainly stem from our application-specific image registration procedure, we find that errors due to a human’s limited visual-motoric and cognitive performance, which have a more general implication for using TPP AR for target designation, are only a few centimeters.

OpenStreetMap (OSM) constitutes an unprecedented, free, geographical information source contributed by millions of individuals, resulting in a database of great volume and heterogeneity. In this study, we characterize the heterogeneity of the entire OSM database and historical archive in the context of big data. We consider all users, geographic elements and user contributions from an eight-year data archive, at a size of 692 GB. We rely on some nonlinear methods such as power law statistics and head/tail breaks to uncover and illustrate the underlying scaling properties. All three aspects (users, elements, and contributions) demonstrate striking power laws or heavy-tailed distributions. The heavy-tailed distributions imply that there are far more small elements than large ones, far more inactive users than active ones, and far more lightly edited elements than heavy-edited ones. Furthermore, about 500 users in the core group of the OSM are highly networked in terms of collaboration.

Examining the complexity of urban form may help to understand human behavior in urban spaces, thereby improving the conditions for sustainable design of future cities. Metrics, such as fractal dimension, ht-index, and cumulative rate of growth (CRG) index have been proposed to measure this complexity. However, as these indicators are statistical rather than spatial, they result in an inability to characterize the spatial complexity of urban forms, such as building footprints. To overcome this problem, this paper proposes a graph-based fractality index (GFI), which is based on a hybrid of fractal theory and deep learning techniques. First, to quantify the spatial complexity, several fractal variants were synthesized to train a deep graph convolutional neural network. Next, building footprints in London were used to test the method, where the results showed that the proposed framework performed better than the traditional indices, i.e., the index is capable of differentiating complex patterns. Another advantage is that it seems to assure that the trained deep learning is objective and not affected by potential biases in empirically selected training datasets Furthermore, the possibility to connect fractal theory and deep learning techniques on complexity issues opens up new possibilities for data-driven GIS science.

Decision-making methods used in geospatial decision-making are often computationally complex prescriptive methods, details of which are rarely transparent to the decision maker. However, having a deep understanding of the details and mechanisms of the applied method is a prerequisite for the efficient use thereof. In this paper, we present a novel decision-making framework that emanates from the need for intuitive and easy-to-use decision support systems for geospatial multi-criteria decision-making. The framework consists of two parts: the decision making model, and the interactive visualization framework. The decision-making model is based on the concept of quasi-satisficing, and as such, it is intuitive and easy to understand and apply. It integrates even swaps, a prescriptive decision-making method, with the findings of behavioural decision-making theories. Providing visual feedback and interaction opportunities throughout the decision-making process, the interactive visualization part of the framework helps the decision maker gain better insight into the decision space and attribute dependencies. Furthermore, it provides the means to analyse and compare the outcomes of different scenarios and decision paths.

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.