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Abstract The polycentric city model has gained popularity in spatial planning policy, since it is believed to overcome some of the problems often present in monocentric metropolises, ranging from congestion to difficult accessibility to jobs and services. However, the concept ‘polycentric city’ has a fuzzy definition and as a result, the extent to which a city is polycentric cannot be easily determined. Here, we leverage the fine spatio-temporal resolution of smart travel card data to infer urban polycentricity by examining how a city departs from a well-defined monocentric model. In particular, we analyse the human movements that arise as a result of sophisticated forms of urban structure by introducing a novel probabilistic approach which captures the complexity of these human movements. We focus on London (UK) and Seoul (South Korea) as our two case studies, and we specifically find evidence that London displays a higher degree of monocentricity than Seoul, suggesting that Seoul is likely to be more polycentric than London.

Abstract As cities increase in size, total wages grow superlinearly, meaning that average wages are higher in larger cities. This phenomenon, known as the urban wage premium, supports the notion that urbanization and the growth of cities contribute positively to human well-being. However, it remains unclear how the distribution of wages changes as cities grow. Here we segment the populations of U.S. cities into wage deciles and determine the scaling coefficient of each decile’s aggregate wages versus city size. We find that, while total wages of all deciles grow superlinearly with city size, the effect is uneven, with total wages of the highest wage earners growing faster than all other deciles. We show that this corresponds with the predominance of high-wage jobs in larger cities. Thus, the effects of urbanization are mixed -- it is associated with higher average wages but with increasing inequality, thus inhibiting prospects for long-term sustainability.

Abstract Linear cities where activity is spread out along a transportation line, aim to offer the highest levels of accessibility to their adjacent populations as well as to the countryside. These city forms are popular amongst architects and planners in envisioning ideal cities but they are difficult to implement as they involve strict controls on development which often ignore human behaviour associated with where we locate and how we move. We briefly explore the history of these ideas, noting the latest proposal to build a 170 km city called Neom in north west Saudi Arabia, a plan that has attracted considerable criticism for its apparent ignorance of how actual cities grow and evolve. We use a standard model of human mobility based on gravitational principles to define a set of equilibrium conditions that illustrate how a theoretical city on a line would, without any controls, successively adapt to such a new equilibrium. First, we represent the city on a line, showing how its population moves to an equilibrium along the line, and then we generalise this to a bigger two-dimensional space where the original line cutting across the grid evolves as populations maximise their accessibility over the entire space. In this two-dimensional world, we simulate different forms that reflect a balance of centralising versus decentralising forces, showing the power of such equilibria in destroying any idealised form. This approach informs our thinking about how far idealised future cities can depart from formal plans of the kind that the linear city imposes.

Abstract Urbanization plays a crucial role in the economic development of every country. The mutual relationship between the urbanization of any country and its economic productive structure is far from being understood. We analyzed the historical evolution of product exports for all countries using the World Trade Web with respect to patterns of urbanization from 1995 to 2010. Using the evolving framework of economic complexity, we reveal that a country’s economic development in terms of its production and export of goods, is interwoven with the urbanization process during the early stages of its economic development and growth. Meanwhile in urbanized countries, the reciprocal relation between economic growth and urbanization fades away with respect to its later stages, becoming negligible for countries highly dependent on the export of resources where urbanization is not linked to any structural economic transformation.

Big data analytics and artificial intelligence, paired with blockchain technology, the Internet of Things, and other emerging technologies, are poised to revolutionise urban management. With massive amounts of data collected from citizens, devices, and traditional sources such as routine and well-established censuses, urban areas across the world have – for the first time in history – the opportunity to monitor and manage their urban infrastructure in real-time. This simultaneously provides previously unimaginable opportunities to shape the future of cities, but also gives rise to new ethical challenges. This paper provides a transdisciplinary synthesis of the developments, opportunities, and challenges for urban management and planning under this ongoing ‘digital revolution’ to provide a reference point for the largely fragmented research efforts and policy practice in this area. We consider both top-down systems engineering approaches and the bottom-up emergent approaches to coordination of different systems and functions, their implications for the existing physical and institutional constraints on the built environment and various planning practices, as well as the social and ethical considerations associated with this transformation from non-digital urban management to data-driven urban management.

It is impossible to predict the future spatial structure of cities from our current models of location and travel behaviour for the forces that have previously determined where people locate, have been turned on their heads by the pandemic. The only way we can explore such an uncertain future is to build hypothetical cities on which we are able to experiment with different urban futures. Here we build a hypothetical, symmetric, monocentric city which we proceed to lockdown by moving 80 percent of its workers to work from home. We then illustrate how we can relax this situation, letting the city return to a new equilibrium and showing how changes in our travel behaviour can lead to very different forms of future city. We argue that only through hypothetical simulations can we explore this future effectively and we point to where we have applied the model to London.

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of Australia and the USA. The number of workers and aggregate incomes in specific high-income knowledge economy-related occupations and industries show increasing returns to scale by city size, showing that localization economies within particular industries account for superlinear effects. However, when total urban area incomes and/or gross domestic products are regressed using a generalized Cobb–Douglas function against the number of workers in different occupations as labour inputs, constant returns to scale in productivity against city size are observed. This implies that the urbanization economies at the whole city level show linear scaling or constant returns to scale. Furthermore, industrial and occupational organizations, not population size, largely explain the observed productivity variable. The results show that some very specific industries and occupations contribute to the observed overall superlinearity. The findings suggest that it is not just size but also that it is the diversity of specific intra-city organization of economic and social activity and physical infrastructure that should be used to understand urban scaling behaviours.

In this paper, we propose a computational approach to Jane Jacobs' concept of diversity and vitality, analyzing new forms of spatial data to obtain quantitative measurements of urban qualities frequently employed to evaluate places. We use smart card data collected from public transport to calculate a diversity value for each research unit. Diversity is composed of three dynamic attributes: intensity, variability, and consistency, each measuring different temporal variations of mobility flows. We then apply a regression model to establish the relationship between diversity and vitality, using Twitter data as a proxy for human activity in urban space. Final results (also validated using data sourced from OpenStreetMap) unveil which are the most vibrant areas in London.

In all cities there is a potential for a mismatch to occur between the demand for and supply of jobs. This mismatch is reflective of the balance struck between jobs and housing. This mismatch is non-uniformly perceived by different occupations. The present paper introduces a method to simulate and represent the mismatch surfaces in the perceptions of different social groups that can be compared through visualization using a standard balanced plane. The three-dimensional visualization of the results of the London metropolitan area demonstrates that the commuting advantages – higher levels of commuting affordability through various transport systems, and the configuration of the land-use system – lead to larger ‘flooded areas’ under the balanced plane ($S_i^m$ = 0) and a more scattered pattern of the job centres from the central city to suburban areas for people in higher managerial occupations. Evaluation of these surfaces further show the east–south and north–south divisions perceived by occupations.

Abstract Newly available data on the spatial distribution of retail activities in cities makes it possible to build models formalized at the level of the single retailer. Current models tackle consumer location choices at an aggregate level and the opportunity new data offers for modeling at the retail unit level lacks an appropriate theoretical framework. The model we present here helps to address these issues. Based on random utility theory, we have built it around the idea of quantifying the role of floor-space and agglomeration in retail location choice. We test this model on the inner area of Greater London. The results are consistent with a super linear scaling of a retailer’s attractiveness with its floorspace, and with an agglomeration effect approximated as the total retail floorspace within a 300 m radius from each shop. Our model illustrates many of the issues involved in testing and validating urban simulation models involving spatial data and its aggregation to different spatial scales.

Since the presentation of the radiation model, much work has been done to compare its findings with those obtained from gravitational models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin–destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However, the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyse the impact of the introduction of a new transportation network, a bus rapid transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able to not only better assess the goodness of fit and the impact of this intervention, but also understand reasons for the systematic similarities and differences in their predictions.

We introduce the 14 articles in the Royal Society Open Science themed issue on City Analytics. To provide a high-level, strategic, overview, we summarize the topics addressed and the analytical tools deployed. We then give a more detailed account of the individual contributions. Our overall aims are (i) to highlight exciting advances in this emerging, interdisciplinary field, (ii) to encourage further activity and (iii) to emphasize the variety of new, public-domain, datasets that are available to researchers.

To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated spatio-temporal scales but when we zoom into finer scales, considerable heterogeneity and diversity is observed instead. The fundamental question we address in this paper is at what scales are the regularities we detect stable, explicable, and sustainable. This paper thus proposes a basic measure of variability to assess the stability of such regularities focusing mainly on changes over a range of temporal scales. We demonstrate this by comparing regularities in the urban mobility patterns in three world cities, namely London, Singapore and Beijing using one-week of smart-card data. The results show that variations in regularity scale as non-linear functions of the temporal resolution, which we measure over a scale from 1 minute to 24 hours thus reflecting the diurnal cycle of human mobility. A particularly dramatic increase in variability occurs up to the temporal scale of about 15 minutes in all three cities and this implies that limits exist when we look forward or backward with respect to making short-term predictions. The degree of regularity varies in fact from city to city with Beijing and Singapore showing higher regularity in comparison to London across all temporal scales. A detailed discussion is provided, which relates the analysis to various characteristics of the three cities. In summary, this work contributes to a deeper understanding of regularities in patterns of transit use from variations in volumes of travellers entering subway stations, it establishes a generic analytical framework for comparative studies using urban mobility data, and it provides key points for the management of variability by policy-makers intent on for making the travel experience more amenable.

Urban systems present hierarchical structures at many different scales. These are observed as administrative regional delimitations which are the outcome of complex geographical, political and historical processes which leave almost indelible footprints on infrastructure such as the street network. In this work, we uncover a set of hierarchies in Britain at different scales using percolation theory on the street network and on its intersections which are the primary points of interaction and urban agglomeration. At the larger scales, the observed hierarchical structures can be interpreted as regional fractures of Britain, observed in various forms, from natural boundaries, such as National Parks, to regional divisions based on social class and wealth such as the well-known North–South divide. At smaller scales, cities are generated through recursive percolations on each of the emerging regional clusters. We examine the evolution of the morphology of the system as a whole, by measuring the fractal dimension of the clusters at each distance threshold in the percolation. We observe that this reaches a maximum plateau at a specific distance. The clusters defined at this distance threshold are in excellent correspondence with the boundaries of cities recovered from satellite images, and from previous methods using population density.

The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Urban migration to and from cities is characterised as non-random and following non-random pathways. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales.

Urban society is undergoing as profound a spatial transformation as that associated with the emergence of the industrial city two centuries ago. To describe and measure this transition, we introduce a new theory based on the concept that large-scale, complex systems composed of many interacting elements, show a surprising degree of resilience to change, holding themselves at critical levels for long periods until conditions emerge which move the system, often abruptly, to a new threshold. This theory is called ‘self-organized criticality’; it is consistent with systems in which global patterns emerge from local action which is the hallmark of self-organization, and it is consistent with developments in system dynamics and their morphology which find expression in fractal geometry and weak chaos theory. We illustrate the theory using a unique space–time series of urban development for Buffalo, Western New York, which contains the locations of over one quarter of a million sites coded by their year of construction and dating back to 1773, some 60 years before the city began to develop. We measure the emergence and growth of the city using urban density functions from which measures of fractal dimension are used to construct growth paths of the way the city has grown to fill its region. These phase portraits suggest the existence of transitions between the frontier, the settled agricultural region, the centralized industrial city and the decentralized postindustrial city, and our analysis reveals that Buffalo has maintained itself at a critical threshold since the emergence of the automobile city some 70 years ago. Our implied speculation is: how long will this kind of urban form be maintained in the face of seemingly unstoppable technological change?

We investigate the growth dynamics of Greater London defined by the administrative boundary of the Greater London Authority, based on the evolution of its street network during the last two centuries. This is done by employing a unique dataset, consisting of the planar graph representation of nine time slices of Greater London's road network spanning 224 years, from 1786 to 2010. Within this time-frame, we address the concept of the metropolitan area or city in physical terms, in that urban evolution reveals observable transitions in the distribution of relevant geometrical properties. Given that London has a hard boundary enforced by its long standing green belt, we show that its street network dynamics can be described as a fractal space-filling phenomena up to a capacitated limit, whence its growth can be predicted with a striking level of accuracy. This observation is confirmed by the analytical calculation of key topological properties of the planar graph, such as the topological growth of the network and its average connectivity. This study thus represents an example of a strong violation of Gibrat's law. In particular, we are able to show analytically how London evolves from a more loop-like structure, typical of planned cities, toward a more tree-like structure, typical of self-organized cities. These observations are relevant to the discourse on sustainable urban planning with respect to the control of urban sprawl in many large cities which have developed under the conditions of spatial constraints imposed by green belts and hard urban boundaries.

We employ a cellular-automata to reconstruct the land use patterns of cities that we characterize by two measures of spatial heterogeneity: (a) a variant of spatial entropy, which measures the spread of residential, business, and industrial activity sectors, and (b) an index of dissimilarity, which quantifies the degree of spatial mixing of these land use activity parcels. A minimalist and bottom-up approach is adopted that utilizes a limited set of three parameters which represent the forces which determine the extent to which each of these sectors spatially aggregate into clusters. The dispersion degrees of the land uses are governed by a fixed pre-specified power-law distribution based on empirical observations in other cities. Our method is then used to reconstruct land use patterns for the city state of Singapore and a selection of North American cities. We demonstrate the emergence of land use patterns that exhibit comparable visual features to the actual city maps defining our case studies whilst sharing similar spatial characteristics. Our work provides a complementary approach to other measures of urban spatial structure that differentiate cities by their land use patterns resulting from bottom-up dispersion and aggregation processes.

The spatial arrangement of urban hubs and centers and how individuals interact with these centers is a crucial problem with many applications ranging from urban planning to epidemiology. We utilize here in an unprecedented manner the large scale, real-time 'Oyster' card database of individual person movements in the London subway to reveal the structure and organization of the city. We show that patterns of intraurban movement are strongly heterogeneous in terms of volume, but not in terms of distance travelled, and that there is a polycentric structure composed of large flows organized around a limited number of activity centers. For smaller flows, the pattern of connections becomes richer and more complex and is not strictly hierarchical since it mixes different levels consisting of different orders of magnitude. This new understanding can shed light on the impact of new urban projects on the evolution of the polycentric configuration of a city and the dense structure of its centers and it provides an initial approach to modeling flows in an urban system.

In this paper, we outline how we have developed a series of technologies to enable detailed interactive 3-D Geographical Information Systems (GIS) based models of cities to be created. Until relatively recently these models have been developed in Computer Aided Design (CAD) software more often then in GIS. One of the main reasons was that ‘3-D GIS’ was often only 2.5-D under closer inspection. This is changing, and by straddling both technologies, and integrating others, we show how these models in turn enable planning information, statistics, pollution levels, sea level rises and much more to be visualised and analysed in the context of the 3-D city model. The client for ‘Virtual London’ is the Greater London Authority (GLA) and their aim is to develop improved dissemination of planning information, which is explored. We then argue that virtual cities should go well beyond the traditional conceptions of 3-D GIS and CAD into virtual worlds and online design. But we also urge caution in pushing the digital message too far, showing how more conventional tangible media is always necessary in rooting such models in more realistic and familiar representations.

A working definition of a complex system is that of an entity which is coherent in some recognizable way but whose elements, interactions, and dynamics generate structures admitting surprise and novelty which cannot be defined. Complex systems are therefore more than the sum of their parts, and a consequence of this is that any model of their structure is necessarily incomplete and partial. Models represent simplifications of a system in which salient parts and processes are simulated and given this definition, many models will exist for any particular complex system. In this paper, we explore the impact of complexity in validating models of such systems. We begin with definitions of complexity, complex systems, and models thereof. We identify the key issues as being concerned with the characterization of system equilibrium, system environment, and the way systems and their elements extend and scale. As our perspective on these issues changes, so do our models and this has implications for their testing and validation. We develop these, introducing changes in the meaning of validity posed by the use to which such models are to be put in terms of their users. We draw these ideas together as conclusions about the limits posed to prediction in complex systems. We illustrate our arguments using various examples from the fields of urban systems theory and urban science.