Michael Batty

The size, scale, and shape of cities.

Despite a century of effort, our understanding of how cities evolve is still woefully inadequate. Recent research, however, suggests that cities are complex systems that mainly grow from the bottom up, their size and shape following well-defined scaling laws that result from intense competition for space. An integrated theory of how cities evolve, linking urban economics and transportation behavior to developments in network science, allometric growth, and fractal geometry, is being slowly developed. This science provides new insights into the resource limits facing cities in terms of the meaning of density, compactness, and sprawl, and related questions of sustainability. It has the potential to enrich current approaches to city planning and replace traditional top-down strategies with realistic city plans that benefit all city dwellers.

Modeling urban dynamics through GIS-based cellular automata

In urban systems modeling, there are many elaborate dynamic models based on intricate decision processes whose simulation must be based on customized software if their space–time properties are to be explored effectively. In this paper we present a class of urban models whose dynamics are based on theories of development associated with cellular automata (CA), whose data is fine-grained, and whose simulation requires software which can handle an enormous array of spatial and temporal model outputs. We first introduce the generic problem of modeling within GIS, noting relevant CA models before outlining a generalized model based on Xies (1996, A general model for cellular urban dynamics. Geographical Analysis, 28, 350–373) “dynamic urban evolutionary modeling” (DUEM) approach. We present ways in which land uses are structured through their life cycles, and ways in which existing urban activities spawn locations for new activities. We define various decision rules that embed distance and direction, density thresholds, and transition or mutation probabilities into the models dynamics, and we then outline the software designed to generate effective urban simulations consistent with GIS data inputs, outputs and related functionality. Finally, we present a range of hypothetical urban simulations that illustrate the diversity of model types that can be handled within the framework as a prelude to more realistic applications which will be reported in later papers.

From cells to cities

Since mathematical models came to be applied to problems of architectural and urban form, new concepts based on predicting large-scale structure from local rules have emerged through insights originating in computation and biology. The clearest of these are computer models based on cellular automata (CA) and their recent generalization in evolutionary biology and artificial life. Here we show how such models can be used to simulate urban growth and form, thus linking our exposition to the longer tradition of ideas in studies of built form emanating from the ‘Cambridge School’. We first review developments of CA in general and then in urban systems in particular. We propose a general class of CA models for urban simulation and illustrate two simple applications, the first a simulation of the development of the historical ‘cell’ city of Savannah, Georgia, the second, a generic hypothetical application. We then show how this generic model can be used to simulate the growth dynamics of a suburban area of a mid-sized North American city, thus illustrating how this approach provides insights into the way microprocesses lead to aggregate development patterns.

Key challenges in agent-based modelling for geo-spatial simulation

Agent-based modelling (ABM) is becoming the dominant paradigm in social simulation due primarily to a worldview that suggests that complex systems emerge from the bottom-up, are highly decentralised, and are composed of a multitude of heterogeneous objects called agents. These agents act with some purpose and their interaction, usually through time and space, generates emergent order, often at higher levels than those at which such agents operate. ABM however raises as many challenges as it seeks to resolve. It is the purpose of this paper to catalogue these challenges and to illustrate them using three somewhat different agent-based models applied to city systems. The seven challenges we pose involve: the purpose for which the model is built, the extent to which the model is rooted in independent theory, the extent to which the model can be replicated, the ways the model might be verified, calibrated and validated, the way model dynamics are represented in terms of agent interactions, the extent to which the model is operational, and the way the model can be communicated and shared with others. Once catalogued, we then illustrate these challenges with a pedestrian model for emergency evacuation in central London, a hypothetical model of residential segregation model tuned to London data, and an agent-based residen- tial location model, for Greater London. The ambiguities posed by this new style of modelling are drawn out as conclusions, and the relative arbitrariness of such modelling highlighted.

Big data, smart cities and city planning:

I define big data with respect to its size but pay particular attention to the fact that the data I am referring to is urban data, that is, data for cities that are invariably tagged to space and time. I argue that this sort of data are largely being streamed from sensors, and this represents a sea change in the kinds of data that we have about what happens where and when in cities. I describe how the growth of big data is shifting the emphasis from longer term strategic planning to short-term thinking about how cities function and can be managed, although with the possibility that over much longer periods of time, this kind of big data will become a source for information about every time horizon. By way of conclusion, I illustrate the need for new theory and analysis with respect to 6 months of smart travel card data of individual trips on Greater London’s public transport systems.

Laws of population growth

An important issue in the study of cities is defining a metropolitan area, because different definitions affect conclusions regarding the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSAs), based on rules attempting to capture the notion of city as a functional economic region, and it is performed by using experience. The construction of MSAs is a time-consuming process and is typically done only for a subset (a few hundreds) of the most highly populated cities. Here, we introduce a method to designate metropolitan areas, denoted “City Clustering Algorithm” (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrats law of proportional growth, which postulates that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster by utilizing the CCA exhibits deviations from Gibrats law, and that the standard deviation decreases as a power law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, which are shown to arise from the existence of long-range spatial correlations in population growth. These results have sociopolitical implications, for example, for the location of new economic development in cities of varied size.

Exploring isovist fields: space and shape in architectural and urban morphology

The space that can be seen from any vantage point is called an isovist and the set of such spaces forms a visual field whose extent defines different isovist fields based on different geometric properties. I suggest that our perceptions of moving within such fields might be related to these geometric properties. I begin with a formal representation of isovists and their fields, introducing simple geometric measures based on distance, area, perimeter, compactness, and convexity. I suggest a feasible computational scheme for measuring such fields, and illustrate how we can visualize their spatial and statistical properties by using maps and frequency distributions. I argue that the classification of fields based on these measures must be a prerequisite to the proper analysis of architectural and urban morphologies. To this end, I present two hypothetical examples based on simple geometries and three real examples based on Londons Tate Gallery, Regent Street, and the centre of the English town of Wolverhampton. Although such morphologies can often be understood in terms of basic geometrical elements such as corridors, streets, rooms, and squares, isovist analysis suggests that visual fields have their own form which results from the interaction of geometry and movement. To illustrate how such analysis can be used, I outline methods of partitioning space, covering it with a small number of relatively independent isovists, and perceiving space by recording properties of the isovist fields associated with paths through that space.

Possible urban automata

New developments in computation based on cellular automata (CA), which are finding widespread application in simulating evolution, are beginning to suggest that science is not simply about the study of actual phenomena but about potential or possible phenomena. This notion is central to design but the prospect of a new science through computation which enables systematic and formal study of ‘possible worlds’ has clear relevance to the scientific understanding of human systems such as cities. In this paper, we provide a framework for such understanding based on a generic model of the dynamics of urban systems. After formally presenting the framework, we show how it can be used to generate existing model structures which can be seen as samples from a wide, indeed infinite, array of possible forms. In fact, the emphasis here is not just upon possible model structures per se but upon possible urban forms which such structures are able to generate. Accordingly we formulate models in terms of ideas from CA which treat space and time in its most disaggregate or local form. We begin by developing models both of areal and of linear growth processes and then combine these into a more general structure which forms the basis for a comprehensive model of urban structure. We illustrate the varieties of form which such models can generate, concluding by suggesting that such an approach might constitute the basis for more systematic exploration of the space within which possible urban morphologies exist.

Structure of Urban Movements: Polycentric Activity and Entangled Hierarchical Flows

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.

Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation

An increasing number of models for predicting land use change in rapidly urbanizing regions are being proposed and built using ideas from cellular automata (CA). Calibrating such models to real situations is highly problematic and to date, serious attention has not been focused on the estimation problem. In this paper, we propose a structure for simulating urban change based on estimating land use transitions using elementary probabilistic methods which draw their inspiration from Bayes’ theory and the related ‘weights of evidence’ approach. These land use change probabilities drive a CA model based on eight cell Moore neighborhoods implemented through empirical land use allocation algorithms. The model framework