Environment and Planning B: Urban Analytics and City Science

Integration with geographic information systems (GIS) has helped move cellular automata (CA)-based urban and regional models from the realm of instructive metaphors to that of potentially useful qualitative forecasting tools. Such models can now be fully interactive for exploratory purposes and they can be based on actual data. New problems, however, arise as the formal integrity of the original CA framework is lost through successive relaxations of the assumptions and as the resulting complicated models become increasingly difficult to implement and understand. In this paper I propose that the theoretical problem can find a satisfactory answer in the notion of proximal space and the practical one can be handled successfully within the formalism of geo-algebra, a mathematical expression of proximal space which builds a bridge between GIS data and operations, on the one hand, and traditional robust classes of urban and regional models, on the other.

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.

The model presented in this paper is an attempt to reexamine spatial dynamics in the light of new concepts and techniques. Among these, cellular automata and parallel processing should contribute to revitalize dynamical studies in the geographical space and deserve consideration. A complete modeling framework is first discussed; then a model consisting of a cellular automaton associated with several distributive functions is described. This model, applied to the von Thünen scheme, shows that a distance function combined with a strong neighborhood effect could produce patterns similar to that expected under the conditions of the classical von Thünen model.

Since the seminal paper by Hotelling (1929) the principle of minimum differentiation has been accepted as one of the basic principles of theoretical and mathematical approaches to competitive location problems. However, despite its popularity, the principle is not robust: if the assumptions underlying the model are relaxed, the principle could be invalid. In this paper we propose an extension of the Hotelling model in the sense that more than two competitors are allowed and the space of the competition is a bidimensional discrete lattice. The discrete grid represents a product space where each firm locates a differentiated product. Competition is based on location only and each competitor can relocate in a finite subset of feasible locations, whenever it is advantageous. Given the discreteness of the space and the deterministic decision rule given to agents, the overall system can be seen as a specification of a cellular automaton. Cellular automata are dynamic systems capable of exhibiting the same kind of dynamics as partial differential equations. Furthermore, in some cases they seem to be capable of represening other behaviours, not detectable in systems of differential equations, such as self-organization. The results of some simulations are discussed both in terms of cellular automaton behaviour and in relation to other works reported in the literature. It was found that the dynamics of the system are quite regular and self-organization emerges.

Contemporary geographic information systems (GIS) suffer from a variety of problems, These include poor performance for many operators, poor ability to handle dynamic spatial models, and poor handling of the temporal dimension. Cellular automata (CA) have much in common with raster GIS and also excel in many of the areas in which GIS are deficient. Specifically, CA provide explicit handling of dynamic spatial models and time. In addition, if special hardware—cellular automata machines—are used, the potential for considerable performance benefits exists. Many spatial analytical operators behave, in effect, as CA, with the specific GIS functions representing the CA transition rules. Examples of such operations include filtering and diffusion. If the spatial operators are considered to be CA, an improved ability to characterize the operators mathematically is achieved, resulting in an improved dynamic spatial modeling ability. In this research the similarities between the two models (GIS and CA) are examined and the ability to implement each in the other is demonstrated. In addition, the advantages of integration of the two systems, by means of a cellular automata machine as the analytical engine for GIS, are discussed.

We present an integrated model of regional spatial dynamics consisting of a cellular automaton-based model of land use linked both to a geographic information system (GIS) and to standard nonspatial models of regional economics and demographics, as well as to a simple model of environmental change. The operation of the model is illustrated with an application to the island of St Lucia developed for the purpose of providing insights into the possible socioeconomic consequences for the island of global climate change. On the basis of results from this and other applications of the model, we conclude that cellular automata not only permit a detailed modelling and realistic prediction of land-use patterns, but they also provide a means of introducing the effects of spatially localized environmental factors, as represented in the GIS, into the operation of standard economic and demographic models, which are otherwise unconstrained.

In this paper we describe a cellular automaton (CA) simulation model developed to predict urban growth as part of a project for estimating the regional and broader impact of urbanization on the San Francisco Bay area's climate. The rules of the model are more complex than those of a typical CA and involve the use of multiple data sources, including topography, road networks, and existing settlement distributions, and their modification over time. In addition, the control parameters of the model are allowed to self-modify: that is, the CA adapts itself to the circumstances it generates, in particular, during periods of rapid growth or stagnation. In addition, the model was written to allow the accumulation of probabilistic estimates based on Monte Carlo methods. Calibration of the model has been accomplished by the use of historical maps to compare model predictions of urbanization, based solely upon the distribution in year 1900, with observed data for years 1940, 1954, 1962, 1974, and 1990. The complexity of this model has made calibration a particularly demanding step. Lessons learned about the methods, measures, and strategies developed to calibrate the model may be of use in other environmental modeling contexts. With the calibration complete, the model is being used to generate a set of future scenarios for the San Francisco Bay area along with their probabilities based on the Monte Carlo version of the model. Animated dynamic mapping of the simulations will be used to allow visualization of the impact of future urban growth.

By conceiving the city as a self-organizing system, we highlight and examine three interrelated phenomena of residential sociospatial segregation in a city: the gap which exists between intentions, preferences, and motives, on the one hand, and actual spatial behavior, on the other; the existence and role of local regions of instability within an otherwise stable urban system; and the conjunction between these two phenomena and the processes related to the emergence of new sociospatial entities. We examine the interplay between these interrelated urban phenomena and illustrate their role in urban dynamics. The discussion throughout the paper is elaborated partly by reference to empirical evidences but mainly by means of ‘city games’ played on a heuristic model (City-2) designed specifically for this purpose. City-2 can be described as a two-layer model composed of a migration submodel, which describes the intercity and intracity migration movements, superimposed on a cellular automata (CA) submodel describing the dynamics of the urban landscape itself. City-2 elaborates on, and extends, two previous heuristic models designed by us: (a) City, which is a probabilistic CA simulation model designed to examine the sociospatial relations between large social groups in a city, and (b) City-1, a planning-oriented cell-space model which introduced, in addition to the sociocultural properties of individuals, their economic status and the changing land value surface of the city.

SIMPOP is a knowledge-based simulation system for the description of the evolution of settlement patterns over long time periods. Rules and parameters are introduced into a multiagent systems formalism where each settlement is considered as a separate entity interacting with the others and transforming itself. The rules may allow for the simulation of the ‘urban transition’ from a set of homogeneous, agriculture-oriented, and scattered villages into a complex system of functionally diverse, competing, and hierarchised urban settlements. In this paper we show how several modifications of rules and parameters alter further the spatial and hierarchical structure of the simulated urban system.