Hierarchies in cities and city systems

Hierarchy is implicit in the very term city. Cities grow from hamlets andvillages into small towns and thence into larger forms such as ?metropolis?,?megalopolis? and world cities which are ?gigalopolis?. In one sense, allurban agglomerations are referred to generically as cities but this sequenceof city size from the smallest identifiable urban units to the largest containsan implicit hierarchy in which there are many more smaller cities thanlarger ones. This organisation approximately scales in a regular but simplemanner, city sizes following a rank-size rule whose explanation is bothmysterious and obvious. In this chapter, we begin with a simple but wellknownmodel of urban growth where growth is randomly proportionate tocity size and where it is increasingly unlikely that a small city becomesvery big. It is easy to show that this process generates a hierarchy which isstatistically self-similar, hence fractal but this does not contain anyeconomic interactions that we know must be present in the way cities growand compete. We thus modify the model adding mild diffusion and thennote how these ideas can be fashioned using network models whichgenerate outcomes consistent with these kinds of order and scaling. Wethen turn this argument on its head and describe how the same sorts ofmorphology can be explained using ideas from central place theory. Thesenotions are intrinsic to the way cities evolve and we conclude by notinghow city design must take account of natural hierarchies which groworganically, rather than being established using top-down, centralizedplanning

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

Space, scale, and scaling in entropy-maximising

Entropy measures were first introduced into geographical analysis during a period when the concept of human systems as being in some sort of equilibrium was in the ascendancy. In particular, entropy-maximising, in direct analogy to equilibrium statistical mechanics, provided a powerful framework in which to generate location and interaction models. This was introduced and popularised by Wilson (1970) and it led to many different extensions that filled in the framework rather than progressed it to different kinds of models. In particular, we review two such extensions here: how space can be introduced into the formulation through defining a ‘spatial entropy’ and how entropy can be decomposed and nested to capture spatial variation at different scales. Two obvious directions to this research, however, have remained implicit. First, the more substantive interpretations of the concept of entropy for different shapes and sizes of geographical systems have hardly been developed. Second, an explicit dynamics associated with generating probability distributions has not been attempted until quite recently with respect to the search for how power laws emerge as signatures of universality in complex systems. In short, the connections between entropy-maximising, substantive interpretations of entropy measures, and the longer term dynamics of how equilibrium distributions are reached and maintained have not been well-developed. This has many implications for future research and in conclusion, we will sketch the need for new and different entropy measures as well as new forms of dynamics that enable us to see how equilibrium spatial distributions can be generated as the outcomes of dynamic processes that converge to the steady state

Planning Support Systems: Progress, Predictions, and Speculations on the Shape of Things to Come

In this paper, we review the brief history of planning support systems, sketching the way both the fields of planning and the software that supports and informs various planning tasks have fragmented and diversified. This is due to many forces which range from changing conceptions of what planning is for and who should be involved, to the rapid dissemination of computers and their software, set against the general quest to build ever more generalized software products applicable to as many activities as possible. We identify two main drivers – the move to visualization which dominates our very interaction with the computer and the move to disseminate and share software data and ideas across the web. We attempt a brief and somewhat unsatisfactory classification of tools for PSS in terms of the planning process and the software that has evolved, but this does serve to point up the state-ofthe- art and to focus our attention on the near and medium term future. We illustrate many of these issues with three exemplars: first a land usetransportation model (LUTM) as part of a concern for climate change, second a visualization of cities in their third dimension which is driving an interest in what places look like and in London, a concern for high buildings, and finally various web-based services we are developing to share spatial data which in turn suggests ways in which stakeholders can begin to define urban issues collaboratively. All these are elements in the larger scheme of things – in the development of online collaboratories for planning support. Our review far from comprehensive and our examples are simply indicative, not definitive. We conclude with some brief suggestions for the future

Visualising space-time dynamics in scaling systems

The signature of scaling in human systems is the well-known power law whose key characteristic is that the size distributions of the elements or objects that comprise such systems, display self-similarity in space and time. In fact, in many of the systems such as cities, firms, and high buildings which we use as examples, power laws represent an approximation to the fat or heavy tails of their rank-size distributions, appearing to be stable in time showing little sign of changes in their scaling over tens or even hundreds of years. However when we examine the detailed dynamics of how their ranks shift in time, there is considerable volatility with the objects in such distributions not often persisting for longer than about 50-100 years. To explore this kind of micro-volatility, we introduce a number of measures of rank shift over space and time and visualise size distributions using the idea of the ‘rank clock’. We use the example of changes in the populations of Italian towns between 1300 and 1861 to introduce these ideas and then compare this analysis with city-size distributions for the World from 430BCE, the US from 1790, the UK from 1901, and Israel from 1950. The morphologies of growth and change displayed by these clocks are all quite different. When we compare these to the distribution of US firms from 1955 in the Fortune 500 and to the distribution of high buildings in New York City and the World from 1909, we generate a panoply of different visual morphologies and statistics. This provides us with a rich portfolio of space-time dynamics that adds to our understanding of how different systems can display stability and regularity at the macro level with a very different dynamics at the micro

Visualizing Creative Destruction

We introduce a series of methods for visualizing the dynamics of firmsize as indicative of the way the creation of new economic entitiesdestroy the existing order in the manner first sketched bySchumpeter (1938). We examine firm size distributions for every yearfrom 1955 to 1994 for the top 100 firms listed in the Fortune 500. Weshow that although rank-size distributions from this data areremarkably stable, this masks a much more detailed microdynamicswhere firms are changing their size and rank in the prevailing orderquite rapidly. These provide the signatures of creation anddestruction and to visualize their form, we introduce the idea of halflives, rank clocks and distance statistics which reveal a cornucopia ofdynamic behaviors. We first examine changes in firm size measuredby revenue earnings and then we contrast this with profits perearnings data which reveals another picture of these processes ofcreation and destruction. We introduce a series of methods for visualizing the dynamics of firmsize as indicative of the way the creation of new economic entitiesdestroy the existing order in the manner first sketched bySchumpeter (1938). We examine firm size distributions for every yearfrom 1955 to 1994 for the top 100 firms listed in the Fortune 500. Weshow that although rank-size distributions from this data areremarkably stable, this masks a much more detailed microdynamicswhere firms are changing their size and rank in the prevailing orderquite rapidly. These provide the signatures of creation anddestruction and to visualize their form, we introduce the idea of halflives, rank clocks and distance statistics which reveal a cornucopia ofdynamic behaviors. We first examine changes in firm size measuredby revenue earnings and then we contrast this with profits perearnings data which reveals another picture of these processes ofcreation and destruction

Network geography: relations, interactions, scaling and spatial processes in GIS

This chapter argues that the representational basis of GIS largely avoidseven the most rudimentary distortions of Euclidean space as reflected, forexample, in the notion of the network. Processes acting on networks whichinvolve both short and longer term dynamics are often absent from GIscience. However a sea change is taking place in the way we view thegeography of natural and man-made systems. This is emphasising theirdynamics and the way they evolve from the bottom up, with networks anessential constituent of this decentralized paradigm. Here we will sketchthese developments, showing how ideas about graphs in terms of the waythey evolve as connected, self-organised structures reflected in theirscaling, are generating new and important views of geographical space.We argue that GI science must respond to such developments and needs tofind new forms of representation which enable both theory andapplications through software to be extended to embrace this new scienceof networks

A new theory of space syntax

Relations between different components of urban structure are often measured in aliteral manner, along streets for example, the usual representation being routesbetween junctions which form the nodes of an equivalent planar graph. A popularvariant on this theme ? space syntax ? treats these routes as streets containing one ormore junctions, with the equivalent graph representation being more abstract, basedon relations between the streets which themselves are treated as nodes. In this paper,we articulate space syntax as a specific case of relations between any two sets, in thiscase, streets and their junctions, from which we derive two related representations.The first or primal problem is traditional space syntax based on relations betweenstreets through their junctions; the second or dual problem is the more usualmorphological representation of relations between junctions through their streets.The unifying framework that we propose suggests we shift our focus from the primalproblem where accessibility or distance is associated with lines or streets, to the dualproblem where accessibility is associated with points or junctions. This traditionalrepresentation of accessibility between points rather than between lines is easier tounderstand and makes more sense visually. Our unifying framework enables us toeasily shift from the primal problem to the dual and back, thus providing a muchricher interpretation of the syntax. We develop an appropriate algebra which providesa clearer approach to connectivity and distance in the equivalent graphrepresentations, and we then demonstrate these variants for the primal and dualproblems in one of the first space syntax street network examples, the French villageof Gassin. An immediate consequence of our analysis is that we show how the directconnectivity of streets (or junctions) to one another is highly correlated with thedistance measures used. This suggests that a simplified form of syntax can beoperationalized through counts of streets and junctions in the original street network

Complexity in city systems: Understanding, evolution, and design

6.4 Exemplars of complex systems There are many signatures of complexity revealed in the space-time patterning of cities (Batty, 2005) and here we will indicate three rather different but nevertheless linked exemplars. Our first deals with ..