Complexity and emergence in city systems: implications for urban planning

Cities can be regarded as the quintessential example of complexity. Insofar as we can define a hidden hand determining their morphology, this is based on the glue that stitches together the actions of individuals and organizations who build and plan the city from the ground-up, so-to-speak. When general systems theory entered the lexicon of science in the mid-20th century, cities were regarded as being excellent examples of systems with interactions between basic elements that demonstrated the slogan of the field: the ‘whole is greater than the sum of the parts’. Since then, as complexity theory has evolved to embrace systems theory and as temporal dynamics has come onto the agenda, cities once again have been used to illustrate basic themes: global organization from local action, emergent morphology from simple spatial decision, temporal order at global levels from volatile, seemingly random change at the level of individual decision-making, evolution and progress through co-evolution, competition, and endless variety. Here we will sketch these ideas with respect to cities illustrating particularly three key ideas which involve the tension between continuously changing systems, qualitative transformations, and radical change based on emergent properties of the whole. Our analysis has many implications for a new theory of urban planning which is built from the bottom up, rather than from the top down which is the traditional way in which such interventions are currently carried out in the name of making better cities. Contemporary problems such as ethnic segregation, urban sprawl, traffic congestion, urban decline, and regeneration are all informed by the perspective on complexity theory that we bring to bear her

Agent-based pedestrian modelling

When the focus of interest in geographical systems is at the very fine scale, at the level of streets and buildings for example, movement becomes central to simulations of how spatial activities are used and develop. Recent advances in computing power and the acquisition of fine scale digital data now mean that we are able to attempt to understand and predict such phenomena with the focus in spatial modelling changing to dynamic simulations of the individual and collective behaviour of individual decision-making at such scales. In this Chapter, we develop ideas about how such phenomena can be modelled showing first how randomness and geometry are all important to local movement and how ordered spatial structures emerge from such actions. We focus on developing these ideas for pedestrians showing how random walks constrained by geometry but aided by what agents can see, determine how individuals respond to locational patterns. We illustrate these ideas with three types of example: first for local scale street scenes where congestion and flocking is all important, second for coarser scale shopping centres such as malls where economic preference interferes much more with local geometry, and finally for semi-organised street festivals where management and control by police and related authorities is integral to the way crowds move

The Linear City: illustrating the logic of spatial equilibrium

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

Integrating space syntax with spatial interaction

In this paper, we attempt to compare space syntax with spatial interaction. At one level, these two approaches to urban spatial structure are non-comparable. Space syntax is largely a descriptive technique for visualising spatial relations at the level of connections between places while spatial interaction is a predictive model that forecasts how much travel there will be between places. Space syntax articulates the system in terms of whether or not a physical link, usually at the level of the street, exists while spatial interaction predicts movements between all origins and destinations which are places often anchored in terms of the street network, but which at the level of prediction, assume connections between all places. Space syntax is grounded at a fine spatial scale while spatial interaction defines places as aggregates of activity in larger zones than the scale of the street system. The main output of space syntax is a connectivity matrix of step lengths between streets whereas in spatial interaction, such networks are predetermined, measurable in terms of Euclidean distance or generalised cost of travel, and the output is the volume of travel prior to this being assigned usually to a street network. There is however a fundamental way of relating the implicit network graph of spatial interaction to the explicit planar graph of the street network. We begin by assuming the planar graph of the network is conceived of as a primal problem of spatial interaction while the dual graph linking streets in the planar graph is the graph which is used in space syntax. We exploit this duality and show how we can move easily between spatial interaction as the primal and space syntax as the dual. This is rooted in a more fundamental graph – the bipartite graph which is a list of streets/arcs and their intersections/nodes from which the primal and dual emerge naturally. We explore various accessibility measures and show how they relate and correlate. We then go one step further and consider how various processes of random walking take place in these networks examining the steady states of the primal and dual problems in terms of the likelihood of a random walker visiting any node or street. We thus define primal and dual Markov chains that enable us to generate these probabilities. This provides a basic framework for comparing primal and dual in comparing spatial interaction with space syntax. We illustrate these measures on simple and easy to articulate graphs, extending this to a synthetic network of nearest neighbour links in Greater London based on 699 nodes and 1972 symmetric ‘streets’ between zones. This is a preliminary attack on the problem of linking these two approaches although many challenges remain

Paradoxical Interpretations of Urban Scaling Laws

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the same territory, time and attribute, depending on the criteria used to delineate cities. The aim of this paper is to present new insights concerning this variation, coupled with a sensitivity analysis of urban scaling in France, for several socio-economic and infrastructural attributes from data collected exhaustively at the local level. The sensitivity analysis considers different aggregations of local units for which data are given by the Population Census. We produce a large variety of definitions of cities (approximatively 5000) by aggregating local Census units corresponding to the systematic combination of three definitional criteria: density, commuting flows and population cutoffs. We then measure the magnitude of scaling estimations and their sensitivity to city definitions for several urban indicators, showing for example that simple population cutoffs impact dramatically on the results obtained for a given system and attribute. Variations are interpreted with respect to the meaning of the attributes (socio-economic descriptors as well as infrastructure) and the urban definitions used (understood as the combination of the three criteria). Because of the Modifiable Areal Unit Problem and of the heterogeneous morphologies and social landscapes in the cities internal space, scaling estimations are subject to large variations, distorting many of the conclusions on which generative models are based. We conclude that examining scaling variations might be an opportunity to understand better the inner composition of cities with regard to their size, i.e. to link the scales of the city-system with the system of cities