Journal of Geographical Systems

, Volume 13, Issue 1, pp 1–16

Phase transitions and path dependence in urban evolution

Original Article

DOI: 10.1007/s10109-010-0134-4

Cite this article as:
Wilson, A. & Dearden, J. J Geogr Syst (2011) 13: 1. doi:10.1007/s10109-010-0134-4


There is a long history of recognising and interpreting discontinuous change—phase transitions—in urban systems. In this paper, we use the aggregate retail model as an archetype to explore some new ideas. For example, we argue that the dependence of paths of development on initial conditions has been understudied, and we offer a new graphical analysis that demonstrates explicitly their influence on discrete change. We introduce an order parameter, and we plot this on a ‘results grid’ to facilitate the discovery of possible phase transitions. We illustrate the use of these new developments with an application to London. We show how retail developers can change the ‘initial conditions’ at a point in time and possibly bring about phase transitions by their actions. This also shows that it should be possible to account for the history of urban development as a sequence of initial conditions, illustrating path dependence. Secondly, the model could be deployed in relation to a new shopping zone, and the tools developed here used to calculate the minimum size of a new development in order for it to compete. We explore the ‘minimum size’ idea in relation to a new shopping zone in London.


Urban evolution Urban models Phase transitions Path dependence 

JEL Classification


Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Centre for Advanced Spatial AnalysisUniversity College LondonLondonUK

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