Basins of attraction around large cities: A study of urban interaction spaces in Europe

Michal Dziecielski, Karima Kourtit*, Peter Nijkamp, Waldemar Ratajczak

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Web of Science)


The geographic dispersion and size distribution of cities seem, at first glance, to exhibit a random pattern. Clearly, physical geography, geo-political history and climatology shape irregular constraints and forms in the global pattern of urban evolution, so that an entirely regular spatial picture of cities and their interactions in space is not plausible. In the history of urban geography, regional science and spatial planning, several attempts have been undertaken to identify or derive organised or stylised structures in the seemingly chaotic system of real-world settlements. Examples are Central Place Theory, the Tinbergen-Bos models of hierarchical spatial systems, or Tellier's topo-dynamic corridors. The present paper seeks to offer a stylised and quantitative depiction of the relative spatial positions and spheres of influence of 14 large European cities in a geo-gravitational force field, based on detailed data on an extensive set of multidimensional indicators from the multi-annual GPCI (Global Power City Index) data set. Assuming an interconnected urban network, the paper tests and maps out the existence of gravitational interactions between urban agglomerations by producing impact fields of spatial attractors (basins of attraction) in the European urban system. This approach forms an illustration of the emerging Systemic Economic Geography (SEG). Given the multi-annual nature of our data, we address particularly the complex urban field dynamics using the principle of gravitational interactions. The dynamics of individual urban agglomerations is calculated and mapped out using Newton's second law of motion for a study on fractal geometry. This ‘neo-Newtonian’ approach is able to trace spatial spheres of influence of urban agglomerations, while the underlying algorithm allows to test the factors responsible for spatial resistance or geographic frictions. In this way, we can delineate the contours of a stylised map for the gravitational fields of cities with different size, distance frictions and geographical locations. The paper addresses in particular the effect of generalized friction parameters for a set of pluriform urban key characteristics on the gravitational urban arena in Europe. It turns out that size, relative spatial position, spatial friction and multidimensional urban moderator variables are responsible for the emergence of a complex and often disorganised urban spatial interaction field. Our analysis frames in a nutshell the principles of spatial attractors in the urban geography of our world, and of Europe in particular. Such ‘virtual reality’ experiments shed light on the dynamic complexity of urban systems.

Original languageEnglish
Article number103366
Number of pages15
Publication statusPublished - Dec 2021


  • Basins of attraction
  • Central Place Theory (CPT)
  • Entropy
  • Fractal modelling
  • Gravitational fields
  • Gravity model
  • LAWS
  • Rank size
  • Spatial equilibrium
  • Systemic Economic Geography (SEG)


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