Papers of the Regional Science Association

, Volume 67, Issue 1, pp 55–69 | Cite as

Diffusion-limited aggregation and the fractal nature of urban growth

  • A. Stewart Fotheringham
  • Michael Batty
  • Paul A. Longley
Article

Abstract

This paper introduces the mechanism of diffusion-limited aggregation (DLA) as a new basis for understanding urban growth. Through DLA, urban form is related to the processes of rural-to-urban migration and contiguous growth. However, despite being based on very simple principles, DLA simulations are shown to have properties found in most urban areas such as negative density gradients and ordered chaotic structures. The paper examines variations in the simulated urban structures produced by different assumptions regarding the rural-to-urban migration mechanism. An important finding is that urban density gradients can occur independently of the generally accepted reasons for their presence. We also comment on boundary effects in the measurement of urban density gradients.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barnsley, M. F. 1988.Fractals everywhere. New York: Academic Press.Google Scholar
  2. Batty, M., Fotheringham, A. S., and Longley, P. 1989. Urban growth and form: scaling, fractal geometry and diffusion-linked aggregation.Environment and Planning A 21: 1447–72.Google Scholar
  3. Burgess, F. W. 1925. Growth of the city. InThe city, eds. R. E. Park, E. W. Burgess, and R. D. McKenzie, Chicago: University of Chicago Press, pp. 47–62.Google Scholar
  4. Clark, C. 1951. Urban population densities.Journal of the Royal Statistical Society, Series A 114: 490–96.Google Scholar
  5. Dutton, G. 1973. Criteria of growth in urban systems.Ekistics 215: 298–306.Google Scholar
  6. Harris, C. and Ullman, E. L. 1945. The nature of cities.Annals of the American Academy of Political and Social Science 242: 7–17.Google Scholar
  7. Hoyt, H. 1939. The structure and growth of residential neighborhoods in American cities. Washington, DC: Federal Housing Administration.Google Scholar
  8. Mandelbrot, B. B. 1982.The fractal geometry of nature. New York: Freeman.Google Scholar
  9. Meakin, P. 1983a. Diffusion-controlled cluster formation in two, three and four dimensions.Physical Review A 27: 604–7.Google Scholar
  10. Meakin, P. 1983b.Diffusion-controlled cluster formation in 2–6 dimensional space.Physical Review A 27: 1495–1507.Google Scholar
  11. Mills, E. S. 1970. Urban density functions.Urban Studies 7: 5–20.Google Scholar
  12. Mills, E. S. and Tan, J. P. 1980. A comparison of urban population density functions in developed and developing countries.Urban Studies 17: 313–21.Google Scholar
  13. Mullins, W. and Sekerka, R. 1963. Morphological stability of a particle growing by diffusion or heat flow.Journal of Applied Physics 34: 323–29.Google Scholar
  14. Muth, R. 1969.Cities and housing. Chicago: Chicago University Press.Google Scholar
  15. Newling, B. 1969. The spatial variation of urban population densities.Geographical Review 59: 242–52.Google Scholar
  16. Peitgen, H.-O. and Saupe, D. 1988. Eds.The science of fractal images. New York: Springer-Verlag.Google Scholar
  17. Sander, L. M. 1987. Fractal growth.Scientific American 256: 82–88.Google Scholar
  18. Stanley, H. E. and Ostrowsky, N. 1986. Eds.On growth and form: fractal and non-fractal patterns in physics. Dordrecht, The Netherlands: Martinus Nijhoff.Google Scholar
  19. Witten, T. A. and Sander, L. M. 1981. Diffusion-limited aggregation, a kinetic critical phenomenon.Physical Review Letters 47: 1400–3.Google Scholar
  20. Witten, T. A. and Sander, L. M. 1983. Diffusion-linked aggregation.Physical Review B 27: 5686–97.Google Scholar

Copyright information

© The Regional Science Association 1989

Authors and Affiliations

  • A. Stewart Fotheringham
    • 1
  • Michael Batty
    • 2
  • Paul A. Longley
    • 2
  1. 1.National Center for Geographic Information and Analysis and Department of Geography SUNY at BuffaloBuffalo
  2. 2.Department of Town PlanningUniversity of WalesCardiffUK

Personalised recommendations