City Shape and the Fractality of Street Patterns

Nahid Mohajeri 1 , Paul Longley 1  and Michael Batty 1
  • 1 Department of Geography and Centre for Advanced Spatial Analysis, University College London, UK

City Shape and the Fractality of Street Patterns

This paper discusses, first, the concepts of fractals and power laws in relation to the street patterns of the city of Dundee, East Scotland and, second, the results of the measurement of 6,004 street segments in the city. The trends of the street segments are presented through rose diagrams and show that there are two main street trends in the city: one is parallel with the coast, the other is roughly perpendicular to the coast. It is clear that the coastline largely regulates the street trend, because both the main street trends change along the city so as to be nearly coast-perpendicular and coast-parallel everywhere. The lengths of the street segments follow power laws. When presented on log-log plots, however, the result is not a single straight line but two straight lines. At the break in line slope, the fractal dimension changes from 0.88 to 2.20. The change occurs at the step length of about 100 m, indicating that the short streets belong to a population that is different from that of the longer streets.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Alexander C., 1964. Notes on the synthesis of form. Harvard University Press, Cambridge MA.

  • Alexander C., 2000. The nature of order. Oxford University Press, New York.

  • Barabási A.L. & Bonabeau E., 2003. Scale-free networks. Scientific American, 288(5): 50-59.

  • Batty M., 2005. Cities and complexity. MIT Press, London.

  • Batty M. & Longley P., 1994. Fractal cities: A geometry of form and function. Academic Press, London.

  • Bovill C., 1996. Fractal geometry in architecture and design. Birkhauser Verlag A.G., Boston.

  • Brown C. & Liebovitch L., 2010. Fractal analysis. SAGE Publications, USA.

  • Clauset A., Chalizi R.C. & Newman M.E.J., 2009. Power-law distributions in empirical data. SIAM Review, 51(4): 661-703.

  • Geddes P., 1915. Cities in evolution: An introduction to the town planning movement and to the study of civics. Benn, London (1968 edition).

  • Hillier B., 1999. The hidden geometry of deformed grids. Environment and Planning, B, 26: 169-191.

  • Jacob J., 1961. The death and life of great American cities. Vintage Books, New York.

  • Mandelbrot B., 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, 156: 636-638.

  • Mandelbrot B., 1982. The fractal geometry of nature. W.H. Freeman and Company Press, New York.

  • Newman M.E.J., 2005. Power laws, Pareto distributions and Zipf's law. Contemporary Physics, 46: 323-351.

  • Newman M.E.J., 2010. Network: An introduction. Oxford University Press, Oxford.

  • Ratajczak W., 1998. Metodologiczne aspekty fraktalnego modelowania rzeczywistości (Methodological aspects of a fractal modelling of reality). Zakład Graficzny UAM, Poznań.

  • Richardson L.F., 1961. The problems of contiguity: An appendix of statistics of deadly quarrels. General Systems Yearbook, 6: 139-187.

  • Salingaros N.A., 2003. Connecting the fractal city. University of Texas at San Antonio, USA.

  • Salingaros N.A., 2005. Principles of urban structure. Techne Press, Amsterdam.

  • Schroeder M.R., 2009. Fractals, chaos, power laws. Dover, New York.

  • Smith M.J., Goodchild M.F. & Longley P., 2009. Geospatial analysis: A comprehensive guide to principles, techniques and software tools. 3rd edition. Troubador Publishing Ltd., UK.

  • Sornette D., 2006. Critical phenomena in natural sciences. Springer, Berlin.

  • Stewart J.Q., 1950. The development of social physics. American Journal of Physics, 18: 290-253.

  • Swan A.R.H. & Sandilands M., 1995. Introduction to geological data analysis. Blackwell, Oxford.

  • Turcotte D.L., 1997. Fractals and chaos in geology and geophysics. 2nd ed. Cambridge University Press, Cambridge.

  • Wolfgang E.L., 2003. Fractal and fractal architecture. PhD thesis, Vienna University of Technology, Vienna.

  • Zipf G.K., 1949. Human behaviour and the principle of least effort: An introduction to human ecology. Addison-Wesley, Cambridge.


Journal + Issues