Friday, July 10, 2009

Urban Growth Patterns

“Are there laws which determine the number, size, and distribution of towns?”

W. CHRISTALLER





MAKSE et al. Developped in the 90s a mathematical model (Correlated Percolation Model) that relates the pysical form of a city and the system within which it exits. This was based on the ideas of percolation theory and they took into account two key points.


First, data on population density of actual urban systems are known to conform to the relation ρ(r)= ρ0e-λr where r is the radial distance from the urban core, and λ is the density gradient.


Second, in actual urban systems, the development units are not positioned at random. Rather, there exist correlations arisin from the fact that when a development unit is located in a given place, the probability of adjacent development units increases. The next figure shows a qualitatie comparison between the actual urban data and the proposed model.



In addition to the strongly correlation between the morphology of actual urban areas and the urban systems obtained in our simulation, the dynamics of the model shows a remarkable pattern of decentralization, a phenomena that occurs in most of the cities in the world.



The use of fractal or chaotic models leads us to view cities as self-organized systems by local actions instead of designs for a centralized intelligence. This fact could give us a wide variety of valuable information concerning the way cities grow and change, and more importantly, the way they might be planned and managed.

5 comments:

  1. hi! congratulations for your blog!
    i really think that this model can be very interesting. but don't forget that the city is not only a mathematical system, it's also a sociological one and sociology is not an exact science, so the city can always do something very different from what you expect. for example in east germany the cities are decreasing nowdays because of the unemployment.
    thanks.
    iñaki

    ReplyDelete
  2. Hi Iñako!

    Thanks for your comment. I agree with your two points.

    First, this mathematical model is just one more feature that helps us to understand the urban ecosystem.

    The second point you discussed is also very interesting too. Besides the decreasing that is showing in cities like Detroit, in this very moment there are still plenty of big cities in developing countries which are growing, maybe you are in one of them...

    ReplyDelete
  3. you're right. lima is a growing system. but there is no "eco" in this system.
    if you want to know it better, i can make advertisment: injaki.blogspot.com
    ; ) thanks. bye bye.

    ReplyDelete
  4. Hey Ramiro, Great work...
    I am really interested in your article "urban complexity: Urban Growth Patterns". I would like to read more about the references from where you got all the information. My email is humairahfarooqui@gmail.com

    thanks.

    ReplyDelete
  5. hi
    you done good work
    I am really interested in your article "urban complexity: Urban Growth Patterns".
    becoz. now a days i have also work on this topic "spatial pattern of urban growth in Faisalabad Pakistan" plz end me your full artical. I would like to read more about the references from where you got all the information. My email is nasarbhalli@yahoo.com

    thanks.

    ReplyDelete