Proximity based city growthProximity based city growth Diego Rybski, Anselmo García Cantú Ros,...
Transcript of Proximity based city growthProximity based city growth Diego Rybski, Anselmo García Cantú Ros,...
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Proximity based city growth
Diego Rybski,
Anselmo García Cantú Ros, Jürgen P. Kropp
SOE 18.4DPG Frühjahrstagung 2012Berlin, H 011029.3.2012 – 11:00
DPG Frühjahrstagung 2012 – SOE 18: Traffic Dynamics, Urban and Regional Systems II
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Motivation
B.J.L. Berry & A. Okulicz-Kozaryn 2011:
- identify different epochs of research on city size distributions + An interesting empirical regularity (1913-1936) + Zipf's Law (1939-...) + Building a body of theory + A stochastic steady-state + Contemporary contentions
- raise three questions: 1. What are the appropriate units of observation? 2. Do the growth rates obey Gibrat's law? 3. Does Zipf's Law apply in the upper tail?
1.+2. Rozenfeld et al., PNAS, 20081.+3. Rozenfeld et al., AER, 2011City Clustering Algorithm (CCA)
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Great Britain
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Greater London
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First Law of Geography
“Everything is related to everything else, but near things are more related than distant things.”
(W.R. Tobler 1970)
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Gravitation Concepts
G.A.P. Carrothers (1956): “An Historical Review of the Gravity and Potential Concepts of Human Interaction”
W.J. Reilly's law (1931): breaking point of boundary of equal attraction
D.L. Huff's law (1963/64): shopper attraction
P. Pöyhönen (1963): “A Tentative Model for the Volume of Trade between Countries”
[F. Simini (2012): “A universal model for mobility and migration patterns”]
… we reexamine the gravitation concept
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Approach
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Example630 x 630γ=2.5
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example
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Example … end
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γ=1.5 i=2 γ=2.0 i=5
γ=2.5 i=10 γ=3.0 i=17
Exponent
- small exponent fills faster
- large exponent more compact
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Percolation transition maximum in the number of clusters
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1 configurationlargestcomponent boundary
disregardinginclusions
Boundary
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Fractal dimension of boundary:box covering
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Cluster size distribution (without largest)
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Summary
Simple & intuitive approach
Fractal boundaryZipf's law
more work necessary
for characterization
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Thank you for your attention.
http://diego.rybski.de/
http://www.pik-potsdam.de/members/rybski/
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