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Alternative Explanations of Hierarchical Differentiation in Urban Systems
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Hierarchy in Cities and City Systems
Hierarchy in Cities and City Systems,10.1007/1402041276_7,Michael Batty
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Hierarchy in Cities and City Systems
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Citations: 12
)
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Michael Batty
Hierarchy is implicit in the very term city. Cities grow from hamlets and villages into small towns and thence into larger forms such as 'metropolis', 'megalopolis' and world cities which are 'gigalopolis'. In one sense, all urban agglomerations are referred to generically as cities but this sequence of city size from the smallest identifiable urban units to the largest contains an implicit hierarchy in which there are many more smaller cities than larger ones. This organisation approximately scales in a regular but simple manner, city sizes following a ranksize rule whose explanation is both mysterious and obvious. In this chapter, we begin with a simple but well known model of
urban growth
where growth is randomly proportionate to city size and where it is increasingly unlikely that a small city becomes very big. It is easy to show that this process generates a hierarchy which is statistically selfsimilar, hence fractal but this does not contain any economic interactions that we know must be present in the way cities grow and compete. We thus modify the model adding mild diffusion and then note how these ideas can be fashioned using network models which generate outcomes consistent with these kinds of order and scaling. We then turn this argument on its head and describe how the same sorts of morphology can be explained using ideas from central place theory. These notions are intrinsic to the way cities evolve and we conclude by noting how city design must take account of natural hierarchies which grow organically, rather than being established using topdown, centralized planning.
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10.1007/1402041276_7
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Citation Context
(8)
...In recent years, several urban and regional scientists (see inter alia Gabaix (1999); Eeckhout (2004);
Batty (2006)
; RossiHansberg and Wright (2007); Córdoba (2008)) investigatedtherelationshipbetweenGibrat’sandZipf’slaws,withGabaix(1999)goingasfarastosuggest that Zipf’s law is a ‘natural’ outcome of Gibrat’s law...
...11 Using computer simulations,
Batty (2006)
showed that even for an initial uniformly distributed population and randomly chosen growth rates, the size distribution of individual localities tends to show ‘every sign of being lognormal.’ 12 Gabaix (1999) takes a strict view of Gibrat’s law, requiring that the entire probability distribution of the growth process (and not only the expected value and variance) should not depend on city size...
Boris A. Portnov
,
et al.
Does Gibrat’s law for cities hold when location counts?
...,
...
Camille Roth
,
et al.
Structure of Urban Movements: Polycentric Activity and Entangled Hiera...
...According to this law, if all cities of a country are ordered from the smallest to the largest, the logarithm of a city’s rank is expected to be in a linear relationship with the logarithm of the city’s size (Nitsch 2005; Soo 2005;
Batty 2006
)...
...Numerous empirical studies have been carried out to date to investigate the validity of this law (see inter alia Fonseca 1988; SuarezVilla 1988; Pumain and MoriconiEbrard 1997; Gabaix 1999; Reed 2002; Ioannides and Overman 2003 ;K wok2004; Anderson and Ge 2005; Nitsch 2005;
Batty 2006;
RossiHansberg and Wright 2007;...
...In another recent paper based on computer simulations,
Batty (2006)
showed that even for an initial uniformly distributed population and randomly chosen rates of growth, the size distribution of individual localities tends to show ‘every sign of being lognormal.’ Further, when truncated to remove the smaller localities, the ranksize relationship expected under Zipf’s Law holds...
...Eeckhout 2004;
Batty 2006;
RossiHansberg and Wright 2007; Córdoba 2008; Portnov et al. 2010) investigated the relationship between Zipf’s Law and another empirical regularity known as Gibrat’s Law, according to which the population growth of cities is strictly proportional to their sizes, with Gabaix (1999) going as far as to suggest that Zipf’s law is a ‘natural outcome’ of Gibrat’s Law...
Boris A. Portnov
.
Does Zipf’s law hold for primate cities? Some evidence from a discrimi...
...However, when adapted to a network where the size of the node grows using proportionate effect and adding network links from which such effects emanate, similar scaling distributions for the size of the hubs emerge (
Batty, 2006b
)...
...We do not show the distance clock here (see
Batty, 2006b
) but distance is defined as...
Michael Batty
.
Visualizing spacetime dynamics in scaling systems
...From the inter‐city hierarchy to intra‐city hierarchy, it reminds us of a recursive definition of a complex system, which reads as ‘a system that is composed of complex systems’ (Batty
2006
)...
Bin Jiang
.
Street hierarchies: a minority of streets account for a majority of tr...
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Journal:
The Journal of Artificial Societies and Social Simulation  JASSS
, vol. 6, no. 2, pp. 7172, 2003
Zipf'S Law For Cities: An Explanation
(
Citations: 377
)
Xavier Gabaix
Journal:
Quarterly Journal of Economics  QUART J ECON
, vol. 114, no. 3, pp. 739767, 1999
Alternative Explanations of Hierarchical Differentiation in Urban Systems
(
Citations: 3
)
Denise Pumain
On a Class of Skew Distribution Functions
(
Citations: 562
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Herbert A. Simon
Published in 2007.
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Citations: 468
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D. Sornette
Published in 2000.
Sort by:
Citations
(12)
Does Gibrat’s law for cities hold when location counts?
(
Citations: 1
)
Boris A. Portnov
,
Ben Reiser
,
Moshe Schwartz
Journal:
Annals of Regional Science  ANN REG SCI
, vol. 45, no. 2, pp. 128, 2012
Structure of Urban Movements: Polycentric Activity and Entangled Hierarchical Flows
Camille Roth
,
Soong Moon Kang
,
Michael Batty
,
Marc Barthélemy
Journal:
PLOS One
, vol. 6, no. 1, 2011
Does Zipf’s law hold for primate cities? Some evidence from a discriminant analysis of world countries
Boris A. Portnov
Published in 2011.
Visualizing spacetime dynamics in scaling systems
Michael Batty
Journal:
Complexity
, vol. 16, no. 2, pp. 5163, 2010
Street hierarchies: a minority of streets account for a majority of traffic flow
(
Citations: 12
)
Bin Jiang
Journal:
International Journal of Geographical Information Science  GIS
, vol. 23, no. 8, pp. 10331048, 2009