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Hierarchy in Cities and City Systems

Hierarchy in Cities and City Systems,10.1007/1-4020-4127-6_7,Michael Batty

Hierarchy in Cities and City Systems   (Citations: 12)
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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 rank-size 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 self-similar, 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 top-down, centralized planning.
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    • ...In recent years, several urban and regional scientists (see inter alia Gabaix (1999); Eeckhout (2004); Batty (2006); Rossi-Hansberg 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 log-normal.’ 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. Portnovet al. Does Gibrat’s law for cities hold when location counts?

    • ...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; Suarez-Villa 1988; Pumain and Moriconi-Ebrard 1997; Gabaix 1999; Reed 2002; Ioannides and Overman 2003 ;K wok2004; Anderson and Ge 2005; Nitsch 2005; Batty 2006; Rossi-Hansberg 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 log-normal.’ Further, when truncated to remove the smaller localities, the rank-size relationship expected under Zipf’s Law holds...
    • ...Eeckhout 2004; Batty 2006; Rossi-Hansberg 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 space-time 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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