Scaling Laws in City Growth: Setting Limitations with Self-Organizing Maps

Abstract

Do scaling relations always provide the means to anticipate the relationships between the size of cities, costs of maintenance, and the socio-economic benefits resulting from their growth? Scaling laws are considered a universal principle that describes the development of complex systems such as cities. It seems that regardless of their location or history, the growth of cities is associated with the super-linear or sublinear scaling of features such as the amount of space required, infrastructure, or human activities. However, the results of our research, based on grouping by Self-Organizing Maps, reveal some limitations in the application of scaling laws: the trends of urban growth behave in a different manner when we consider both a large and diverse collection of cities and a subset of cities alike. This finding complements the existing body of knowledge on the growth of cities and allows for a more accurate prediction of their future.

Urban scaling, geography, centrality: Relation with local government structures

“…This figure shows that apart from the usual statistical errors there is another source of uncertainty in the measurement of scaling in an entire country: the set of cities for which the scaling is calculated may consist of different subsets (which together form the entire set) each with their own scaling. This effect is for instance clearly present in the scaling of Polish cities where the authors show that when dividing the entire set into two subsets according to specified criteria, the scaling of the entire set differs significantly from the scaling of two subsets separately [25]. Thus the measured scaling is sensitive to the delineation of a set of specific entities (cities, Kreise).…”

“…This is a new and little explored approach: two scaling systems are compared not only in terms of the scaling exponent, but also in terms of the differences in the gross urban product. Recent work in this context relates to scaling and differences in GUP for two groups of Indian cities a [ 24 ], and to scaling and differences in GUP for two groups of Polish cities [ 25 ]. Similar comparative analyses are scaling and differences in number of homicides for two groups of Indian cities [ 26 ], scaling and difference in the number of domestic electricity connections for two groups of Indian cities [ 27 ], and scaling and differences in number of votes in US and UK urban agglomerations for two different parties [ 28 ].…”

Explaining transit expenses in US urbanised areas: Urban scale, spatial form and fiscal capacity

“…They argue further that deviation from the norm defined by these scaling laws is sub-optimal (Bettencourt and West, 2010; Bettencourt et al, 2007). Recent work casts doubt on the robustness of scaling law predictions when applied to variation across place and time within a single country (Cebrat and Sobczyński, 2016). We believe that there are several potential problems with the application of this theory to explain patterns of urban infrastructure, and with its prediction of sub-linear growth of infrastructure relative to population.…”

Information Extraction and Population Estimates of Settlements from Historic Corona Satellite Imagery in the 1960s

“…Scaling laws and the associated power models have been widely used to model the relationship between urban settlement area and population [ 51 ]; however, scaling relationships may not apply to small settlements like villages [ 52 ]. This is because settlements with higher densities lead to increasingly structured land use and the segregation of buildings, roads and other infrastructure [ 52 , 53 ]. For this reason, apart from the power model, we tested the exponential model as well.…”