Abstract
It is a remarkable fact that the size of slums is similar across the globe, regardless of city, country, or culture [Friesen et al., Habitat Int. 73, 79 (2018)0197-397510.1016/j.habitatint.2018.02.002]. The main thesis of this paper is that this universal scale is intrinsic to the slum-city system and is independent from external factors. By interpreting reaction and diffusion as long- and short-distance migration, our paper explains this universal length scale as resulting from a Turing instability of the interaction of two social groups: poor and rich.
Highlights
Friesen et al [1] point out that slums in Mumbai, India; Manila, the Philippines; Cape Town, South Africa; and Rio de Janeiro, Brazil all show the same scale, independent from city, country, or culture: on average, a slum occupies an area of 15 800 m2, i.e., the length scale is φ ≈ 125 m; cf
By using the Turing mechanism to model the similar sizes of slums, the concept of continuum mechanics is transferred to urban modeling
The solution of the equation leads to a regular concentration distribution with wavelength λ = 2π/k depending on the Jacobian aij and the diffusion ratio d
Summary
Friesen et al [1] point out that slums in Mumbai, India; Manila, the Philippines; Cape Town, South Africa; and Rio de Janeiro, Brazil all show the same scale, independent from city, country, or culture: on average, a slum occupies an area of 15 800 m2, i.e., the length scale is φ ≈ 125 m; cf. Table I. There are plenty of different models to describe slum formation using cellular automata or agentbased models [2,3] Many of these models try to describe the development of slums with an ever increasing number of influencing factors. We hypothesize that the intraurban pattern can be explained by a Turing instability [7] occurring through the interaction of two social groups: rich and poor. By using the Turing mechanism to model the similar sizes of slums, the concept of continuum mechanics is transferred to urban modeling This approach has some limitations and is not sufficient to describe all aspects of the phenomenon of slum emergence, the major characteristics can be modeled
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