Quantitative prediction of the characteristic wavelength in slum pattern formation

Derive and validate a quantitative estimate of the dominant wavelength λ predicted by the reaction–diffusion migration model for rich–poor interactions, and assess whether this theoretical value matches the empirically observed characteristic scale of morphological slum sizes across cities.

Background

The review reports that morphological slum sizes across diverse cities tend to cluster around a characteristic area and edge length, suggesting a common spatial scale potentially arising from a Turing-type instability in a reaction–diffusion model of migration between socio-economic groups.

Although the mechanism yields a dominant wavenumber and corresponding wavelength λ in principle, the authors note that a concrete quantitative estimate of λ has not been provided, leaving unresolved whether the theory can predict the empirically observed scale of slum units.