Is segregation encoded in urban form? An entropy-based analysis
For urban planners and sociologists, this work provides a novel quantitative framework linking physical urban form to social segregation, though the findings are specific to São Paulo and may not generalize.
The study investigates whether urban form encodes residential segregation by quantifying built-form entropy (BFE) in São Paulo. It finds non-linear relationships: income and clustering increase at both extremes of the entropy spectrum, with a stronger effect at high-entropy ends, indicating that built form both reflects and reinforces segregation.
The footprints of residential segregation have long been documented, yet the role of urban form as both medium and manifestation of segregation remains under-specified. We investigate whether the configuration of the built fabric may encode residential segregation in its spatial structure, hypothesising that built-form entropy (BFE) regimes are associated with the spatial distribution of income groups and their local clustering in non-linear ways. We examine this by quantifying BFE through a Shannon-based measure computed from building footprints, characterising income-based distributions using the Gini index and Moran's I, and placing both on a common spatial footing through a regular tessellation. Applying this framework to Sao Paulo, Latin America's largest city, we find non-linear relationships between BFE, income, and segregation: income levels and residential clustering increase toward both extremes of the entropy spectrum, with a stronger rise at the high-entropy end. This asymmetry suggests that high-entropy urban forms are associated with distinct spatial processes of segregation, including elite enclaving and incremental development in lower-income settlements, while low-entropy forms reflect more selective occupation shaped by planning and market filtering. Overall, the findings suggest that built form is more than a neutral backdrop, functioning as both affordance and signal of segregation.