Is segregation encoded in urban form? An entropy-based analysis

TL;DR

This study explores whether urban form encodes residential segregation by analyzing the relationship between built-form entropy and income distribution in Sao Paulo, revealing non-linear associations and implications for segregation patterns.

Contribution

It introduces an entropy-based framework to quantify built form and links it to income segregation, highlighting the encoding of segregation in urban spatial structure.

Findings

High-entropy urban forms are associated with income extremes and clustering.

Non-linear relationships exist between built-form entropy, income, and segregation.

High-entropy forms relate to elite enclaves and incremental development.

Abstract

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.