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

2026-04-19

AI Summary

This study investigates whether urban built form encodes the spatial structure of residential segregation. By constructing a Shannon entropy–driven Built Form Entropy (BFE) metric on a regular grid and integrating Gini coefficients with Moran’s I, the authors systematically analyze the nonlinear associations between building footprints, income distribution, and clustering patterns in São Paulo. The findings reveal an asymmetric, nonlinear relationship between BFE and income segregation: high-entropy areas correspond to enclaves of elite gated communities alongside low-income informal settlements, whereas low-entropy zones reflect selective residential sorting shaped by planning or market mechanisms. Income levels and spatial clustering intensify at both ends of the entropy spectrum, particularly at the high-entropy end. These results demonstrate that the built environment not only embodies segregation but also actively participates in its generation and spatial signaling, highlighting the potential of morphological entropy as a novel indicator of socio-spatial differentiation.

Technology Category

Game Theory and Economic Paradigms: Behavioral Game TheoryNatural Language Processing: Lexical Semantics and MorphologyComputer Vision: Segmentation

Application Category

Web Mining and Content Analysis: Models for Web evolutionSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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.

Problem

• residential segregation
• urban form
• built fabric
• spatial structure
• entropy

Innovation

• built-form entropy
• residential segregation
• urban form
• Shannon entropy
• spatial inequality