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.

翻译：居住隔离的痕迹早已被记录，但城市形态作为隔离的媒介和表现的作用仍未被充分阐明。我们研究建筑肌理的配置是否可能将居住隔离编码在其空间结构中，假设建筑形态熵（BFE）模式与收入群体的空间分布及其局部聚类呈非线性关联。为此，我们通过基于建筑足迹的香农熵测量来量化BFE，使用基尼指数和莫兰指数表征基于收入的空间分布，并通过规则镶嵌将两者置于共同的空间基础上。将该框架应用于拉丁美洲最大城市圣保罗，我们发现BFE、收入与隔离之间存在非线性关系：收入水平和居住聚类向熵谱的两端增加，并在高熵端呈现更强增长。这种不对称性表明，高熵城市形态与隔离的不同空间过程相关，包括精英聚集和低收入住区的渐进发展，而低熵形态则反映了由规划与市场筛选塑造的更具选择性的居住模式。总体而言，研究结果表明，建筑形态并非中性背景，而是作为隔离的提供和信号发挥作用。