Multifractal analysis of racially-constrained population patterns and residential segregation in the US cities

Abstract: A phenomenon of racial segregation in U.S. cities is a multifaceted area of study. A recent advancement in this field is the development of a methodology that transforms census population count-by-race data into a grid of monoracial cells. This format enables assessment of heterogeneity of segregation within a city. This paper leverages such a grid for the quantification of race-constrained population patterns, allowing for the calculation and mapping of binary segregation patterns within arbitrary region. A key innovation is the application of Multifractal Analysis (MFA) to quantify the residency patterns of race-constrained populations. The residency pattern is characterized by a multifractal spectrum function, where the independent variable is a local metric of pattern's "gappiness", and the dependent variable is proportional to the size of the sub-pattern consisting of all locations having the same value of this metric. In the context of binary populations, the gappiness of the race-constrained population's pattern is intrinsically linked to its segregation. This paper provides a comprehensive description of the methodology, illustrated with examples focusing on the residency pattern of Black population in the central region of Washington, DC. Further, the methodology is demonstrated using a sample of residency patterns of Black population in fourteen large U.S. cities. By numerically describing each pattern through a multifractal spectrum, the fourteen patterns are clustered into three distinct categories, each having unique characteristics. Maps of local gappiness and segregation for each city are provided to show the connection between the nature of the multifractal spectrum and the corresponding residency and segregation patterns. This method offers an excellent quantification of race-restricted residency and residential segregation patterns within U.S. cities.