  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.
