# A bivariate multifractal analysis approach to understanding socio-spatial segregation dynamics

## TL;DR

This paper introduces a new method using multifractal analysis to study how social and spatial segregation changes across different urban scales.

## Contribution

The novel contribution is a bivariate multifractal approach using wavelet leaders to analyze socio-spatial segregation dynamics.

## Key findings

- The method extends traditional segregation indices and is less affected by spatial scale issues.
- It reveals intermittent segregation patterns where one group's dominance is locally interrupted.
- The approach provides a robust framework for analyzing multiscale urban dynamics.

## Abstract

Although the study of multifractal properties is now an established approach for the statistical analysis of urban data, the joint multifractal analysis of several spatial signals remains largely unexplored. The latter is crucial for understanding complex multiscale relationships in cities, such as socio-spatial segregation processes, where the evolution of behavior across geographical scales traditionally plays a central role. In this context, the proposed approach, which uses wavelet leaders for multifractal analysis of irregular point processes, estimates self-similarity and intermittency exponents as well as self-similar and multifractal cross-correlation by combining classical multifractal and geographic analysis methods. Results show that a local bivariate multifractal analysis can not only be related to classical two-group segregation indices but also extends them to provide a robust analytical framework that (1) is less susceptible to the modifiable areal unit problem and normalization methods and that (2) can reveal more pronounced evolution across spatial scales. In addition, multifractal analysis (3) can also delineate more “perturbed” areas in which the dominance of one group is occasionally interrupted by local concentrations of the other group, referred to here as intermittent segregation.