Rényi’s spectra of urban form for different modalities of input data

Abstract

Morphologies of urban patterns display multifractal scaling. However, what data should be used to represent an urban pattern and its scaling? Here, we calculated Renyi's generalized dimensions (RGD) spectra using data corresponding to different urban modalities including urban land cover, urban impervious surface, population density, and street intersection points. All

Spatio-Temporal Changes in Racial Segregation and Diversity in Large US Cities from 1990 to 2020: A Visual Data Analysis

“…Hill's number is referred to as the effective diversity or the effective number of subpopulations because it represents the number of equally abundant subpopulations that would yield the same entropy value as the actual subpopulation composition. In practice, Hill's number is often not an integer, so we estimate the number of substantial groups by rounding the value of N H to the nearest integer (see Saeedimoghaddam et al (2020) for further details). The major advantage of Hill's number over entropy is that it does not require interpretation; it simply express a diversity Jost (2006).…”

Complexity in patterns of racial segregation

“…Email address: stepintz@uc.edu [10]. Analysis of various datasets revealed that urban structure has a multifractal rather than a monofractal nature [11; 12; 13; 14; 10] with the degree of multifractality depending on the modality of the data [15]. Additional spatial evidence comes from the time-evolution of cities that shows spreading, leapfrogging [12], and hotspots behavior which suggest a complex, non-linear mechanism.…”