Euclidean–Fractal Measures of Spatial–Temporal Urban Form and Growth with Data Fusion: The Case of Charlotte and Its Environs, USA

This research presents a comprehensive spatial–temporal analysis of urban form and growth in Charlotte and Mecklenburg County, North Carolina, USA, from 1900 to 2017 at the land parcel level. Employing a data fusion framework, we integrate diverse datasets—including historical cadastral records, census data, remote sensing imagery, and infrastructure maps—to examine urban morphology through Euclidean and fractal geometries. Urban growth was reconstructed and visualized by decade and cumulatively, revealing dynamic patterns of expansion, densification, and fragmentation. Using scatterplot matrices and the Hausdorff box-counting algorithm, we quantified urban form across major land use types and temporal intervals. The fusion of socio-physical variables with mathematical functions enabled multi-scale modeling of urban transitions, aligning spatial, temporal, and thematic dimensions. Key findings include: (1) multidirectional spatial expansion resulting in a sprawling urban footprint at different rates over 117 years; (2) exponential growth between 1950 and 2000 with slower rates before and after manifesting a classic S-curve urban development by Northam; (3) a pivotal moment in 1993 when urbanized and rural lands reached parity, reflecting balanced urbanization in terms of population and land area for cities and rural areas for Mecklenburg; and (4) consistent quantitative relationships—linear, polynomial, exponential, logarithmic, and proportional—between urban form and growth metrics. This study’s novelty lies in its integrated spatial–temporal framework not only for combining both Euclidean and fractal geometric analyses with fused multi-source data to uncover the evolving structure of urban landscapes, but also for offering valuable insights into efficient land uses to assess equitable land and population dynamics, all aiming to achieve a good understanding of and sound policies for Charlotte, Mecklenburg and beyond.