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<p>The Île-de-France region faces significant challenges in achieving sustainable urban development amid increasing demands for urbanization. This study conducts a comprehensive analysis of the spatial dynamics of urban areas in Île-de-France (IDF) up to the years 2050 and 2100. The region’s complex urban nature makes it an ideal case for examining various aspects of urbanization, characterized by dense development, modern infrastructure, and a complex coexistence between urban and natural spaces. Employing fractality, cluster, and hotspot analyses, the research integrates land-use/land-cover data with socioeconomic, infrastructural, topographic, and environmental data, utilizing machine-learning models to forecast future land-use configurations. The findings indicate a slight increase in the complexity and densification of urban areas, emphasizing a growth-pattern that aims to enhance connectivity and compactness. The study underscores the importance of proactive planning and management strategies, such as Zones-d’Aménagement-Concerté (ZAC) and Schéma-Directeur-de-la-Région-Île-de-France (SDRIF), to address urban densification and sprawl. The research’s originality lies in the integration of multiple spatial-analysis techniques, offering a valuable tool applicable beyond Île-de-France. Future research directions include examining socioeconomic factors influencing urban growth at finer multi-agent spatial-scales, investigating the impacts of urban growth on transportation and infrastructure, and exploring the spatial relationship between employment and housing opportunities in high-density urban hotspots.</p> Graphical Abstract <p>The schematic integrates multi‑temporal Urban Atlas LULC maps for 2006, 2012 and 2018—rasterized to eight unified classes—and a comprehensive suite of spatial covariates (elevation, slope; population and employment density; proximity and density metrics for roads, public‑transport stops and parking; distances to green/non‑urban areas, waterways and transmission lines; plus evidence‑likelihood surfaces) to drive a multilayer‑perceptron–Markov‑chain (MLP‑MCM) transition model implemented in TerrSet’s Land Change Modeler. The central workflow depicts network architecture (31 input nodes, dynamically trained hidden layer), calibration metrics (Kappa = 0.988; AUC = 0.722) and the projection of LULC scenarios to 2050 and 2100. Subsequent panels present global fractal‑dimension trends—estimated via box‑counting and fitted with a logistic growth curve—to quantify rising urban complexity, alongside multi‑radial fractal maps that reveal local heterogeneity around primary and secondary centers. Final frames apply Local Moran’s I hotspot and cluster/outlier statistics to the 2100 projection, isolating statistically significant concentration zones and anomalous growth patterns. By unifying data inputs, algorithmic workflow, quantitative validation, fractal geometry and spatial‑statistics analyses into one cohesive graphic, the abstract conveys the study’s core methodologies and principal findings for Île‑de‑France urban dynamics with scientific rigor.</p>

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Decoding the Geometry of Growth: Unveiled Urban Complexity, Fractality and Spatial Dynamics in Île-de-France

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Walid Al-Shaar,
  • Xavier Lehmann,
  • Olivier Bonin,
  • Pierre Frankhauser,
  • Tatiana Seregina,
  • Mohamad Al-Shaar

摘要

The Île-de-France region faces significant challenges in achieving sustainable urban development amid increasing demands for urbanization. This study conducts a comprehensive analysis of the spatial dynamics of urban areas in Île-de-France (IDF) up to the years 2050 and 2100. The region’s complex urban nature makes it an ideal case for examining various aspects of urbanization, characterized by dense development, modern infrastructure, and a complex coexistence between urban and natural spaces. Employing fractality, cluster, and hotspot analyses, the research integrates land-use/land-cover data with socioeconomic, infrastructural, topographic, and environmental data, utilizing machine-learning models to forecast future land-use configurations. The findings indicate a slight increase in the complexity and densification of urban areas, emphasizing a growth-pattern that aims to enhance connectivity and compactness. The study underscores the importance of proactive planning and management strategies, such as Zones-d’Aménagement-Concerté (ZAC) and Schéma-Directeur-de-la-Région-Île-de-France (SDRIF), to address urban densification and sprawl. The research’s originality lies in the integration of multiple spatial-analysis techniques, offering a valuable tool applicable beyond Île-de-France. Future research directions include examining socioeconomic factors influencing urban growth at finer multi-agent spatial-scales, investigating the impacts of urban growth on transportation and infrastructure, and exploring the spatial relationship between employment and housing opportunities in high-density urban hotspots.

Graphical Abstract

The schematic integrates multi‑temporal Urban Atlas LULC maps for 2006, 2012 and 2018—rasterized to eight unified classes—and a comprehensive suite of spatial covariates (elevation, slope; population and employment density; proximity and density metrics for roads, public‑transport stops and parking; distances to green/non‑urban areas, waterways and transmission lines; plus evidence‑likelihood surfaces) to drive a multilayer‑perceptron–Markov‑chain (MLP‑MCM) transition model implemented in TerrSet’s Land Change Modeler. The central workflow depicts network architecture (31 input nodes, dynamically trained hidden layer), calibration metrics (Kappa = 0.988; AUC = 0.722) and the projection of LULC scenarios to 2050 and 2100. Subsequent panels present global fractal‑dimension trends—estimated via box‑counting and fitted with a logistic growth curve—to quantify rising urban complexity, alongside multi‑radial fractal maps that reveal local heterogeneity around primary and secondary centers. Final frames apply Local Moran’s I hotspot and cluster/outlier statistics to the 2100 projection, isolating statistically significant concentration zones and anomalous growth patterns. By unifying data inputs, algorithmic workflow, quantitative validation, fractal geometry and spatial‑statistics analyses into one cohesive graphic, the abstract conveys the study’s core methodologies and principal findings for Île‑de‑France urban dynamics with scientific rigor.