Urban complexity: Izmir’s adaptive capacity through sub-fractal difference analysis

This study examines the adaptive capacity of İzmir, Türkiye, through a systematic application of sub-fractal and difference analysis to the city’s urban complexity across multiple decades, spanning from the 1950s to the 2020s. Drawing on fractal geometry (Batty and Longley, 1994), the research rigorously assesses the structural evolution of İzmir’s road networks, offering a quantitative account of the city’s capacity to absorb and respond to urban and environmental transformations. The analysis delineates the Adaptive Capacity Range (ACR) within a stable interval of 0 to 0.25, indicating a moderate degree of adaptability. This range suggests that, although İzmir demonstrates an ability to accommodate shifting socio-economic and ecological pressures, its resilience remains bounded within defined thresholds (Erdoğan, 2021; Özdemir, 2021). By incorporating principles from statistical mechanics and theoretical physics into urban morphological analysis, the study introduces computational tools that enhance predictive modeling and governance of urban growth (Salingaros, 2010). The findings highlight the pivotal role of strategic planning in augmenting urban adaptive capacity and propose a replicable methodological framework for assessing resilience in diverse urban contexts (Jiang and Yin, 2014; Triantakonstantis, 2012). Through this interdisciplinary inquiry, the research not only refines the conceptualization of urban complexity but also establishes a benchmark for subsequent analyses seeking to quantify resilience in complex spatial systems. This analysis demonstrates that the Adaptive Capacity Range (ACR) becomes visible in intra-urban form when examined through sub-fractal differences, exposing polycentric nodes, development corridors, and ecological linkages shaped by successive master plans.