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.