Fractal and morphometric characterization of drainage and fault systems in the tectonically active Mereg Basin, Western Iran

This study investigates the drainage and fault systems in the tectonically active Mereg River basin in western Iran using fractal geometry. We applied three main methods – fractal tree analysis, box-counting (capacity dimension and Turcotte method), and Horton’s laws to calculate fractal dimensions across 63 third-order sub-basins. The river network exhibited fractal dimensions of 1.714–1.809 (fractal tree), 1.561 (capacity dimension), and 1.185 (Turcotte method), while fault lines showed lower complexity, with slope dimensions typically around 1.05. A strong inverse correlation (r = −0.7) between the fractal dimensions of faults and rivers suggests that fault activity reduces river branching. Although traditional morphometric indices were analysed, they alone did not fully capture spatial complexity. In contrast, fractal analysis provided a scale-independent framework for understanding how tectonics influence drainage structure. These findings underscore the benefits of combining fractal geometry with geomorphological analysis to better understand basin evolution in active mountain regions and support the use of quantitative methods in geomorphic research.