Fractal templates in the Quran: hierarchical multifractality and long-range memory in the semantic structure of Surat Yasin

This study investigates whether a canonical text exhibits inherent complexity signatures in its semantic organization, bridging quantitative linguistics and nonlinear science. We applied detrended fluctuation analysis (DFA) and multifractal DFA (MF-DFA) to a semantic inter-occurrence interval series derived from Arabic root recurrence dynamics of the Quranic text Surat Yasin (Chapter 36). The text long-range scaling exponent (α2 = 1.01) is consistent with near-ideal 1/f dynamics, at both chapter and verse levels, indicating strong long-range memory, despite comparatively weaker short-range correlations (α1≈ 0.71). MF-DFA revealed pronounced multifractality at the chapter level (Δα = 0.73), persistent correlations (h(2) = 0.97) and a right-skewed singularity spectrum (Aα = 0.74). A pronounced hierarchical decoupling (α2/α1 ≈ 1.43) and a 2.71-fold increase in multifractal width from verse to chapter level, indicate scale-emergent complexity. In contrast, a control corpus of classical Arabic prose (Kalila wa-Dimna) exhibited weaker long‑range persistence (α2 = 0.67) and no hierarchical complexity amplification, despite comparable Zipf–Mandelbrot lexical scaling. Moreover, multifractality in the control corpus was substantially more sensitive to noise (ρ(Δα) = 1.06) than in Surat Yasin, which exhibited strong robustness across scales (ρ(Δα) ≈ 0.07). These findings suggest that the semantic architecture of Surat Yasin exhibits multiscale hierarchical organization, long-range memory and fractal characteristics consistent with patterns commonly reported in complex adaptive systems.