Additomultiplicative cascades sustain multifractal reliability across fluctuation intensities

Multifractality is a hallmark of healthy physiological dynamics, reflecting structured variability across timescales and fluctuation intensities. Yet the generative mechanisms that sustain robust multifractal scaling — particularly across both weak and strong fluctuations — remain poorly understood, limiting our ability to build physiologically plausible models. We systematically compared how additive, multiplicative, and additomultiplicative cascade processes preserve multifractal structure under controlled conditions. Crucially, we introduced the coefficient of determination profile, r2(q), as a diagnostic measure that reveals the stability of scaling laws across moment orders q∈[−10,10], distinguishing reliable multifractality in weak (q<0) versus strong (q>0) fluctuations. Using synthetic time series from each cascade type across seven generational depths and five noise environments (white, fractal, defractalizing, fractalizing, and mixed), we computed multifractal spectra f(α) and mapped r2(q) to assess scaling fidelity. Heatmaps revealed that additive cascades exhibited reliable scaling only for strong fluctuations, while multiplicative cascades maintained structure only near moderate q. In stark contrast, additomultiplicative cascades sustained consistently high r2 across the full q-range and all noise conditions, demonstrating robust, symmetric multifractal scaling. This performance proved remarkably insensitive to noise type, confirming that cascade structure — not input statistics — determines scaling reliability. Only hybrid cascades captured both the fine-grained regulatory control and burst-like adaptations characteristic of physiological processes. An illustrative analysis of heart rate variability data provided preliminary evidence that such additomultiplicative structures may constitute a plausible generative mechanism for biological multifractality. Our findings establish the r2(q) profile as a powerful diagnostic for multifractal model evaluation and identify hybrid cascade dynamics as uniquely capable of sustaining the dual regulatory demands of precision and adaptability across fluctuation intensities.