Additomultiplicative Cascades Govern Multifractal Scaling Reliability Across Cardiac, Financial, and Climate Systems

TL;DR

This paper introduces a new method to identify the type of multifractal scaling in complex systems like the heart, financial markets, and climate, revealing a universal pattern across these domains.

Contribution

The paper introduces threshold sensitivity analysis to classify cascade types and identifies a universal diagnostic signature of additomultiplicative cascades.

Findings

Symmetric expansion of valid scaling behavior under relaxed thresholds is a universal fingerprint of additomultiplicative cascades.

Cardiac, financial, and climate systems all exhibit this signature, with variations in robustness and geography.

The method can detect early dysfunction and assess resilience across different domains.

Abstract

The generative mechanisms underlying multifractal scaling in complex systems remain a fundamental unsolved problem, limiting our ability to distinguish healthy from pathological dynamics, predict system failures, or understand how scale-invariant organization emerges across vastly different physical domains. We resolve this challenge by introducing threshold sensitivity analysis—an extension of Chhabra–Jensen’s direct method—as a framework that classifies cascade types by examining how scaling reliability varies across moment orders q. Different q values systematically probe weak fluctuations (negative q) versus strong fluctuations (positive q), and the coefficient of determination (r2) of partition function regressions quantifies scaling reliability at each q. Analyzing r2(q) patterns in 280 cardiac recordings (healthy controls through fatal heart failure), 200 financial time series (global equity markets and currencies, 2000–2025), and 80 climate stations (tropical to continental zones, 2000–2025), we discover a universal diagnostic signature: symmetric expansion of valid scaling behavior under relaxed r2 thresholds, spanning both weak and strong fluctuations. This threshold sensitivity fingerprint—predicted by synthetic cascade simulations but never before validated empirically—uniquely identifies additomultiplicative cascades, hybrid processes that randomly alternate between additive stabilization and multiplicative amplification. Critically, this symmetric signature persists universally across domains: cardiac dynamics maintain consistent patterns across health and disease states, financial markets show varying robustness across asset classes (currencies more variable than US equities) while preserving a hybrid structure, and climate systems exhibit geographical variations (subtropical/continental stronger than tropical) without altering fundamental cascade type. These findings suggest that additomultiplicative organization is a unifying feature of complex adaptive systems, offering a resolution to decades of debate between additive and multiplicative models. The r2(q) profiling provides a mechanistic diagnostic capable of detecting early dysfunction, assessing system resilience, and revealing how environmental constraints shape—but do not determine—the fundamental principles governing multifractal complexity.

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