Additivity suppresses multifractal nonlinearity due to multiplicative cascade dynamics

An enduring controversy in biological and psychological sciences has centered on the tension between the role of random multiplicative cascade processes and the sometimes independent, additive effects of seemingly modular, scale-dependent component processes. The former supports the fluid interactivity of an organism’s faculties for perception, action, and cognition, and the latter entails a set of constraints over and across which the interactivity may unfold. These random multiplicative cascades embody nonlinear phenomena wherein structures repeatedly divide, branch, or aggregate across successive generations, giving rise to multiplicative interactions spanning various space and time scales. We examined the impact of introducing additivity within an array of multiplicative interactions among component processes. Our findings reveal that additivity suppresses the multifractal nonlinearity engendered by multiplicative cascade dynamics. This discovery carries profound implications. Theoretically, it underscores the significance of multiplicative interactions in producing multifractality within empirical time series. At an operational level, it suggests that systems undergoing simplification due to factors such as disease or adaptive strategies may temporarily cultivate additivity to dampen the multifractality arising from multiplicative interactions among constituent components. We advocate for further exploration into the roles of additive and multiplicative interactions in understanding and facilitating multifractal support for the adaptive use of perception, action, and cognition.