Fractal Fluctuations and Complexity: Current Debates and Future Challenges

Abstract

Complexity is perhaps one of the less properly understood concepts, even within the scientific community. Recent theoretical and experimental advances, however, based on the close relationship between the complexity of the system and the presence of 1/f fluctuations in its macroscopic behavior, have opened new domains of investigation, which consider fundamental questions as well as more applied perspectives. These approaches allow a better understanding of how essential macroscopic functions could emerge from complex interactive networks. In this review we present the current state of the theoretical debate about the origins of 1/f fluctuations, with special focus on recent hypotheses that establish a direct link between complexity and fractal fluctuations. Further, we clarify some lines of opposition, especially between idiosyncratic versus nomothetic conceptions, and global versus componential approaches. Finally, we discuss the deep questioning that this approach can generate with regard to current theories of motor control and psychological processes, as well as some future developments which may be evoked, especially in the domain of physical medicine and rehabilitation.

Resting-state EEG delta power is associated with psychological pain in adults with a history of depression

“…The direction of the association indicated greater left (F3) than right (F4) complexity with increasing psychological pain. Research has indicated that greater signal complexity, that is a greater fractal dimension, is associated with a healthier, more adaptive system (Delignieres & Marmelat, 2012; Voss et al, 2009). This suggests that right frontal brain activity might be more adversely affected by current psychological pain, and is supported by our previously noted finding that right and not left frontal delta power predicted current psychological pain.…”

“…Conflicting results were reported for depressed individuals compared to healthy controls, as some found that resting-state EEG complexity was lower in adults with depression (Lee et al, 2007), some did not find a significant difference (Ahmadlou, Adeli, & Adeli, 2012), and still others reported that complexity was higher in depression (Bachmann et al, 2013). Building on the proposition that greater complexity is generally associated with a healthier, more adaptive system (Delignieres & Marmelat, 2012; Voss, Schulz, Schroeder, Baumert, & Caminal, 2009), we hypothesized that frontal fractal dimension would decrease with increasing psychological pain.…”

Embodiment of intersubjective time: relational dynamics as attractors in the temporal coordination of interpersonal behaviors and experiences

“…The hypothesis according to which fractal properties are generated by component processes (Pressing and Jolley-Rogers, 1997; Wagenmakers et al, 2004) is therefore fragile. Alternatively, fractality is thought to emerge from multiplicative interactions between processes that operate at multiple timescales (Van Orden et al, 2003; see Torre and Wagenmakers, 2009 and Delignières and Marmelat, 2012, 2013, for debates about these hypothesis). The latter hypothesis is supported by recent studies showing that behavioral dynamics actually exhibit multifractal properties (Ihlen and Vereijken, 2010; Dixon et al, 2012).…”

The complexities of keeping the beat: dynamical structure in the nested behaviors of finger tapping

“…Although there is not yet a consensus scientific definition (Delignières & Marmelat, 2012;Gell-Mann, 1995; Goldberger, Peng, & Lipsitz, 2002;Kelty-Stephen & Dixon, 2012;Kloos & Van Orden, 2010;Mainzer, 2005), Bcomplexity^here is intended to mean not only that behavior involves Ba lot of parts^(neurons, muscles, and bones within an actor, the behavior of other actors, the perpetually changing state of the environment) but also that these parts are interdependently coupled via nonlinear and sometimes nonobvious interactions. Understanding such complexity is no easy task, especially given that even the simplest of behaviors can reveal a surprising degree of complexity.…”

“…There is currently debate, between two primary approaches, as to how these patterns originate in behavior and to what their presence implies (Delignières & Marmelat, 2012;Diniz et al, 2011). Proponents of the Bmechanisticâ pproach champion a method of developing domain-specific models that demonstrate how a specific system organization could give rise to the observed dynamics in a specific type of behavior (Torre & Wagenmakers, 2009).…”