Using 1/f noise to examine planning and control in a discrete aiming task

Experimental control of scaling behavior: what is not fractal?

The list of psychological processes thought to exhibit fractal behavior is growing. Although some might argue that the seeming ubiquity of fractal patterns illustrates their significance, unchecked growth of that list jeopardizes their relevance. It is important to identify when a single behavior is and is not fractal in order to make meaningful conclusions about the processes underlying those patterns. The hypothesis tested in the present experiment is that fractal patterns reflect the enactment of control. Participants performed two steering tasks: steering on a straight track and steering on a circular track. Although each task could be accomplished by holding the steering wheel at a constant angle, steering around a curve may require more constant control, at least from a psychological standpoint. Results showed that evidence for fractal behavior was strongest for the circular track; straight tracks showed evidence of two scaling regions. We argue from those results that, going forward, the goal of the fractal literature should be to bring scaling behavior under experimental control.

Fitts' index of difficulty predicts the 1/f structure of movement amplitude time series

Studies using a variety of experimental tasks have established that when humans repeatedly produce an action, fluctuations in action output are highest at the lowest frequencies and fluctuation magnitude (power) systematically declines as frequency increases. Such time series structure is termed pink noise. However, the appearance of pink noise seems to be limited to tasks where action is executed in the absence of task-related feedback. A few studies have demonstrated that when action was executed in the presence of task-related feedback, power was evenly distributed across all spectral frequencies--i.e., white noise was revealed. Here, participants produced cyclical aiming movements under visual feedback conditions and we sought to determine whether variations of both the movement amplitude requirement (A) and the target width (W)--in the form of the index of difficulty [ID = log2(2A/W)]--would predict the structure of movement amplitude (MA) time series. There were two ID levels, and there was a small- and large-scale version of each ID: The A and W values of the large-scale version were twice those used for the small-scale version. Given that increases in ID are known to induce increased reliance on the available visual feedback, we predicted an ID-induced shift in MA time series structure from pink to white noise. Indeed, that is what we found. Further, there were no changes in MA structure when scale level changed within each ID level. Such scale invariance of MA time series structure reinforces the notion that MA structure depends on the combined influence of A and W.

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

A trade-off study revealing nested timescales of constraint

This study investigates human performance in a cyclic Fitts task at three different scales of observation, either in the presence (difficult condition) or in the absence (easy condition) of a speed–accuracy trade-off. At the fastest scale, the harmonicity of the back and forth movements, which reflects the dissipation of mechanical energy, was measured within the timeframe of single trials. At an intermediate scale, speed and accuracy measures were determined over a trial. The slowest scale pertains to the temporal structure of movement variability, which evolves over multiple trials. In the difficult condition, reliable correlations across each of the measures corroborated a coupling of nested scales of performance. Participants who predominantly emphasized the speed-side of the trade-off (despite the instruction to be both fast and accurate) produced more harmonic movements and clearer 1/f scaling in the produced movement time series, but were less accurate and produced more random variability in the produced movement amplitudes (vice versa for more accurate participants). This implied that speed–accuracy trade-off was accompanied by a trade-off between temporal and spatial streams of 1/f scaling, as confirmed by entropy measures. In the easy condition, however, no trade-offs nor couplings among scales of performance were observed. Together, these results suggest that 1/f scaling is more than just a byproduct of cognition. These findings rather support the claim that interaction-dominant dynamics constitute a coordinative basis for goal-directed behavior.

Motor imagery may incorporate trial-to-trial error

The authors tested for 1/f noise in motor imagery (MI). Participants pointed and imagined pointing to a single target (Experiment 1), to targets of varied size (Experiment 2), and switched between pointing and grasping (Experiment 3). Experiment 1 showed comparable patterns of serial correlation in actual and imagined movement. Experiment 2 suggested increased correlation for MI and performance with increased task difficulty, perhaps reflecting adaptation to a more complex environment. Experiment 3 suggested a parallel decrease in correlation with task switching, perhaps reflecting discontinuity of mental set. Although present results do not conclusively reveal 1/f fluctuation, the emergent patterns suggest that MI could incorporate trial-to-trial error across a range of constraints.