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.