Multifractal Nonlinearity in Behavior During a Computer Task with Increasing Difficulty: What Does It Teach Us?

The complex systems approach to cognitive–motor processing values multifractal nonlinearity as a key formalism in understanding internal interactions across multiple scales that preserve adequate task-directed behaviors. By using a computer task with increasing difficulty, we focused on the potential link between the difficulty threshold during a task, assessed by the individual’s score ceiling, and the corresponding level of multifractal nonlinearity in movement behavior, assessed based on a time series of cursor displacements. Entropy-based multifractality (MF) and multifractal nonlinearity obtained using a t-test comparison between the original and linearized surrogate series (tMF) of the time series characterized individual adaptive capacity. A time-varying increase in the score helped in assessing performance when facing increasing difficulty. Twenty-one participants performed a herding task (7 min), which involves keeping three moving sheep near the center of a screen by controlling the mouse pointer as a repelling shepherd dog. The more the score increased, the more the increased herd movement amplitude amplified task difficulty. The time course of the score, score dynamics (score-dyn), markedly diverged across participants, exhibiting a ceiling effect in some during the last third of the task (phase 3). This observation led us to arbitrarily distinguish three phases of the same duration and focus on phase 3, where marked differences in score-dyn emerged. Hierarchical clustering of principal components, starting with principal component analysis, identified three clusters among the participants: cluster 1 was defined by an underrepresentation of score-dyn, MF, and tMF; cluster 2 was defined by an overrepresentation of MF; and, as a critical outcome, cluster 3 was defined by an overrepresentation of score-dyn and tMF. Accordingly, participants belonging to cluster 3 had the highest score-dyn and tMF. Our interpretative hypothesis is that internal interactions that adequately perform the task are reflected in a high degree of multifractal nonlinearity. These findings extend the notion that multifractal nonlinearity is a useful conceptual framework for shedding light on adaptive behavior during complex tasks.