The Fractal Structure of Gaze Patterns for Young Children, and Its Relationship to Visual Social Engagement.
We propose that clarifying the fractal properties of children’s gaze patterns will provide meaningful insights into the emergence of these complex systems. Specifically, complex, non-linear processes often carry organizational structures known as fractals—repeated, self-similar patterns across a variety of scales (Mandelbrot, 1977). This mathematical approach has been used to characterize the temporal and spatial structure of adults’ gaze behavior (Stephen & Anastas, 2010).
Previously our lab has shown that infants’ visual engagement exhibits a fractal structure indicating optimal flexibility when viewing social scenes, and that their gaze becomes more self-organized over developmental time. To follow-up, we investigated whether fractal complexity changes as a function of what infants spontaneously visually engage with onscreen.
Objectives: To investigate how 5- to 36-month-old infants’ attention to faces predicts the fractal complexity of their eye-gaze. We hypothesized an Age x Face-looking interaction: for younger infants, attention to the face will be associated with higher fractal complexity. As infants gain competency in visual social engagement, face-looking will be less predictive of fractal complexity.
Methods: Eye-tracking data were collected as participants watched four 20-second movies. Each movie included 3 females performing child-friendly actions, and was divided into 3-4 movement-based segments. Time-series, comprised of amplitude changes between consecutive gaze coordinates, were used for analyses (Fig. 1a).
We calculated the fractal complexity of each movie segment for each child (N=137 sessions, 1,076 segments), using detrended fluctuation analysis (DFA; Ihlen et al., 2015). DFA produces a parameter called the Hurst exponent (H), an index of the overall fractal structure of the time-series, on a continuum from white noise (more random; ~0.5); to pink noise (optimal flexibility; ~0.7-1.0); to brown noise (more rigid; ~1.5).
Results: H values for children’s gaze behavior were normally distributed (M=0.85, SD=0.10; Fig.1b). Preliminary results suggest that in segments during which infants looked at a face, H increased by .05 (p=.004) (Fig. 2). H also increased linearly with age by .002 per month (p=.06), but remained within the pink noise range for all ages. There was a trending Age x Face-looking interaction (p=.09).
Conclusions: Results suggest that, similar to findings in adults, infant gaze patterns exhibit a fractal micro-structure. Moreover, this fractal structure is partially determined by what infants spontaneously fixate on; infants’ gaze patterns have higher H values – indicating optimal flexibility – when they look at faces compared to non-social information. This suggests that H values may be used as an index of subjective salience, and could be a critical tool for assessing the subjective value of social information for infants at-risk for ASD. Future work will include longitudinal data to probe within-person changes.