<p>This study presents a fractal-based framework for quantifying visual expertise using eye-gaze data. A longitudinal experiment was conducted across three consecutive semesters of the medical program at Macquarie University, where the eye movements of 13 medical students were recorded with a high-resolution eye tracker while they viewed pathological images from multiple imaging modalities. In addition, eye-tracking data from 13 consultant neurosurgeons were included as expert reference data to assess whether longitudinal changes in students’ approach mirror expert-like visual behavior. Three metrics were computed: the two- and three-dimensional fractal dimensions of eye-gaze to capture spatiotemporal complexity of the eye-gaze data, and a fractal-dimension–based correlation to quantify the relationship between gaze patterns and stimulus structure. These metrics were combined into a composite Fractal Eye-Gaze Expertise Index (FEI). The results show systematic reductions in fractal complexity across sessions, indicating increasingly structured and efficient gaze strategies, with trends approaching those of experts. Crucially, conventional fixation-duration–based measures failed to consistently capture this progression, unlike the proposed fractal metrics. Statistical analyses confirm significant session-related effects for all metrics, and receiver operating characteristic curve (ROC) analysis shows that the FEI effectively discriminates longitudinal differences in visual expertise. This work demonstrates that fractal-based eye-gaze modelling provides an objective and scalable approach to characterizing visual expertise.</p> Graphical abstract <p></p>