In experiments investigating dynamic tasks, it is often useful to examine eye movement scan patterns. We can present trials repeatedly and compute within-subjects/conditions similarity in order to distinguish between signal and noise in gaze data. To avoid obvious repetitions of trials, filler trials must be added to the experimental protocol, resulting in long experiments. Alternatively, trials can be modified to reduce the chances that the participant will notice the repetition, while avoiding significant changes in the scan patterns. In tasks in which the stimuli can be geometrically transformed without any loss of meaning, flipping the stimuli around either of the axes represents a candidate modification. In this study, we examined whether flipping of stimulus object trajectories around the x- and y-axes resulted in comparable scan patterns in a multiple object tracking task. We developed two new strategies for the statistical comparison of similarity between two groups of scan patterns, and then tested those strategies on artificial data. Our results suggest that although the scan patterns in flipped trials differ significantly from those in the original trials, this difference is small (as little as a 13 % increase of overall distance). Therefore, researchers could use geometric transformations to test more complex hypotheses regarding scan pattern coherence while retaining the same duration for experiments.