Paradigm and pupil entrainment. A, We presented sequences of faces in structured or random order. In the random condition, faces were shown in random order at 2 Hz, the image rate. In the structured condition, faces were shown at the same rate (2 Hz). To induce statistical structure, images were grouped into pairs, such that one particular image always followed on another particular image. This gives rise to the pair rate at 1 Hz. B, Pupil entrainment was evident at the single-subject level (here: mean over 83 trials). The structured condition (orange) shows a clear modulation at the 2 Hz image rate and slower dynamics, including the pair rate at 1 Hz. The predominant frequency in the random condition (blue) is the image rate (2 Hz). C, Pupil entrainment at 1 and 2 Hz is also clearly evident when averaged across all runs and subjects. In B and C, gray vertical lines indicate image onsets, shading represents the SEM, and data are lightly detrended.