Saccade Amplitude and Pupil Diameter Information Channels: Extending the Gaze Information Channel Framework and...

The gaze information channel paradigm models fixation sequences as a first-order Markov chain and quantifies gaze behaviour through Shannon entropy and mutual information (MI), where I(X;Y) measures the reduction in uncertainty about the next fixation state given the current one. This paper extends the framework by introducing two new channels: the saccade amplitude channel, which discretises saccade angular distance into three categories (short, medium, long) with a four-category variant also analysed, and the pupil diameter channel, which discretises fixation-period pupil size into three categories. Both are applied to 10 observers viewing 12 Van Gogh paintings. The amplitude channel shows that observer-driven variation exceeds stimulus-driven variation. The pupil channel yields the highest I(X;Y) among the two new channels (0.489±0.209 bits per participant), consistent with the slow dynamics of pupil responses. Goodness-of-fit tests confirm significantly non-random sequential structure in both channels (p<0.01) for all pooled matrices. A simultaneous cross-channel association analysis across all five channels finds that 19 of 20 pairwise Spearman correlations are non-significant; the single nominally significant result (pupil-duration, ρ=+0.697, p=0.025) does not survive Bonferroni correction and is not robust to outlier removal. Two theoretical observations are presented: an upper bound on conditional entropy in terms of transition persistence (Proposition 1), and a refinement monotonicity result showing that finer discretisation cannot decrease channel MI (Remark 2). An exploratory comparison with five computational aesthetics measures finds a nominally significant negative correlation between pupil I(X;Y) and Bense's palette redundancy (ρ=-0.692, p=0.013, uncorrected), suggesting that diverse colour palettes are associated with stronger sequential pupil dynamics; permutation entropy and statistical complexity show no association with any channel.