  The movement of the eyes has been the subject of intensive research as a way
to elucidate inner mechanisms of cognitive processes. A cognitive task that is
rather frequent in our daily life is the visual search for hidden objects. Here
we investigate through eye-tracking experiments the statistical properties
associated with the search of target images embedded in a landscape of
distractors. Specifically, our results show that the twofold process of eye
movement, composed of sequences of fixations (small steps) intercalated by
saccades (longer jumps), displays characteristic statistical signatures. While
the saccadic jumps follow a log normal distribution of distances, which is
typical of multiplicative processes, the lengths of the smaller steps in the
fixation trajectories are consistent with a power-law distribution. Moreover,
the present analysis reveals a clear transition between a directional serial
search to an isotropic random movement as the difficulty level of the searching
task is increased.
