Sensory organs are thought to sample the environment rhythmically thereby providing periodic perceptual input. Whisking and sniffing are governed by oscillators which impose rhythms on the motor-control of sensory acquisition and consequently on sensory input. Saccadic eye movements are the main visual sampling mechanism in primates, and were suggested to constitute part of such a rhythmic exploration system. In this study we characterized saccadic rhythmicity, and examined whether it is consistent with autonomous oscillatory generator or with self-paced generation. Eye movements were tracked while observers were either free-viewing a movie or fixating a static stimulus. We inspected the temporal dynamics of exploratory and fixational saccades and quantified their first-order and high-order dependencies. Data were analyzed using methods derived from spike-train analysis, and tested against mathematical models and simulations. The findings show that saccade timings are explained by first-order dependencies, specifically by their refractory period. Saccade-timings are inconsistent with an autonomous pace-maker but are consistent with a "self-paced" generator, where each saccade is a link in a chain of neural processes that depend on the outcome of the saccade itself. We propose a mathematical model parsimoniously capturing various facets of saccade-timings, and suggest a possible neural mechanism producing the observed dynamics.