The understanding of the mechanisms behind focus of attention in a visual scene is a problem of great interest in visual perception and computer vision. In this paper, we describe a model of scanpath as a dynamic process which can be interpreted as a variational law somehow related to mechanics, where the focus of attention is subject to a gravitational field. The distributed virtual mass that drives eye movements is associated with the presence of details and motion in the video. Unlike most current models, the proposed approach does not estimate directly the saliency map, but the prediction of eye movements allows us to integrate over time the positions of interest. The process of inhibition-of-return is also supported in the same dynamic model with the purpose of simulating fixations and saccades. The differential equations of motion of the proposed model are numerically integrated to simulate scanpaths on both images and videos. Experimental results for the tasks of saliency and scanpath prediction on a wide collection of datasets are presented to support the theory. Top level performances are achieved especially in the prediction of scanpaths, which is the primary purpose of the proposed model.