28 Rothkegel et al. essary to explain scanpath statistics of the time-dependence of mean horizontal distance. Given the above experimental results, we were looking for potential principles of eye guid- ance that drive the trajectory faster away from the current fixation position than a simple random process. We investigated two principals in computational models: saccadic mo- mentum (Smith & Henderson, 2009; Wilming et al., 2013) and spatial inhibitory tagging (Itti et al., 1998; Le Meur & Liu, 2015). A model based on saccadic momentum that samples from the joint probability distribu- tion of saccade angles and amplitudes and keeps the first two saccades observed in the experiments. As a trivial result, the first three fixations in each trial from the simulations fit the experimental data better than any other model, however, the model did not repro- duce the overshoot component to the opposite image side. We also used the SceneWalk model (Engbert et al., 2015), a dynamical model for eye-movement control in scenes that aimed at reproducing first- and second-order statistics, i.e., densities of fixations and clustering, respectively. The SceneWalk model uses inhibitory tagging, a mechanism motivated by the findings on inhibition of return (Posner & Cohen, 1984; Posner et al., 1985; Klein, 1988). We demonstrated that the SceneWalk model generates the overshoot effect for MHD via inhibitory tagging in contrast to the two random-sampling models or the saccadic momentum model. With the parameters that were fitted from a different experiment, the SceneWalk model produced MHD curves that were qualitatively similar to the curves computed from the experimental data. The fit to the data was improved by reducing the influence of the inhibition map by reduction of a parameter controlling the strength of inhibition. A facilitation of return (Smith & Henderson, 2009) back to the starting position was not observed. Inspections of a left-focus image from a starting position on the left show different dy-