density at a particular location translated into probability to generate a fixation at this position. Fixation durations and numbers of fixations were chosen as in the corresponding experimental data 

Gaussian Model . Next, we implemented a statistical model that sampled from the em- pirical saliency map via a Gaussian-shaped aperture to mimic a limited attentional span for saccade target selection. For a given fixation position x , the empirical saliency map was weighted by a two dimensional Gaussian, centered at x , with a standard deviation of 4 . 88 ◦ visual angle. This is the same standard deviation used for the attention map of the SceneWalk model by Engbert et al. (see after next section). Sampling from the resulting weighted map, which was recomputed after each fixation, generated a scanpath in this model. As in the previous model, simulations were run with experimentally observed fixation durations, numbers of fixations and starting positions. Effectively, this model is similar to the SceneWalk model without an inhibitory tagging mechanism. 

Saccadic Momentum Model . The third model reproduced the behavior that saccades, on average, tend to follow the direction of the previous saccade—a phenomenon termed saccadic momentum (Smith & Henderson, 2009). This was applied in a similar way as in a recently published model of saccade generation (Le Meur & Liu, 2015). In order to reproduce the typical angles between two subsequent saccades, while keeping the saccade amplitude distribution similar to the experimental data, saccades were sampled from the joint probability distribution of amplitudes and angles. To also include the behavior produced by the manipulation of the starting position, the first two saccades of each trial were taken from the experimental data. Again, numbers of fixations and fixation durations were also taken from the experimental data. 

