Rothkegel et al. 12 line. Afterwards a Gaussian kernel with σ = 100 ms was applied to obtain a smoothed curve of ¯ X$_{MHD}$ ( t ). Another possible analysis would be the vertical or the overall distance to the starting position. The vertical distance showed no interesting effect, as the starting position was always on the vertical midline. The overall distance did hence only depend on the horizontal distance, which was, therefore, our analysis of choice. To interpret the experimental results of the temporal evolution of mean horizontal dis- tance X$_{MHD}$ ( t ) we performed numerical simulations using statistical control models, a model emulating saccadic momentum and a recently proposed dynamical model for scan- path generation using inhibitory tagging (Engbert et al., 2015). For the model runs, simulations started at initial positions corresponding to the experimentally manipulated starting positions. Fixation durations and number of fixations in each trial were equal to the experimental data. We obtained the same number of trials from numerical simulations as from the experimental data und performed the same analysis on the MHD function X$_{MHD}$ ( t ). Sampling from density map . As the most straightforward statistical control, we simulated scanpaths by randomly sampling from the 2D density map of all fixations (or empirical saliency map) generated by all participants for a given image. First, we applied ker- nel density estimation using the SpatStat package (Baddeley & Turner, 2005) of the R Language of Statistical Computing (R Core Team, 2014). Based on a Gaussian kernel function with a bandwidth parameter according to Scott’s rule (Scott, 2012), ranging from 1.81 ◦ to 2.72 $^{◦}$, we computed the fixation density map for each image. Second, to simulate a scanpath (i.e., a fixation sequence), we sampled randomly from this map where local Model simulations with controlled initial positions