Rothkegel et al. 14 Simulations of the SceneWalk model . In a recently proposed mathematical model of scanpath generation in scene viewing (Engbert et al., 2015), it was assumed that eye movements are driven by the interaction of two neural activation maps. A fixation map f ( x ; t ) keeps track of previous fixations by adding activation at fixation position x . The time dependence of this map results from the addition of activation at each time step in combination with fixation-position independent decay. Thus the fixation map implements inhibitory tagging (Itti & Koch, 2001). The distribution of visual attention at time t is given by a second activation map a ( x ; t ). The assumption of maps of visual space is consistent with recent neurophysiological work on an allocentric motor map in the primate entorhinal cortex (Killian, Jutras, & Buffalo, 2012; Stensola et al., 2012), which is spatially discrete like that in the model with discrete activations f$_{ij}$ ( t ) and a$_{ij}$ ( t ), where subscripts i and j denote horizontal and vertical dimensions. In the SceneWalk model, the difference of the normalized fixation map f$_{ij}$ ( t ) and the normalized attention map a$_{ij}$ ( t ) is a time-dependent potential function u$_{ij}$ ( t ) computed as where the exponent γ is a free parameter that is important for controlling the amount of aggregation (or clustering) of realized gaze positions (Engbert et al., 2015). Since the potential u$_{ij}$ ( t ) is the difference of activation maps, it can be positive or negative at position ( i, j ). We implemented stochastic selection of saccade targets proportional to relative activations (Luce, 1959) among the lattice sites with negative values ( S ). The probability for saccadic target selection is given by π$_{ij}$ ( t ) = max ( k,l ) ∈S ( u$_{ij}$ ( t ) ∑ kl u$_{k,l}$ ( t ) , η$^{)}$ , (3) u$_{ij}$ ( t ) = − a$_{ij}$ ( t ) ∑ kl a$_{kl}$ ( t ) + [ f$_{ij}$ ( t )] γ $^{∑}$$_{kl}$[ f$_{kl}$ ( t )] γ , (2)