Smoothed maps of the dust distribution in the proximity of the planets. The top panel shows the density distribution, normalized to the total number of dust particles in the model, around two planets in 2:1 resonance (Figs. 10 and 11). The color bar range is in units of 10⁻³ ; the azimuthal resolution is 0.2 rad while the radial resolution is 0.15 au. The bottom panel illustrates the dust distribution for a single planet with mass m = 200 M_⊕. As smoothing function, we applied a simple bell-shaped function (Lucy 1977).