Evolution of the inner debris disk as seen on the plane of the sky. The subsequent panels show the instantaneous positions of two inner planets and small asteroids in stable orbits (small colored dots) with a mass of 10⁻⁶ M_Jup at the epoch labeled in the lower-left corner of each graph. We collected 3.3 × 10⁵ particles. Their distribution in the (a₀, e₀)-plane of osculating, canonical elements at the initial epoch 1998.830 is shown in Fig. 11. The largest filled circles correspond to the positions of the planets HR 8799e and HR 8799d at the snapshot epoch (large filled circles) and the initial osculating epoch (shaded filled circles), respectively. The asteroid colors are for the lowest order MMR types, as indicated in the bottom two plots, or those belonging to the innermost quasi-homogeneous disk (gray points). The 2024.83 epoch covers roughly one orbital period in a 2:1e MMR resonance (dark blue circles) with the innermost planet.