Diversity of dark matter structures for Poisson and Monge-Ampère simulations. We show projected density maps of a 20 Mpc/h slice of the full cosmological box (top panels) and of zoomed regions of 25 Mpc/h on a side (middle and bottom panels). In the top panels, we overplotted the filaments identified by DisPerSE using the DM density field. For this visualisation, we used the same persistence level (7σ) to extract the cosmic web for both gravity theories. It can be seen that this alternative gravity theory enhances more abundant filament structures. In the bottom panels, the orange circles are drawn at one virial radius of their halo with M_vir > 10¹³ M_⊙, identified by adaptaHOP. For this zoomed-in region, we also represent the cosmic filaments (in blue) reconstructed by DisPerSE for the halo distribution using the CP_max-halos calibration with the parameters specified in Table 1.