Filament properties at z = 2 (dark colours and solid lines) compared to z = 0 (light colours, dashed lines). For clarity, only EAGLE is shown. In analogy to Fig. 7, we show the filament widths, central densities, and lengths in the top, middle, and bottom panels, respectively. Histograms represent the (normalised) differential distribution, whereas lines give the corresponding cumulative distributions. Even in co-moving coordinates, filaments are ≈30% thinner at z = 2 than at z = 0, while their central overdensities and (co-moving) lengths are consistent between the two epochs.