Simulated ideal filament observed at various distances. Top row: The simulated observation of the filament at the original resolution, and 500, 1000, and 2000 pc. Added Gaussian clumps are emphasized with black outlines. Middle row: Components of the observation at different distances. The background (orange solid lines), the original Plummer (blue dotted line), the wide Gaussian structure to simulate hierarchical structure (green dash-dotted lines), the mean small-scale Gaussian clump profile, and the resulting profile (pink solid lines). Frame e shows the original profile at the initial location of 125 pc, frames f-h the profiles from d = 500 pc to d = 2 kpc. The Plummer fit to the filament profile is shown with black dashed lines. Bottom row: Violin plots of derived R_flat (frame i), p (frame j), and FWHM (frame l). The mean and median values at each distance are plotted with gray lines. On frame l, we plot the intrinsic FWHM = 0.1 pc (teal solid line), as well as the fit where the FWHM of the fitted Plummer is fixed to 0.1 pc (blue dash-dotted line).