Azimuthal mode of the filaments (m_fil) and various instabilities, shown with the ℳ_c ( ∼ v_c/σ) of our galaxies. Black circular points with error bars show the mean and 16th to 84th percentile range of the m_fil and corresponding physical spacing λ_fil for the snapshots shown in Figure 7. The dashed line is a linear fit to the median values of m_fil (Equation (13)). Purple, red, and orange points with error bars represent the radial averages ⟨λ⟩ and standard deviations σ_λ (Equation (14) and Equation (15)) of the wavelength of the most unstable Toomre mode, the Jeans length and the Swing amplification length – see main text for details. These points are slightly offset from their overlapping ℳ_c values for visibility. The simulations show an increase in the median value of m_fil and a broadening of the 16th to 84th percentile range with increasing ℳ_c. The median filament spacing agrees well with the Toomre length of the ℳ_c = 21, 29 and 36 runs, and with the swing length for ℳ_c = 14 run.