Fig. 2: Spatial arrangement of the topological defects.
Topological filaments in a particular normal mode at different frequencies ω. Blue and red dots represent, respectively, TDs with winding number + 1 and − 1. Snapshots of the TD at higher frequencies are shown in Supplementary Fig. 6 of the SI, and Supplementary Fig. 6 also shows a zoom of the snapshot for ω = 1.211. Most isolated dots in the panels are not genuine point singularities but cross-sections or short, sub-resolution pieces of vortex filaments introduced by the discrete grid. As one recognizes from the figure, these dots are not randomly dispersed but outline a one-dimensional structure; increasing spatial resolution (decreasing voxel size) causes them to approach each other, thus outlining the one-dimensional structure better, see Supplementary Fig. 7 in the SI for a resolution-dependent illustration of this effect. Note that the filaments formed by the TDs do not end within the bulk of the sample arbitrarily, since, for topological reasons, this is forbidden. The apparent termination of these filaments is thus due to insufficient spatial resolution of the eigen-vector field or approaching line junctions.
