The information accessible can be useful in identifying broad mechanisms by which key processes are taking place, but may be insufficient for obtaining sufficient statistical information. A systematic approach can be enabled by using a persistence diagram with the time filtration function f (x, R) as shown in Figure . This persistence diagram correlates well with the qualitative analysis performed earlier -the hexagon lifetimes are solid from 0 µs to 20.0 µs, and begin to break from 25.0 µs to 50.0 µs, with a few 'stragglers' lasting for a long time. Next, mid size rings form, as shown by redder lines, some of which live for a long time. For example, the 16-sided shape in the top left of the snapshots at 30.0 µs to 50.0 µs is represented as a long red line. A few decagons form as the stretching gets more intense, but they have short lifetimes. For stretching times from 40.0 µs onwards, we observe that very large rings with extremely short lifetimes are observed; this matches what we see in the snapshots