Minkowski structure metrics are well-suited to detect order in amorphous point patterns [1].

For example, in this simulation of a granular gas in a shallow cell, an ordered cluster forms:

(Data by Thomas Schindler [2])

In projection, the the particles of the cluster form a hexagonal lattice. This kind of order is obvious in the order parameter, because all the normals of the Voronoi cells point into directions which are multiples of 60 degrees.

In a histogram, the growth of the cluster is evidenced by a growing peak at :

The unordered background appears as the continuous part of this “spectrum”.

The shallow cell granular gas has a few more phases with different symmetries which can be analysed using other IMT order parameters such as [2].