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].
[1] ![[doi]](https://morphometry.org/wp-content/plugins/papercite/img/external.png)
W. Mickel, S. C. Kapfer, G. E. Schröder-Turk, and K. Mecke, “Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter,” Journal of Chemical Physics, vol. 138, iss. 4, p. 44501, 2013.
W. Mickel, S. C. Kapfer, G. E. Schröder-Turk, and K. Mecke, “Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter,” Journal of Chemical Physics, vol. 138, iss. 4, p. 44501, 2013. [2] T. Schindler and S. C. Kapfer, “Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter,” Phys. Rev. E, vol. 99, p. 22902, 2019.
T. Schindler and S. C. Kapfer, “Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter,” Phys. Rev. E, vol. 99, p. 22902, 2019.