Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both VE and CSM is investigated. To compare the correlation between the two measures of orderliness, the Pearson correlation coefficient (PCC) was calculated. The maximum correlation between the VE and CSM was found for clusters containing the number of droplets enabling the formation of hexagons, i.e., droplet clusters possessing 6-fold symmetry. In other cases, the maxima and minima of the VE and CSM are not always well correlated; moreover, in certain cases, maxima of the CSM may correspond to the minima of the VE. Symmetry and orderliness of 2D patterns could not be quantified with a single mathematical measure.