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Macroscopic spherical particles spontaneously form rich patterns on astanding Faraday wave. These patterns are found to follow a very systematictrend depending on the floater concentration $\phi$: The same floaters thataccumulate at amplitude maxima (antinodes) of the wave at low $\phi$,surprisingly move towards the nodal lines when $\phi$ is beyond a certainvalue. In more detail, circular irregularly packed antinode clusters at low$\phi$ give way to loosely packed filamentary structures at intermediate$\phi$, and are then followed by densely packed grid-shaped node clusters athigh $\phi$. Here, we successfully characterize the morphology of these richpatterns using a metric analysis, i.e., the Minkowski functionals. We modifythe Minkowski functionals such that we are able to measure the physicalquantities of the clusters such as area, perimeter, and aspect ratio.

Quantfying rich patterns in agglomeration of floating beads