  Macroscopic spherical particles spontaneously form rich patterns on a
standing Faraday wave. These patterns are found to follow a very systematic
trend depending on the floater concentration $\phi$: The same floaters that
accumulate at amplitude maxima (antinodes) of the wave at low $\phi$,
surprisingly move towards the nodal lines when $\phi$ is beyond a certain
value. 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 at
high $\phi$. Here, we successfully characterize the morphology of these rich
patterns using a metric analysis, i.e., the Minkowski functionals. We modify
the Minkowski functionals such that we are able to measure the physical
quantities of the clusters such as area, perimeter, and aspect ratio.
