  A hydrophilic floating sphere that is denser than water drifts to an
amplitude maximum (antinode) of a surface standing wave. A few identical
floaters therefore organize into antinode clusters. However, beyond a
transitional value of the floater concentration $\phi$, we observe that the
same spheres spontaneously accumulate at the nodal lines, completely inverting
the self-organized particle pattern on the wave. From a potential energy
estimate we show (i) that at low $\phi$ antinode clusters are energetically
favorable over nodal ones and (ii) how this situation reverses at high $\phi$,
in agreement with the experiment.
