  Bogomolny and Schmit proposed that the critical edge percolation on the
square lattice is a good model for the nodal domains of a random plane wave.
Based on this they made a conjecture about the number of nodal domains. Recent
computer experiments showed that the mean number of clusters per vertex and the
mean number of nodal domains per unit area are very close but different. Since
the original argument was mostly supported by numerics, it was believed that
the percolation model is wrong. In this paper we give some numerical evidence
in favour of the percolation model.
