  The nodal lines of random wave functions are investigated. We demonstrate
numerically that they are well approximated by the so-called SLE_6 curves which
describe the continuum limit of the percolation cluster boundaries. This result
gives an additional support to the recent conjecture that the nodal domains of
random (and chaotic) wave functions in the semi classical limit are adequately
described by the critical percolation theory. It is also shown that using the
dipolar variant of SLE reduces significantly finite size effects.
