  We present a technique, which we call "etching," which we use to study the
harmonic measure of Fortuin-Kasteleyn clusters in the Q-state Potts model for
Q=1-4. The harmonic measure is the probability distribution of random walkers
diffusing onto the perimeter of a cluster. We use etching to study regions of
clusters which are extremely unlikely to be hit by random walkers, having
hitting probabilities down to 10^(-4600). We find good agreement between the
theoretical predictions of Duplantier and our numerical results for the
generalized dimension D(q), including regions of small and negative q.
