The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.
"Harmonic explorer and its convergence to SLE4." Ann. Probab. 33 (6) 2127 - 2148, November 2005. https://doi.org/10.1214/009117905000000477