 This was derived by using the martingale property of

and Itô's lemma to obtain the following partial differential equation for formula_18

For "κ" = 4, the RHS is formula_20, which was used in the construction of the harmonic explorer, and for "κ" = 6, we obtain Cardy's formula, which was used by Smirnov to prove conformal invariance in percolation.used SLE6 to prove the conjecture of that the boundary of planar Brownian motion has fractal dimension 4/3.Critical percolation on the triangular lattice was proved to be related to SLE6 by Stanislav Smirnov.