I knew i should have taken that left turn at albuquerque

We study the Laplacian-∞ path as an extreme case of the Laplacian-α random walk. Although, in the finite α case, there is reason to believe that the process converges to SLE _κ, with κ = 6/(2α + 1), we show that this is not the case when α = ∞ In fact, the scaling limit depends heavily on the lattice structure, and is not conformal (or even rotational) invariant.