In this note we prove that appropriately scaled threshold dynamics-type
algorithms corresponding to the fractional Laplacian of order α∈(0,2) converge to moving fronts. When α≧1 the resulting interface
moves by weighted mean curvature, while for α<1 the normal velocity is
nonlocal of ``fractional-type.'' The results easily extend to general nonlocal
anisotropic threshold dynamics schemes.Comment: 19 page