  Motion by (weighted) mean curvature is a geometric evolution law for
surfaces, representing steepest descent with respect to (an)isotropic surface
energy. It has been proposed that this motion could be computed by solving the
analogous evolution law using a "crystalline" approximation to the surface
energy. We present the first convergence analysis for a numerical scheme of
this type. Our treatment is restricted to one dimensional surfaces (curves in
the plane) which are graphs. In this context, the scheme amounts to a new
algorithm for solving quasilinear parabolic equations in one space dimension.
