  Consider a deterministically growing surface of any dimension, where the
growth at a point is an arbitrary nonlinear function of the heights at that
point and its neighboring points. Assuming that this nonlinear function is
monotone, invariant under the symmetries of the lattice, equivariant under
constant shifts, and twice continuously differentiable, it is shown that any
such growing surface approaches a solution of the deterministic KPZ equation in
a suitable space-time scaling limit.
