  We have investigated the dynamics of domain walls in the cubic anisotropy
model. In this model a global O(N) symmetry is broken to a set of discrete
vacua either on the faces, or vertices of a (hyper)cube. We compute the scaling
exponents for $2\le N\le 7$ in two dimensions on grids of $2048^2$ points and
compare them to the fiducial model of $Z_2$ symmetry breaking. Since the model
allows for wall junctions lattice structures are locally stable and
modifications to the standard scaling law are possible. However, we find that
since there is no scale which sets the distance between walls, the walls appear
to evolve toward a self-similar regime with $L\sim t$.
