  By viewing $\tilde{A}$ and $\tilde{D}$ type cluster algebras as triangulated
surfaces, we find all cluster variables in terms of either (i) the frieze
pattern (or bipartite belt) or (ii) the periodic quantities previously found
for the cluster map associated with these frieze patterns. We show that these
cluster variables form friezes which are precisely the ones found in [1] by
applying the cluster character to the associated cluster category.
