  We construct continuous Frobenius categories of type $D$. The stable
categories of these Frobenius categories are cluster categories which contain
the standard cluster categories of type $D_n$. When $n=\infty$, maximal
compatible sets of indecomposable objects are laminations of the punctured
disk. Discrete laminations are clusters. This new construction is topological
and it also gives an algebraic interpretation of the "tagged arcs" which occur
in Schiffler's geometric description of clusters of type $D_n$.
