Abstract: Affine type cluster algebras provide the simplest examples of non-finite type cluster algebras. The source-sink mutation pattern on seeds whose underlying quiver is an affine Dynkin diagram is an example of a path of mutations which produces infinitely many cluster variables, and it is a natural question to describe the limiting behavior of variables along this path. I will describe a solution to this problem similar to that of Keller-Scherotzke (arXiv:1004.0613) using a notion of mutation invariant functions on a cluster algebra. Furthermore, I will show how these functions identify a natural finite quotient of the exchange complex of an affine cluster algebra. If time, I will discuss generalizations of these ideas to cluster algebras associated with elliptic Dynkin diagrams.