  Kusuoka and Zhou have defined the Laplacian on the Sierpinski carpet using
average values of functions on small cells and the graph structure of cell
adjacency. We have implemented an algorithm that uses their method to
approximate solutions to boundary value problems. As a result we have a wealth
of data concerning harmonic functions with prescribed boundary values, and
eigenfunctions of the Laplacian with either Neumann or Dirichlet boundary
conditions. We will present some of this data and discuss some ideas for
defining normal derivatives on the boundary of the carpet.
