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Kusuoka and Zhou have defined the Laplacian on the Sierpinski carpet usingaverage values of functions on small cells and the graph structure of celladjacency. We have implemented an algorithm that uses their method toapproximate solutions to boundary value problems. As a result we have a wealthof data concerning harmonic functions with prescribed boundary values, andeigenfunctions of the Laplacian with either Neumann or Dirichlet boundaryconditions. We will present some of this data and discuss some ideas fordefining normal derivatives on the boundary of the carpet.

Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet