  The existence of a self similar Laplacian on the Projective Octagasket, a
non-finitely ramified fractal is only conjectured. We present experimental
results using a cell approximation technique originally given by Kusuoka and
Zhou. A rigorous recursive algorithm for the discrete Laplacian is given.
Further, the spectrum and eigenfunctions of the Laplacian together with its
symmetries are categorized and utilized in the construction of solutions to the
heat equation.
