Introduction

In a similar fashion to fractals given by Strichartz in [1] we give an overview of the construction of the Projective Octagasket,
an approximation of its Laplacian and its spectrum. This fractal is not finitely ramified meaning that cells border along more than
just vertices. As such analytical study upon it, and the existence of a self-similar Laplacian is only conjectured. Using a cell
approximation given by Kusuoka and Zhou in [2] we construct the discrete graph Laplacian on a given level. This gives access to the
spectrum where the eigenvalues and their eigenfunctions line up concerning symmetry and multiplicity. Solutions to the heat and
wave equation are also given using an orthonormal basis of the eigenspace and computation of the heat kernel approximation.