  We construct a strongly local regular Dirichlet form on the golden ratio
Sierpinski gasket, which is a self-similar set without any finitely ramified
cell structure, via a study on the trace of electrical networks on an infinite
graph. The Dirichlet form is self-similar in the sense of an infinite iterated
function system, and is decimation invariant with respect to a graph-directed
construction. A theorem of uniqueness is also provided. Lastly, the associated
process satisfies the two-sided sub-Gaussian heat kernel estimate.
