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.
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