Harmonic extension on Level-3 Sierpinski Gasket via electrical network

In this paper we introduce a new approach to compute an energy renormalization factor and harmonic extension of a Level-3 Sierpinski Gasket (SG₃). There are several methods to compute the harmonic extension for fractal objects. SG₃ is one of the examples of fractal objects. But here we apply the electrical network interpretation which is done by applying the Delta-wye transforms procedure iteratively on SG₃. This is useful to find the resistance (energy renormalization factor) of the network as well as voltages (harmonic extension rule). This method motivates and explicates the notion of effective resistance metric.