We study self-similar local
regular Dirichlet, or energy, forms on a class of fractal N-gaskets, which are
generalizations of polygaskets. This is directly related to self-similar diffusions and
resistor networks (electrical circuits). We prove existence and uniqueness, and also
obtain explicit formulas for scaling factors and resistances (transition probabilities).
We also study asymptotic behavior of these quantiles as the number of “sides” N of
an N-gasket tends to infinity.