  For a given pcf self-similar fractal, a certain network (weighted graph) is
constructed whose ideal boundary is (homeomorphic to) the fractal. This
construction is the first representation of a connected self-similar fractal as
the boundary of a reversible Markov chain (i.e., a simple random walk on a
network). The boundary construction is effected using certain functions of
finite energy which behave like bump functions on the boundary. The random walk
is shown to converge to the boundary almost surely, with respect to the
standard measure on its trajectory space.
