  This paper studies the concept of power dissipation in infinite graphs and
fractals associated with passive linear networks consisting of non-dissipative
elements. In particular, we analyze the so-called Feynman-Sierpinski ladder, a
fractal AC circuit motivated by Feynman's infinite ladder, that exhibits power
dissipation and wave propagation for some frequencies. Power dissipation in
this circuit is obtained as a limit of quadratic forms, and the corresponding
power dissipation measure associated with harmonic potentials is constructed.
The latter measure is proved to be continuous and singular with respect to an
appropriate Hausdorff measure defined on the fractal dust of nodes of the
network.
