  Iterative construction of a Sierpinski carpet or sponge is shown to be a
critical phenomenon analogous to uncorrelated percolation. Critical exponents
are derived or calculated (by random walks over the carpet or sponge at
infinite iteration) that are related by equations identical to those obtained
from percolation theory. Finite-size scaling then gives accurate values for the
scalar transport properties (e.g., effective conductivity) of the carpet or
sponge at any stage of iteration.
