The classic Sierpinski triangle comprised of conducting bonds is multifractal. Thus the critical exponents and dimensions related to the conductivity are obtained asymptotically--that is, in the limit that the correlation length {\xi} of the recursive triangle goes to infinity.
@article{arxiv.1710.06346,
title = {Conductivity properties of the Sierpinski triangle},
author = {Clinton DeW. Van Siclen},
journal= {arXiv preprint arXiv:1710.06346},
year = {2017}
}