  We prove Barlow--Bass type resistance estimates for two random walks
associated with repeated barycentric subdivisions of a triangle. If the random
walk jumps between the centers of triangles in the subdivision that have common
sides, the resistance scales as a power of a constant $\rho$ which is
theoretically estimated to be in the interval $5/4\leqslant\rho\leqslant3/2$,
with a numerical estimate $\rho\approx1.306$. This corresponds to the
theoretical estimate of spectral dimension $d_S$ between 1.63 and 1.77, with a
numerical estimate $d_S\approx1.74$. On the other hand, if the random walk
jumps between the corners of triangles in the subdivision, then the resistance
scales as a power of a constant $\rho^T=1/\rho$, which is theoretically
estimated to be in the interval $2/3\leqslant\rho^T\leqslant4/5$. This
corresponds to the spectral dimension between 2.28 and 2.38. The difference
between $\rho$ and $\rho^T$ implies that the the limiting behavior of random
walks on the repeated barycentric subdivisions is more delicate than on the
generalized Sierpinski Carpets, and suggests interesting possibilities for
further research, including possible non-uniqueness of self-similar Dirichlet
forms.
