It is established that the trapping of a random walker undergoing unbiased, nearest-neighbor displacements on a triangular lattice of Euclidean dimension d =2 is more efficient (i.e., the mean walklength (n)
before trapping of the random walker is shorter) than on a fractal set, the Sierpinski tower, which has a
Hausdorff dimension D exactly equal to the Euclidean dimension of the regular lattice.