  We study the Abelian sandpile model (ASM), a process where grains of sand are
placed on a graph's vertices. When the number of grains on a vertex is at least
its degree, one grain is distributed to each neighboring vertex. This model has
been shown to form fractal patterns on the integer lattice, and using these
fractal patterns as motivation, we consider the model on graph approximations
of post critically finite (p.c.f) fractals. We determine asymptotic behavior of
the diameter of sites toppled and characterize graphs which exhibit a periodic
number of grains with respect to the initial placement.
