  We study numerically the spatial properties of relaxation clusters in a two
dimensional sandpile automaton with dynamic rules depending stochastically on a
parameter p, which models the effects of static friction. In the limiting cases
p=1 and p=0 the model reduces to the critical height model and critical slope
model, respectively. At p=p_c, a continuous phase transition occurs to the
state characterized by a nonzero average slope. Our analysis reveals that the
loss of finite average slope at the transition is accompanied by the loss of
fractal properties of the relaxation clusters.
