  We study numerically the local low-energy excitations in the 3-d
Edwards-Anderson model for spin glasses. Given the ground state, we determine
the lowest-lying connected cluster of flipped spins with a fixed volume
containing one given spin. These excitations are not compact, having a fractal
dimension close to two, suggesting an analogy with lattice animals. Also, their
energy does not grow with their size; the associated exponent is slightly
negative whereas the one for compact clusters is positive. These findings call
for a modification of the basic hypotheses underlying the droplet model.
