  We present evidence that, below a certain threshold scale, the horizon of a
black hole is strongly wrinkled, with its shape manifesting a self-similar
(``fractal'') spectrum of fluctuations on all scales below the threshold. This
threshold scale is small compared to the radius of the black hole, but still
much larger than the Planck scale. If present, such fluctuations might account
for a large part of the horizon entropy.
