  In this article we investigate the energy spectrum statistics of fractals at
the quantum level. We show that the energy-level distribution of a fractal
follows a power-law behaviour, if its energy spectrum is a limit set of
piece-wise linear functions. We propose that such a behaviour is a general
feature of fractals, which can not be described properly by random matrix
theory. Several other arguments for the power-law behaviour of the energy
level-spacing distributions are proposed.
