  We consider the Harper model which describes two dimensional Bloch electrons
in a magnetic field. For irrational flux through the unit-cell the
corresponding energy spectrum is known to be a Cantor set with multifractal
properties. In order to relate the maximal and minimal fractal dimension of the
spectrum of Harper's equation to the irrational number involved, we combine a
refined version of the Hofstadter rules with results from semiclassical
analysis and tunneling in phase space. For quadratic irrationals $\omega$ with
continued fraction expansion $\omega = [0;\overline{n}]$ the maximal fractal
dimension exhibits oscillatory behavior as a function of $n$, which can be
explained by the structure of the renormalization flow. The asymptotic behavior
of the minimal fractal dimension is given by $\amin \sim {\rm const.} \ln n /
n$. As the generalized dimensions can be related to the anomalous diffusion
exponents of an initially localized wavepacket, our results imply that the time
evolution of high order moments $< r^{q} >, q \to \infty$ is sensible to the
parity of $n$.
