  The concept of fractal index is introduced in connection with the idea of
universal class $h$ of particles or quasiparticles, termed fractons, which obey
fractal statistics. We show the relation between fractons and conformal field
theory(CFT)-quasiparticles taking into account the central charge $c[\nu]$ and
the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for
integer-value $\nu$ of the statistical parameter. The Hausdorff dimension $h$
which labelled the universal classes of particles and the conformal anomaly are
therefore related. We also establish a connection between Rogers dilogarithm
function, Farey series of rational numbers and the Hausdorff dimension.
