  The moduli space of all rational conformal quantum field theories with
effective central charge c_eff = 1 is considered. Whereas the space of unitary
theories essentially forms a manifold, the non unitary ones form a fractal
which lies dense in the parameter plane. Moreover, the points of this set are
shown to be in one-to-one correspondence with the elements of the modular group
for which an action on this set is defined.
