  The influence of a layered aperiodic modulation of the couplings on the
critical behaviour of the two-dimensional Ising model is studied in the case of
marginal perturbations. The aperiodicity is found to induce anisotropic
scaling. The anisotropy exponent z, given by the sum of the surface
magnetization scaling dimensions, depends continuously on the modulation
amplitude. Thus these systems are scale invariant but not conformally invariant
at the critical point.
