  We write exact renormalization-group recursion relations for nearest-neighbor
ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a
distribution of aperiodic exchange interactions according to a class of
substitutional sequences. For small geometric fluctuations, the critical
behavior is unchanged with respect to the uniform case. For large fluctuations,
as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the
parameter space cannot be reached from any physical initial conditions. We
derive a criterion to check the relevance of the geometric fluctuations.
