  Fractal Hofstadter bands have become widely accessible with the advent of
moir\'e superlattices, opening the door to studies of the effect of
interactions in these systems. In this work we employ a renormalization group
(RG) analysis to demonstrate that the combination of repulsive interactions
with the presence of a tunable manifold of Van Hove singularities provides a
new mechanism for driving unconventional superconductivity in Hofstadter bands.
Specifically, the number of Van Hove singularities at the Fermi energy can be
controlled by varying the flux per unit cell and the electronic filling,
leading to instabilities toward nodal superconductivity and chiral topological
superconductivity with Chern number $\mathcal{C} = \pm 6$. The latter is
characterized by a self-similar fixed trajectory of the RG flow and an emerging
self-similarity symmetry of the order parameter. Our results establish
Hofstadter quantum materials such as moir\'e heterostructures as promising
platforms for realizing novel reentrant Hofstadter superconductors.
