  We theoretically study the Hofstadter butterfly of a triangular network model
in minimally twisted bilayer graphene (mTBLG). The band structure manifests
periodicity in energy, mimicking that of Floquet systems. The butterfly
diagrams provide fingerprints of the model parameters and reveal the hidden
band topology. In a strong magnetic field, we establish that mTBLG realizes
low-energy Floquet topological insulators (FTIs) carrying zero Chern number,
while hosting chiral edge states in bulk gaps. We identify the FTIs by
analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by
explicitly computing the chiral edge states. Our theory paves the way for an
effective practical realization of FTIs in equilibrium solid state systems.
