  The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field
antiferromagnetic patterns is theoretically studied. We report on a specific
tight-binding model of artificial antiferromagnetic structures incorporating
both nearest and next-to-nearest neighbour tunnelings and allowing for the
formation of the fractal spectra even with the vanishing gauge field flux
through the lattice. The model is applied to square and honeycomb lattices.
Possible experimental realization is suggested for the lattices of microring
resonators connected by waveguides. Finally, the structure of the butterflies
is analyzed for different points in the magnetic Brillouin zone for both the
ferromagnetic and antiferromagnetic patterns.
