  We describe a simple technique for generating a cold-atom lattice pierced by
a uniform magnetic field. Our method is to extend a one-dimensional optical
lattice into the "dimension" provided by the internal atomic degrees of
freedom, yielding a synthetic 2D lattice. Suitable laser-coupling between these
internal states leads to a uniform magnetic flux within the 2D lattice. We show
that this setup reproduces the main features of magnetic lattice systems, such
as the fractal Hofstadter butterfly spectrum and the chiral edge states of the
associated Chern insulating phases.
