  We study the non-Hermitian Hofstadter dynamics of a quantum particle with
biased motion on a square lattice in the background of a magnetic field. We
show that in quasi-momentum space the energy spectrum is an overlap of
infinitely many inequivalent fractals. The energy levels in each fractal are
space-filling curves with Hausdorff dimension 2. The band structure of the
spectrum is similar to a fractal spider net in contrast to the Hofstadter
butterfly for unbiased motion.
