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

Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics