We develop a generic $mathbf{k}cdot mathbf{p}$ open momentum space method for calculating the Hofstadter butterfly of both continuum (Moire) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the Moire model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers ($t_ u,s_ u$) of a gap $ u$ satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While $t_ u$ is known as the Chern number, our theory identifies $s_ u$ as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility $gamma_{xy}=eBs_ u$.
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