Anisotropy can make a moving active fluid membrane rough or crumpled

We present a hydrodynamic theory of anisotropic and inversion-asymmetric moving active permeable fluid membranes. These are described by an anisotropic Kardar-Parisi-Zhang equation. Depending upon the anisotropy parameters, the membrane is either effectively isotropic and algebraically rough with translational short, but orientational long range order, or unstable, suggestive of membrane crumpling.