  Analyses of TeV-PeV cosmic ray (CR) diffusion around their sources usually
assume either isotropic diffusion or anisotropic diffusion due to the regular
Galactic magnetic field. We show that none of them are adequate on distances
smaller than the maximal scale Lmax ~ 100 pc of fluctuations in the turbulent
interstellar magnetic field. As a result, we predict anisotropic gamma-ray
emissions around CR proton and electron sources, even for uniform densities of
target gas. The centers of extended emission regions may have non-negligible
offsets from their sources, leading to risks of misidentification. Gamma-rays
from CR filaments have steeper energy spectra than those from surrounding
regions. We point out that gamma-ray telescopes can be used in the future as a
new way to probe and deduce the parameters of the interstellar magnetic field.
