  We investigate the diffusion of cosmic rays (CR) close to their sources.
Propagating individual CRs in purely isotropic turbulent magnetic fields with
maximal scale of spatial variations Lmax, we find that CRs diffuse
anisotropically at distances r <~ Lmax from their sources. As a result, the CR
densities around the sources are strongly irregular and show filamentary
structures. We determine the transition time t* to standard diffusion as t* ~
10^4 yr (Lmax/150 pc)^b (E/PeV)^(-g) (Brms/4 muG)^g, with b ~ 2 and g =
0.25-0.5 for a turbulent field with Kolmogorov power spectrum. We calculate the
photon emission due to CR interactions with gas and the resulting irregular
source images.
