We present results obtained with a three-dimensional , Ly \alpha radiative transfer code applied to a fully cosmological galaxy formation simulation . The developed Monte Carlo code is capable of treating an arbitrary distribution of source Ly \alpha emission , neutral hydrogen density , temperature , and peculiar velocity of the interstellar medium . We investigate the influence of resonant scattering on the appearance and properties of young galaxies by applying the code to a simulated “ Lyman-break galaxy ” at redshift z = 3.6 , and of star formation rate 22 M _ { \odot } yr ^ { -1 } and total Ly \alpha luminosity 2.0 \times 10 ^ { 43 } erg s ^ { -1 } . It is found that resonant scattering of Ly \alpha radiation can explain that young galaxies are frequently observed to be more extended on the sky in Ly \alpha than in the optical . Moreover , it is shown that , for the system investigated , due to the anisotropic escape of the photons , the observed maximum surface brightness can differ by more than an order of magnitude , and the total derived luminosity by a factor of \sim 4 , depending on the orientation of the system relative to the observer .