  During epitaxial crystal growth a pattern that has initially been imprinted
on a surface approximately reproduces itself after the deposition of an integer
number of monolayers. Computer simulations of the one-dimensional case show
that the quality of reproduction decays exponentially with a characteristic
time which is linear in the activation energy of surface diffusion. We argue
that this life time of a pattern is optimized, if the characteristic feature
size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface
diffusion constant, $F$ the deposition rate and $d$ the surface dimension.
