  Although still poorly understood, the chemistry that occurs on the surfaces
of interstellar dust particles profoundly affects the growth of molecules in
the interstellar medium. An important set of surface reactions produces icy
mantles of many monolayers in cold and dense regions. The monolayers are
dominated by water ice, but also contain CO, CO_{2}, and occasionally methanol
as well as minor constituents. In this paper, the rate of production of
water-ice dominated mantles is calculated for different physical conditions of
interstellar clouds and for the first time images of the morphology of
interstellar ices are presented. For this purpose, the continuous-time
random-walk Monte Carlo simulation technique has been used. The visual
extinction, density, and gas and grain temperatures are varied. It is shown
that our stochastic approach can reproduce the important observation that ice
mantles only grow in the denser regions.
