We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata. Using this efficient approach difficult, unanswered questions of surface growth and its scaling can be studied. The mapping onto binary variables facilitates effective simulations and enables one to consider very large system sizes. We have confirmed that the fundamental Kardar-Parisi-Zhang (KPZ) universality class is stable against a competing roughening diffusion, while a strong smoothing diffusion leads to logarithmic growth, a mean-field type behavior in two dimensions. The model can also describe anisotropic surface diffusion processes effectively. By analyzing the time-dependent structure factor we give numerical estimates for the wavelength coarsening behavior. (C) 2011 Elsevier B. V. All rights reserved.