We present a new model of a two-dimensional computing device called Sgraffitoautomaton. In general, the model is quite simple, which allows a clear designof computations. When restricted to one-dimensional inputs, that is, strings, theSgraffito automaton does not exceed the power of finite-state automata. On the other hand,for two-dimensional inputs, it yields a family of picture languages with good closureproperties that strictly includes the class REC of recognizable picture languages. Thedeterministic Sgraffito automata define a class of picture languages that includes theclass of deterministic recognizable picture languages DREC, the class of picture languagesthat are accepted by four-way alternating automata, those that are accepted bydeterministic one-marker automata, and the sudoku-deterministically recognizable picturelanguages, but the membership problem for the accepted languages is still decidable inpolynomial time. In addition, the deterministic Sgraffito automata accept some unarypicture languages that are outside of the class REC.
