We consider a simple two-dimensional layered automaton. Each processor in the automaton performs the same nonlinear, thresholdlike operation (so that the row-to-row evolution of the array can also be seen as the time development of a one-dimensional automaton). One row of the machine is reserved for input, another is singled out as output. We study the output space in detail, as restricted by the very wiring of the array, enumerating the output configurations, and characterizing them statistically. We demonstrate that input configurations flow to a set of zero measure in output space. The variations in output that are to be expected when input is subjected to perturbations are also examined.