Recent simple cellular models of self-organized geomorphic patterns embody a new understanding of complex, spatially extended systems. Such models can be difficult to test quantitatively because the statistics traditionally used can be insensitive even to visually obvious variations in a complex pattern. Here we develop a new approach to evaluating such models. We begin by applying to spatial patterns the state-space reconstruction techniques developed for dynamical systems, producing plots that summarize the patterns in a way that preserves more information than do the statistics usually used in geomorphology. Methods exist for characterizing some aspects of such plots. Here we develop a complementary method for quantitatively comparing state-space plots in a way that more directly evaluates the similarity between the typical features of spatial patterns. An application of this method to the patterns produced by a cellular braided- stream model and real braided streams indicates that this approach provides a relatively sensitive way of comparing model-generated and real spatial patterns.