Perception of two-dimensional Markov constraints within visual displays

A method is described for constructing visual displays in which statistical constraints are encoded within two spatial dimensions without introducing one-dimensional linear constraints. Within each local group of four elements, the state of one element was determined with a given probability by the previously generated states of the other three. Ss rated such displays on a scale from “lumpy” (or crude texture) to “lacy” (or even texture). The consistency of classification obtained for displays with strong aggregated (“lumpy”) properties was substantially higher than that obtained for displays with strong distributed (“lacy”) properties. An incidental feature of the Ss’ behavior was their deliberate degrading of the visual quality of the displays. Comparison is made with one-dimensional displays concatenated in two dimensions.