Color-from-motion displays consist of a sparse array of dots which never move but change color according to various algorithms. Yet such displays can trigger human vision to construct apparent motion of a subjective surface which is uniformly colored and bounded by a subjective contour. We show that the perceptual strength of this construction depends on the density and regularity of dot placement. We studied three objective measures of density and regularity: nearest-neighbor distance, mean of maximal disks, and variance of maximal disks. We found that nearest-neighbor mechanisms alone are inadequate to account for the perceptual strength of the subjective surfaces and contours. Mechanisms sensitive to areal gaps provide a more adequate account.