judgements of the numerousness of dots vary depending on their arrangement. it has been demonstrated that regular patterns are perceived as more numerous than random ones. labeled the regular-random numerosity illusion (rrni), explanations of this phenomenon are based on the faulty premise that features are randomly distributed in nature. natural features tend to be contagiously (systematically clumped) rather than randomly distributed. there is, in fact, a continuum from regularity through randomness to contagiousness, which can be mathematically represented. to more completely investigate the consequence which arrangement has for visual percreption, this study yields numerosity estimates for four levels of arrangement (regular, random, contagious 1, contagious 2) at three levels of number (n = 37, 74, 111), each spread over a hexagonal display field. a second experiment obtained numerosity estimates for random and contagious displays spread over a square display field. the third task required participants to sort random versus contagious stimulus cards into homogeneous sets. speed of sorting determined whether one class of arrangement was more easily discriminated than was another. results indicate that 1) numerosity estimates are highest for regular, lower for random, and lowest for contagious, and 2) superior facility in discriminating among random versus contagious displays. results are discussed in relation to memory, contrast with expectancy, and ease of subitizing distinct clusters. clustering is proposed as an ecologically valid means of specifying stimulus structure.