Perceived complexity and the grouping effect in band patterns

Symmetry properties have been shown to determine the perceived complexity of certain patterns. We used a paired-comparison method to obtain judgments of relative complexity for a family of two-dimensional regular patterns called band patterns. Although the complexity of these patterns is well predicted by their symmetry properties we were unable to explain an interaction observed between two of these properties for our experimental patterns. We discuss the implications of our results for two predominant approaches to the perceived complexity of patterns. Neither approach takes into account that the presence of grouping sometimes makes it difficult to perceive a relationship within the pattern that would--were it not for the grouping--simplify it. We conclude that grouping can mask simplicity and that this phenomenon is crucial to the understanding of perceived complexity.