Physical Determinants of the Judged Complexity of Shapes

Many psychological tasks vary in difficulty with the complexity of the stimulus objects involved. Complex visual objects are not only harder to reproduce from memory than simple ones (4, 6), but also harder to learn by name (4, 7) and to match (11). Complexity is an ill-defined variable, however. No two of the experiments referenced above employ exactly the same operations of physical measurement , and an essential communality between them is not easy to specify in objective terms. In the study reported here, ratings of the complexity of nonrepresenta-tional shapes were obtained from a large number of Ss and related to measurable physical characteristics of the shapes. The results not only have interest in their own right, but also serve to indicate the physical variables most likely to be relevant to other tasks, like those initially mentioned , on which data are typically harder to get and less precise. The relationship of judged complexity to informational content, "degrees of freedom," compactness, and certain other variables will be considered. METHOD Materials.-—The stimuli were 72 "random" shapes, each constructed by the following general method. In a k X k matrix, n random points were plotted, i.e., all coordinates of the points were random numbers between 1 and k. The points were then connected randomly into a polygon of n sides. This connecting process involved two steps. First, peripheral points were connected into a convex polygon which enclosed all the points not included in its contour (as if a pin were stuck into each point and a rubber band snapped around the whole cluster). Second, the unconnected points were given a random order and each in turn was "taken into" a randomly chosen segment of the surrounding polygon (as if by hooking that segment of the rubber band over the interior pin). Since lines connecting the points were not permitted to cross, the number of alternative segments into which a given point might be taken could either increase or decrease as the process continued; hence the assignment of a random sequence to the unconnected points. Connections which placed certain points outside the polygon were permitted, though in consequence the ways in which such points could themselves be connected were restricted. Some of the polygons thus constructed were further developed into curved figures by replacing angles with inscribed arcs of random 221