Perceptual-cognitive explorations of a toroidal set of free-form stimuli

A polar-coordinate analogue of Fourier synthesis generates organic-appearing “free forms” that can be continuously deformed along any desired number of difficult-to-verbalize dimensions. Since the dimensions are also circular, the forms correspond to points on the surface of a torus which, though conveniently finite, is free of bounding edges. Two experiments explore a particular two-dimensional set of 81 such forms. The first shows that perceived pair-wise similarities among the individual forms are well explained purely in terms of the distances among their corresponding points in the toroidal parameter space. The second, however, establishes that forms that tend to be grouped together as having the same cognitive interpretation define regions in parameter space that are variously shaped or even bimodal and, hence, that cannot be explained solely on the basis of the fixed set of pair-wise similarities. The stimuli appear to offer a novel combination of cognitive richness and low-dimensional parametric control.