Perceptual-Cognitive Explorations of a Toroidal Set of Free-Form Stimuli. Shepard, Cermak. Cognitive Psychology 1973.

<I’m just going to post images because it explains the important stuff>

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  1. But also people tended to view shapes based on what object they were most similar to (classifying them based on whether they looked like a gingerbread man, for example)
    1. “a striking aspect of the subsets is their very marked variation in size and shape in the underlying two-dimensional toroidal surface.”
    2. So these clusters don’t match the earlier contour maps either in size or shape (they are not necessarily symmetric or convex, although they seem to be L/R symmetric mostly but not up/down)
    3. Sometimes a category formed two disconnected clusters
  2. The general conclusions, here, seem to be the following: On the one hand, the underlying parameter space provides a very convenient frame- work for representing the groups into which Ss tend to sort the forms. Moreover this space is directly relevant in the sense that most of the forms sorted into any one group typically cluster together into one or two internally connected subsets in the space. But, on the other hand, the fact that the spatial representations of the spontaneously produced sub- sets vary greatly in size and shape and sometimes even consist of two or more widely separated clumps seems to establish that Experiment II taps a variety of cognitive functioning that was not operative in Experi- ment I. Just what forms will be seen as representing the same object ap- parently cannot be adequately explained solely in terms of the metric of perceptual proximity among the free forms themselves…”

  3. Each cluster can be further broken down in to subsequent subclusters
  4. Parameter space is toroidal, so top links to bottom and side to side

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