them to determine which ones caused certain elements to be grouped together
perceptually.
Logically, a set of elements can be partitioned in a number of different ways,
corresponding to the number of possible ways of dividing them into mutu-
ally exclusive subsets. This number becomes very large very quickly: For 10
elements, there are 42 possible groupings; but for 100 elements, there are
190,569,292. The number of logically possible groupings is even larger than the
number of partitions if one considers hierarchical embedding of subsets and/or
overlap among their members. Psychologically, however, only one of these
groupings is perceived at one time, and the first one is usually the only one.
How does this happen? And what properties of the stimulus image determine
which grouping people perceive?
8.1.1 The Classical Principles of Grouping
In his investigations, Wertheimer started with a single line of equally spaced
dots as shown in figure 8.2A. These dots do not group together into any larger
perceptual units—except the line of dots as a whole. He then noted that when
he altered the spacing between adjacent dots so that some pairs were closer to-
gether and others were farther apart, as in figure 8.2B, the closer ones grouped
Figure 8.2
Classical principles of grouping. Gestalt psychologists identified many different factors that govern
which visual elements are perceived as going together in larger groups. (See text for details.)
192 Stephen E. Palmer