Grouping by Proximity and Multistability in Dot Lattices: A Quantitative Gestalt Theory

Gestalt phenomena have long resisted quantification. In the spirit of Gestalt field theory, we propose a theory that predicts the probability of grouping by proximity in the six kinds of dot lattices (hexagonal, rhombic, square, rectangular, centered rectangular, and oblique). We claim that the unstable perceptual organization of dot lattices is caused by competing forces that attract each dot to other dots in its neighborhood. We model the decline of these forces as a function of distance with an exponential decay function. This attraction function has one parameter, the attraction constant. Simple assumptions allow us to predict the entropy of the perceptual organization of different dot lattices. We showed dot lattices tachistoscopically to 7 subjects, and from the probabilities of the perceived organizations, we calculated the entropy of each lattice for each subject. The model fit the data exceedingly well. The attraction constant did not vary much over subjects.