The classic Gestalt laws of grouping by proximity and grouping by similarity have never been quantified, nor have their interactions been specified with any degree of precision. I will present a number of experimental and theoretical results from my lab, based on the responses of human observers to repeated brief (approximately 300 ms) presentations of perceptually multi-stable periodic dot patterns. I will show that the distribution of the probability of seeing any one of the possible perceptual interpretations is: (1) scale invariant, (2) changes little with reductions in duration to 100 ms, (3) can be predicted exactly on the assumption that dots are attracted to group with each other by a force that decays exponentially with the distance between them. I will also show that factors such the non-uniformity of lightness of dots in the lattice interact additively with the strength of grouping by proximity. I will also show how the fact that grouping is a hierarchical process expresses itself within the framework of the proposed model.