THE PERCEPTUAL ORGANIZATION OF DOT LATTICES

Bravais (1850/1949) demonstrated that there are five types of periodic dot patterns (or lattices): oblique, rectangular, centered rectangular, square, and hexagonal. Gestalt psychologists studied grouping by proximity in rectangular and square dot patterns. In the first part of the present paper, I (1) describe the geometry of the five types of lattices, and (2) explain why, for the study of perception, centered rectangular lattices must be divided into two classes (centered rectangular and rhombic). I also show how all lattices can be located in a two-dimensional space. In the second part of the paper, I show how the geometry of these lattices determines their grouping and their multistability. I introduce the notion of degree of instability and explain how to order lattices from most stable to least stable (hexagonal). In the third part of the paper, I explore the effect of replacing the dots in a lattice with less symmetric motifs, thus creating wallpaper patterns. When a dot pattern is turned into a wallpaper pattern, its perceptual organization can be altered radically, overcoming grouping by proximity. I conclude the paper with an introduction to the implications of motif selection and placement for the perception of the ensuing patterns.