Pattern variants on a square field

A quantitative approach to the psychology of pattern recognition requires knowledge of the number of possible variants of any particular pattern. The general solution for the number p/m ²] of pattern variants thatp counters can form on a square network ofm ² positions is obtained by elementary group theory. The exact solution is given in terms of the different types (symmetric, asymmetric, etc.) of patterns possible and an approximate formula for the total number of patterns is also developed.The author is indebted to Mr. J. Sandiford for his invaluable assistance on the theoretical aspects of the problem and to Mr. J. L. Griffith for his helpful criticism.