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Pattern Variants on a Square Field

Published online by Cambridge University Press:  01 January 2025

S. J. Prokhovnik
S. J. Prokhovnik*
Affiliation:
The University of New South Wales
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Abstract

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/m2] of pattern variants that p counters can form on a square network of m2 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.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 4 , December 1959 , pp. 329 - 341
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

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.