Dipole Information Complementarity in Discrete 2D Patterns.
An information theoretic approach is used to derive equations describing the dipole information in discrete two-dimensional (2D) patterns. Dipoles are pair-wise, or second-order, interactions of pattern states. It is shown that the basic dipole information equation can be decomposed into two complementary representations of the total information. One of these representations expresses the total information in terms of the sum of two components: the dipole spatial information and the permutation set information. The spatial information component describes the information in the distribution of spatial transitions for each type of color transition. The permutation set information component is a second-order function of the single color probabilities. The second representation is also the sum of two components: the dipole color information and the array information. The dipole color information describes the information in the distribution of color transitions for each possible spatial transition. The array information is a function of the size and geometry of the pattern array. These two representations characterize the total information from complementary perspectives, each emphasizing different aspects of the pattern's structure. Implications of this approach for the understanding of patterns and pattern perception are examined. Copyright 1999 Academic Press.