Measuring the complexity of two-dimensional binary patterns — Sub-symmetries versus Papentin complexity

This paper describes an experimental comparison of two measures of the complexity of binary patterns with respect to how well they predict human judgement of visual complexity. The experiments are performed with a data set consisting of 45 binary patterns defined on a square 6×6 array of black and white squares. The measures compared are generalizations of the measures previously explored for one-dimensional binary sequences by Alexander and Carey as well as Papentin. The former is based on counting the number of sub-symmetries present in the pattern, and the latter is an upper bound on the Kolmogorov complexity. This upper bound is obtained by calculating the shortest length of all possible descriptions of the pattern among a hierarchy of description languages.