Birkhoff revisited: beauty as a function of effect and means.

The beauty of visual patterns is quantified, starting from the assumption that beauty is maximal when a maximum of effect is attained with a minimum of means applied. Birkhoff has based his theory of beauty on this assumption, but his specification of means and effect differs from the one presented here. In our conception, effect is specified as the number of independent regularities (R) of a pattern not accounted for by the simplest interpretation of the pattern. This variable is closely allied to the concept of conjunctive ambiguity. The irregularities of a pattern that are not constrained by additional regularities (P) make up the means term of the means-effect analogy. An index of beauty (M) is defined, M = R - P. It is shown that there is substantial correlation between M and preference judgments for a set of Birkhoff's polygons. It is further demonstrated that M has relevance to describe properties of the relation of beauty to complexity, data of experiments on the aesthetic attractivity of combinations of patterns, and preferences for certain proportions of simple figures above others.