  In this paper we propose numerical measures for evaluating the aesthetic
interest of simple patterns. The patterns consist of elements (symbols, pixels,
etc.) in regular square arrays. The measures depend on two characteristics of
the patterns: the number of different types of element, and the number of
symmetries in their arrangement. We define two complementary composite measures
L and C for the degree of pattern in a design, and compute them here for 2x2
and 6x6 arrays. The results distinguish simple from high-variation cases. We
suspect that the measure L corresponds to the degree that human beings
intuitively feel a design to be "interesting", so this model would aid in
quantifying the visual connection of two- dimensional designs with viewers. The
other composite measure C based on these numerical properties characterizes the
extent of randomness of an array. Combining symbol variety with symmetry
calculations allows us to employ hierarchical scaling to count the relative
impact of different levels of scale. By identifying substructures we can
distinguish between organized patterns and disorganized complexity. The
measures described here are related to verbal descriptors derived from work by
psychologists on responses to visual environments.
