A group theoretical model of symmetry cognition.

We report on two experiments, published originally in Japanese, on judged goodness and simplicity of dot patterns with reflectional and rotational symmetries (with 1-4 reflection axes and repeats, respectively) under free-viewing tasks. We found that (a) both goodness and simplicity increase monotonously with the number of transformations under which a pattern is invariant; (b) stimulus outlines, such as squares and hexagons, affect both goodness and simplicity; and (c) factors such as contrast polarity and collinearity affect simplicity rather than goodness. The employed free-viewing tasks contrast with detection tasks involving short presentation times, and based on behavioural and neurophysiological evidence, we conclude that this transformational approach captures late rather than early aspects of visio-cognitive processing of visual regularities.

[Goodness of compound patterns based on symmetry groups].

This study examined the ordinal agreement and order conservation hypotheses of Imai (1986), which predict that a pattern is considered good if it is invariant for more transformations. Undergraduates (N = 144) made goodness ratings for 21-dot compound patterns. The patterns consisted of 8-dot and 13-dot figures with solid and/or open circles.