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. Both the figures and the patterns were invariant under the transformations of rotation and reflection, forming cyclic (C1, C2, C4) or dihedral (D1, D2, D4) groups. The results showed no significant differences among the four combinations of solid and open circles. When the 13-dot C1 figure was overlapped with the 8-dot figures, the C1 compound patterns were rated the poorest. The goodness ratings of the Cn and Dn patterns were the increasing functions of the number of transformations, which supports the ordinal agreement hypothesis. When alternated with the 8-dot D4 figure, the 8-dot C1 figure superimposed with the 13-dot figures reduced the goodness ratings of the C1 patterns, but the order of the ratings was conserved, which supports the order conservation hypothesis.