Effects of dot number and symmetry group order on goodness and complexity of dot patterns in a group theoretical approach

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  • 群論アプローチにもとづく要素数と群の位数が要素パターンの良さと複雑さに及ぼす効果
  • グンロン アプローチ ニ モトズク ヨウソスウ ト グン ノ イスウ ガ ヨウソ パターン ノ ヨサ ト フクザツ サ ニ オヨボス コウカ

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<p>Two experiments on goodness and complexity judgments of dot patterns in a square matrix framework were conducted based on studies by Hamada et al. (2016, 2017). Four groups of 52 undergraduates (N=208) judged the goodness and complexity of original and expanded patterns consisting of six 8-dot and six 13-dot prototype patterns and thirty-six 21-dot compound patterns. Rotational/reflectional symmetries were invariant, generating cyclic (Cn) and dihedral (Dn) groups (n=1, 2, 4). Results showed that only complexity increased consistently as the number of dots increased. Adding twelve 8-dot and 13-dot patterns increased the complexity of 21-dot patterns. Apart from the complexity of 8-dot D2 patterns, goodness and simplicity increased one-dimensionally with respect to the order of the matrix. The complexity of 8-dot D2 patterns decreased because of spatial filters on linearity, which did not affect goodness. Concerning the original and expanded patterns, configurations of 21-dot patterns did not influence goodness or complexity. In conclusion, results of goodness and complexity judgments supported our group theoretical model and showed that the complexities of dot count and 8-dot D2 patterns were influenced by physical factors.</p>

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