Fig 1.
Example patterns from Stimulus Set 1 [63] and Stimulus Set 2 [37–39].
Top row shows the most complex patterns. Middle row shows examples with mean complexity, and bottom row the least complex patterns. Below the patterns, mean complexity ratings are given. For both stimulus sets, three example patterns are depicted for the whole stimulus set (“All”) and exclusively for the symmetric patterns (“Symmetric”). In addition, in case of Stimulus Set 1, example patterns with highest, mean, and lowest complexity are also shown for the group of patterns with broken symmetry (“Broken”). Note that in both stimulus sets, the pattern with the lowest complexity is symmetric, and the pattern with the highest complexity is asymmetric.
Table 1.
Performance measures of single linear predictors of visual complexity for Stimulus Set 1.
Fig 2.
Best five linear models predicting mean visual complexity for Stimulus Set 1 containing one (bottom), two (middle), or three (top) parameters.
Each row corresponds to a linear model and squares symbolize the inclusion of a predictor. The quality of the models is evaluated with respect to explained variance (R2). Note that the best single predictor is RMSGIF, the best two-predictor model contains the predictors MS and RMSGIF, and the inclusion of a third predictor only slightly increases the explained variance.
Table 2.
Linear prediction models of visual complexity for Stimulus Set 1.
Fig 3.
Scatterplot of mean visual complexity versus predictions of the linear model containing mirror symmetry (MS) and RMSGIF as predictors for Stimulus Set 1 (r = .823).
A LOWESS (locally weighted scatterplot smoothing) [112] regression line—a smooth curve allowing to represent linear and non-linear functions—is used to visualize the linearity of the relation. The diagonal is depicted as dashed line. It can be seen that asymmetric patterns (triangles) are mostly perceived as highly complex. In addition it looks like, that the perceived visual complexity of patterns with broken symmetry (stars) is somewhat underestimated.
Fig 4.
Linear models containing RMSGIF and (transformed and untransformed) measures of mirror symmetry for Stimulus Set 1.
Each row corresponds to a linear model and squares symbolize the inclusion of a predictor. The names of the predictors correspond to the power function used to transform them (i.e., MSA6 was transformed by a power function with exponent a = 6; cf. S1 Fig). Note that a power function with exponent a = 20 seems to be a somewhat optimal non-linear transformation. It increases the explained variance (R2) of the model from 68% (MS) to 82% (MSA20).
Fig 5.
Scatterplot of mean visual complexity versus predictions of the linear model containing mirror symmetry transformed by a power function with exponent a = 20 (MSA20) and RMSGIF as predictors for Stimulus Set 1 (r = .903).
A LOWESS (locally weighted scatterplot smoothing) [112] regression line—a smooth curve allowing to represent linear and non-linear functions—is used to visualize the linearity of the relation. The diagonal is depicted as dashed line. Note that the perceived visual complexity of patterns with broken symmetry (stars) seems to be no longer underestimated (cf. Fig 3).
Table 3.
Comparison of performance measures of prediction models for Stimulus Set 1.
Table 4.
Performance measures of single linear predictors of visual complexity for Stimulus Set 2.
Fig 6.
Best five linear models predicting mean visual complexity for Stimulus Set 2 containing one (bottom), two (middle), or three (top) parameters.
Each row corresponds to a linear model and squares symbolize the inclusion of a predictor. The quality of the models is evaluated with respect to explained variance (R2). Note that just like for Stimulus Set 1, the best single predictor is RMSGIF, the best two-predictor model contains the predictors MS and RMSGIF, and the inclusion of a third predictor only slightly increases the explained variance.
Fig 7.
Scatterplot of mean visual complexity versus predictions of the linear model containing mirror symmetry (MS) and RMSGIF as predictors for Stimulus Set 2 (r = .810).
A LOWESS [112] regression line is used to visualize the linearity of the relation. Note that a few highly complex patterns seem to be overestimated by the linear model.
Table 5.
Linear prediction models of visual complexity for Stimulus Set 2.
Fig 8.
Linear models containing RMSGIF and (transformed and untransformed) measures of mirror symmetry for Stimulus Set 2.
Each row corresponds to a linear model and squares symbolize the inclusion of a predictor. The names of the predictors correspond to the power function used to transform them (i.e. MSA6 was transformed by a power function with exponent a = 6; cf. S1 Fig). While similar to Stimulus Set 1, on the first glance there seems to be an optimal non-linear transformation, in contrast to Stimulus Set 1, the explained variance (R2) does practically not improve.
Table 6.
Comparison of performance measures of prediction models for Stimulus Set 2.