Art’s hidden topology: A window into human perception
Fig 16
The distribution of violation of Alexander duality demonstrated as the normalised differences in the area under the Betti curves for: for (a) and
and (b)
and
, all art images and all pseudo-art.
The vertical axis shows the Alexander duality violation measure ADV, as defined in Equation 1. The data presented are art images extended by a group of paintings of popular abstract painters (we include a list of paintings in S6 Appendix) and all 4500 generated pseudo-art images. There is a significant difference between the two groups in both comparisons (Mann-Whitney U test, (a) and (b) – statistic values: 356695 and 338429; two-sided: p < 0.001 and p < 0.001; point estimate (median of all possible pairwise differences): 0.2764 and 0.2282; rank sums: and
; number of observations in each group: 844500 and 844500). The statistics for the distributions are presented in S3 Table.