Weighted Shannon entropy as a quantitative measure of façade pattern regularity

The article presents an original measure of facade pattern regularity, SVE (Shannon-Variance-Entropy), based on weighted Shannon entropy, which aims to quantitatively describe the internal diversity of a composition. The analysis showed that simply taking into account the distance between elements does not improve the accuracy of the regularity description. The variance of element proportions and angular relationships proved to be key factors, significantly increasing the indicator's consistency with aesthetic perception. The best results were obtained for the composite measure SVEDAS, which combines all three components. This measure shows high consistency with expert assessments and effectiveness in the algorithmic generation of facade patterns. The use of the designated metric as a design parameter enables quantitative control of aesthetics, supporting sustainable design in line with SDG 11.