On the Regularity of Opening Patterns in Building Facades

The regularity of patterns of rectangular facade openings is investigated by proposing a prototypical instance of such patterns, together with an associated mathematical expression that quantifies the similarity of an arbitrary opening pattern with the prototype. By this, the degree of regularity of the arbitrary pattern becomes subject to prediction. The aim of the paper is to gain insight into this architectural attribute, because of its relevance to aesthetics, and because what exactly regularity is in this context, and what factors influence it, has not been described with precision to date. The principle of the novel regularity prediction states that the regularity of a facade decreases when its opening pattern is dissimilar to a grid of openings having equal shape, where the decrease is proportional to the number of variables the dissimilarity comprises. The validity of the prediction is successfully verified through experiments, based on a survey and inferential statistics.