Multifractal analysis of heritage architecture: quantifying complexity in 30 iconic historic buildings

Abstract Architectural heritage exhibits complex multiscale organization, yet building-scale comparison remains difficult. This study develops a reproducible multifractal framework to quantify and compare 30 iconic historic buildings. For each case, two standardized 2D views are analyzed—a floor plan and a vertical drawing—each represented at two levels, prototype and refined. Multifractal spectra are estimated by box counting, summarized through spectral descriptors, and examined by hierarchical clustering. Across the dataset, generalized dimensions satisfy D 0 > D 1 > D 2 , while refined representations show higher q–D ( q ) levels and right-shifted α–f ( α ) distributions, indicating greater space filling and stronger geometric integration. In both plan and vertical representations, clustering yields three interpretable families and nested subtype structures, with silhouette analysis serving as auxiliary validation of these comparative groupings. Overall, multifractal spectra provide a consistent basis for documenting, comparing, and digitally archiving the multiscale morphological organization encoded in standardized architectural drawings.