The Mathematical Regularity Coefficient for Facade Patterns

This article investigates whether the visual regularity of a building's facade can objectively be expressed by a numerical value. Grounded in universal neurobiological principles and modern digital image processing methods from mathematical and information theories, this study analyzes 245 architectural compositions using an interdisciplinary approach that combines perception, mathematics, programming, and architectural theory. A coefficient was derived with an almost ideal average correlation to regularity and minimal variability. Building on these findings, an open-source computer tool was developed to measure the regularity of flat architectural compositions. These results enhance our understanding of compositional perception and support the development of advanced architectural design tools, including generative algorithms.