Aesthetic modular source and carbon potential as mathematical foundations for architectural AIGC design

Abstract Most architects rely on aesthetic intuition, often neglecting the mathematical foundations that underlie aesthetic judgement in design. This study addresses this gap by proposing a mathematical framework that supports both aesthetic excellence and low-carbon performance in architecture. The first contribution is to identify the essence of modular aesthetics as rooted in classical mathematical constructs—ratio, sequence, and spiral. The second contribution is an empirical investigation of 100 award-winning architectural projects using multivariate algorithms to examine the relationships among ratio–sequence–spiral features, award recognition, and decarbonization. The results indicate statistically significant associations between ratio-derived sequences and spiral configurations and both aesthetic recognition and carbon reduction, suggesting a viable pathway for integrating these principles into low-carbon architectural design. Overall, the proposed framework advances a mathematically grounded approach to architectural design that aligns aesthetic quality with environmental goals, while also offering foundational mathematical logic that may inform future robotic 3D-printing applications in extreme environments (e.g., lunar and Martian habitats) and the emerging AI-driven transformation of architectural design and construction.