Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been ana...Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been analysed in a holistic manner.There is little evidence of how mathematical beauty may be embodied in his architecture.This research investigates complexity(fractal dimension or D)and diversity(perplexity or PP)as aesthetic indices,aiming to capture distinct characteristics of Palladian architecture.The D and PP values of 22 Palladian villa fac¸ades are measured and analysed,before being compared with those of three Renaissance facades by Sebastiano Serlio.The combination of D and PP captures the geometric and semantic aesthetic qualities of architectural compositions.Importantly,the developed scatter plot of D and PP results supports the identification of four distinct aesthetic types of Palladian fac¸ade designs.The novel combination of D and PP measures contributes to a better understanding of one definition of the mathematical beauty of architecture,wherein“the whole is other than the sum of the parts”in compositional terms(a famous Gestalt principle).Specifically,this research provides new mathematical insights into the visual character of Palladian architecture and compares two important measures thereof.展开更多
基金supported by the ARC(DP220101598)UNSW Scientia program.
文摘Palladio’s design principles,including proportion and harmony,have often been associated with mathematical definitions of beauty.However,the geometric and semantic properties of his fac¸ades have rarely been analysed in a holistic manner.There is little evidence of how mathematical beauty may be embodied in his architecture.This research investigates complexity(fractal dimension or D)and diversity(perplexity or PP)as aesthetic indices,aiming to capture distinct characteristics of Palladian architecture.The D and PP values of 22 Palladian villa fac¸ades are measured and analysed,before being compared with those of three Renaissance facades by Sebastiano Serlio.The combination of D and PP captures the geometric and semantic aesthetic qualities of architectural compositions.Importantly,the developed scatter plot of D and PP results supports the identification of four distinct aesthetic types of Palladian fac¸ade designs.The novel combination of D and PP measures contributes to a better understanding of one definition of the mathematical beauty of architecture,wherein“the whole is other than the sum of the parts”in compositional terms(a famous Gestalt principle).Specifically,this research provides new mathematical insights into the visual character of Palladian architecture and compares two important measures thereof.
