The Mathematics of ‘Natural Beauty’ in the Architecture of Andrea Palladio and Le Corbusier: An Analysis of Colin Rowe’s Theory of Formal Complexity Using Fractal Dimensions

Abstract

In a famous architectural discussion, Colin Rowe links the geometric properties of two sixteenth century villas by Andrea Palladio and two twentieth century villas by the architect Le Corbusier. Rowe observed that different structural systems produced heightened geometric complexity in cross sections through Palladio’s villas and in Le Corbusier’s plans. Rowe also described a particular type of geometric scaling in portions of the four villas which he partially explains as a type of mathematical ‘natural beauty’ akin to the golden ratio and Fibonacci sequence. In his writings, Rowe refers to several geometric properties that encapsulate complex, scaled structures, but he lacked a mathematical system to rigorously describe and test his ideas. The present paper utilises the box-counting method for calculating fractal dimensions to analyse 100 images, consisting of architectural plans, sections, and elevations of the four villas and two Fibonacci sequences, to test Rowe’s ideas. Ultimately, the results of this research do not support the majority of Rowe’s claims about geometric complexity in the villas of Palladio and Le Corbusier, but they do provide insights into Rowe’s discussion of geometric scaling and the properties of four famous houses.