Measuring Architecture: Questioning the Application of Non-Linear Mathematics in the Analysis of Historic Buildings

In the late 1970s the mathematician Benoit Mandelbrot argued that natural systems frequently possess characteristic geometric or visual complexity over multiple scales of observation. This proposition suggests that systems which have evolved over time may exhibit certain local visual qualities that also possess deep structural resonance. In mathematics this observation lead to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity. 

During the 1990s a number of researchers developed this concept in relation to architectural design and urban planning and more recently architectural scholars have suggested that such approaches might be used in the analysis of historic buildings. At the heart of this approach, in both its theoretical and computational forms, is a set of processes initially developed by Carl Bovill for analyzing buildings. However, the assumptions implicit in Bovill’s method (itself an extrapolation of an approach proposed by Mandelbrot) have never been adequately questioned. The present paper returns to the origins of Bovill’s analytical method to reconsider his original investigation of key works of 20th century architecture and the way in which Bovill frames images for analysis. The aim of this analysis is to question several assumptions present in Bovill’s method about the way in which computer technology is used to understand the visual qualities of historic buildings.