Approaching Euclidean limits: a fractal analysis of the architecture of Kazuyo Sejima

Fractal Geometry evolved in mathematics during the late 1970’s and early 1980’s; building on Benoit Mandelbrot’s proposal that natural systems frequently possess characteristic geometric complexity over multiple scales of observation. In 1996 Carl Bovill demonstrated a method for determining an approximate fractal dimension, or characteristic visual complexity, of architectural elevations and plans. This “box-counting” method, as used by Bovill, is the only known way to calculate and compare the fractal geometries of buildings. Significantly, past architectural analysis using the boxcounting approach has only been applied to the works of Frank Lloyd Wright, Le Corbusier and a limited selection of ancient buildings. This paper will expand the set of cases tested by the boxcounting method to incorporate five house designs by Kazuyo Sejima, a famous, late 20th century minimalist architect. The fractal dimensions are calculated using a combination of Archimage and Benoit software, the former of which uses an extrapolation of Bovill’s box-counting method for the fractal analysis of house designs. Being the first examples of minimalist architecture tested by this method, this paper will also explore the extremities of this method, and Bovill’s suggestion that modern architecture with minimal visual complexity should result in a more Euclidean, rather than highly fractal, results.