A Computational Investigation into the Fractal Dimensions of the Architecture of Kazuyo Sejima

Abstract

In the late 1980's and early 1990's a range of approaches to using fractal geometry for the design and analysis of the built environment were developed. Mandelbrot's "box counting" approach was later refined and developed by Carl Bovill (1996) who demonstrated a method for determining an approximate fractal dimension of architectural elevations and plans. This paper is the first investigation of the fractal dimensions of five house designs by Kazuyo Sejima, a famous, late 20th century minimalist designer (Aoki 2003; Hasegawa 2006). 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. Significantly, past research using the box-counting approach has only been applied to the works of Frank Lloyd Wright, Le Corbusier and a limited selection of ancient buildings. This paper will not only expand the set of cases tested by adding a selection of late Twentieth Century examples, but these will also be the first examples of minimalist architecture tested by this method. This paper will conclude by first providing a discussion of the five houses of Kazuyo Sejima, with a comparison between their design features and their boxcounting results. Second, a brief description will be presented of how the fractal geometry of Sejima's architecture differs from that of other architects' works recorded in past research.

A Quantitative Comparison between the Formal Complexity of Le Corbusier’s Pre-Modern (1905-1912) and Early Modern (1922-1928) Architecture

“…But exactly how visually different are they? Fractal analysis is rare method which has been employed on multiple occasions to examine historical buildings (Burkle-Elizondo and Valdez-Cepeda, 2006;Ostwald, Vaughan Tucker, 2008;Ostwald, Vaughan, Chalup, 2008;). Bovill's (1996) method in particular, has been widely used even though it has only recently begun to be sufficiently refined for widespread application (Lorenz, 2003).…”

Representing architecture for fractal analysis: a framework for identifying significant lines

“…Architectural researchers have also used a manual variation of fractal analysis to measure the visual properties of contemporary and historic buildings (Bovill 1996;Bechhoefer and Appleby 1997;Burkle-Elizondo, Sala, and Valdéz-Cepeda 2004;Burkle-Elizondo and Valdéz-Cepeda 2006;Gozubuyuk, Cagdas, and Ediz 2006). More recently, a dedicated computational version of the method has been developed specifically for architectural analysis (Ostwald, Vaughan, and Chalup 2009;Ostwald and Vaughan 2010;Ediz and Ostwald 2012). However, despite the growing number of applications of this method, past research has noted that, because of inconsistencies in the way it has been applied, different measures can be derived from an analysis of the same elevation of a building (Zarnowiecka 2002;Lorenz 2003;Vaughan and Ostwald 2009a).…”

A face-house paradigm for architectural scene analysis

“…What factors influence our well-being when living in a particular urban neighbourhood ? Some studies proposed, for example, the involvement of harmonic ratios, others calculated the fractal dimension of façades and skylines to determine the aesthetic value of façades, street-and cityscapes [5,7,24,31,32,43].…”