Determining the fractal dimension of the architecture of Eileen Gray

Fractal geometry, emerging from Benoit Mandelbrot’s mathematical proposals in the late 1970’s, has evolved from its initial domain in the sciences of non-linearity and complexity to a much broader disciplinary field that has recently included architecture. Inspired by Mandelbrot’s work, Carl Bovill’s 1996 research describes the “box-counting” method for calculating the approximate fractal dimension of the elevations and plans of buildings. Apart from box-counting, there are currently no methods available to determine, and thus compare, the fractal dimensions of buildings. Only a small number of buildings have been previously analysed by this method; these include houses by Le Corbusier and Frank Lloyd Wright. This paper is the first investigation of the fractal dimensions of five of the house designs of Eileen Gray; a prominent architect working mainly in France between 1922 and 1956. In this paper, a computational variation of the box-counting approach is applied to a multi-dimensional review of the houses of Gray. This research is important because it expands the limited pool of examples of early Twentieth Century architects who have been analysed using the method. The paper concludes with a comparison between Gray’s results and outcomes from previous research on the fractal dimensions of the domestic architecture of her contemporary, Le Corbusier. This last component is important because it is the first attempt in any research project to validate the presumed correspondence between architectural style and fractal dimension.