Complexity across scales in the work of Le Corbusier, Using box-counting as a method for analysing facades

Abstract

Since Benoît Mandelbrot raised the question about the length of Brit-ain’s coastline in 1967, it has become obvious that fractal geometry is appropriate for describing irregular forms. In 1996 Carl Bovill applied box-counting, a fractal analysis method, for the first time to architecture in order to quantify the charac-teristic visual complexity of facades. This paper presents an approach utilizing fractal analysis to provide another view on Le Corbusier’s architectural compo-sition. Altogether 17 house designs are considered, 14 of them have been built be-tween 1916 (Schwob Villa) and 1928 (Savoye House). Throughout this paper an implementation of the box-counting method written by the author is used. Besides discussing the results, the implementation itself with its advantages and disad-vantages is explored.