In the late 1970s Mandelbrot argued that natural systems frequently possess characteristic geometric or visual complexity over multiple scales of observation, suggesting that systems which have evolved over time may exhibit certain local visual qualities that also possess deep structural resonance. In mathematics this realization, founded on seemingly irrational or "monstrous" numbers, lead to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity. During the last decade this concept was developed 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 rules for analyzing buildings. However, the assumptions implicit in this method have never been adequately questioned. The present paper returns to the origins of the conventional "box counting" method of fractal analysis for historic buildings to reconsider the initial interpretations of the architecture of Le Corbusier and Frank Lloyd Wright. This new analysis uses "Archimage" software, developed by the authors, to undertake a multi-dimensional review of the fractal dimension of the houses of Wright and Le Corbusier and, in doing so, to develop a more consistent method for the application of such mathematical tools to the analysis of historic buildings.
Nexus VII: Architecture and Mathematics p. 217-231