The relationship between the fractal dimension of plans and elevations in the architecture of Frank Lloyd Wright: comparing the Prairie Style, Textile Block and Usonian periods

Fractal geometry was first used as a quantifiable method for analyzing the visual complexity of a building in the mid 1990’s. Since then the method has been repeated many times – by scholars using both its manual and computational variations – to mathematically analyse architectural elevations. As a result of this practice, a large amount of comparative data describing the visual complexity of the exterior facades of famous buildings has become available. However, very little research has been undertaken into the fractal analysis of architectural plans and even less into the relationship, if any, that exists between visual complexity in plans and elevations. In order to test whether there is any pattern to the relationship between visual complexity in plans and associated elevations, this paper undertakes a comparative fractal analysis of 15 houses by Frank Lloyd Wright. Importantly, these houses are drawn from three distinct stylistic periods in Wright’s work. This suggests that, if the relationship between plan and elevation is significant, then clear trends should be discernable for each period. This paper describes the standard method of fractal analysis along with its computational variation that is used to calculate the present results. A description of each of the houses is then provided, followed by the presentation of the fractal dimension results. Finally, the paper analyses these results in detail and provides a conclusion regarding the proposed relationship between the visual complexity of plans and elevations in Wright’s domestic architecture.