Since the late 1980's a range of applications of fractal geometry, for the analysis of the built environment, have been proposed. One of these, the mathematician Benoit Mandelbrot's "box counting" approach, was developed by Carl Bovill who demonstrated a manual method for determining an approximate fractal dimension of architectural plans and elevations. Since that time, a computational variation of the method has been developed and tested providing a mathematical determination of the characteristic visual complexity of a building. The present chapter records research into the changing formal strategies employed by Frank Lloyd Wright for the design of houses. Wright designed many houses during his almost 70 year professional career. Historians have defined three distinct stylistic periods in his housing oeuvre; the Prairie style (generally the first decade of the 201 century), the "Textile Block" era (the 1920s) and the Usonian era (the 1930s to the 1950s). This chapter undertakes the first mathematical analysis of visual complexity in the domestic architecture of Wright. The research analyzes five houses from each of these three eras using the computational fractal approach to measuring visual properties of architecture. In this way it is possible to provide a mathematical determination of the relationship between the three major stylistic periods in Wright's work.
Built Environment: Design Management and Applications p. 63-88