The Fractal Analysis of Architecture: Calibrating the Box-Counting Method Using Scaling Coefficient and Grid Disposition Variables

Since the mid-1990s architectural researchers have used the box-counting method to calculate the fractal dimension of a range of buildings and urban forms. While this approach has been widely adopted, there has been little consistency in how the multiple variables in the method have been applied. Furthermore, despite precedents in the sciences, no attempt has been made in architectural or urban analysis to use these parameters to calibrate or refine the method. In this paper the computational version of the box-counting approach is presented along with its methodological variables. Thereafter, nine mathematical fractals with known dimensions are tested using this method to identify the optimal approach to the scaling coefficient and grid disposition variables. Finally, using these new settings, two classic architectural test cases are reexamined: Robie House and the Villa Savoye.