Building?s fractal dimension trend and its application in visual complexity map

Research on applying fractals into the architectural field has a long history, and the fractal dimension contributes as a measurement to investigate the complexity of a building's geometric pattern, especially in terms of its visual complexity. However, as general multi-fractal patterns, a building's fractal dimension does not maintain one number but varies with observation scales; therefore, in this study, a building's fractal dimension trend connected to the observation distance is presented as a more comprehensive description of a building's visual complexity. Methodologically, a generic method is proposed to compute a building's fractal dimension trend, which includes an image-processing program (foreground extraction and edge detection) and a computation program for fractal dimension based on the box-counting method. According to the method, the application of visual complexity map is subsequently applied to evaluate a building's visual characteristics in terms of its visual complexity. As a result, this study demonstrates that the fractal dimension trend is an instrument that can be used to understand, analyze, and utilize a building's environment of visual complexity, and has potential to be further developed through more extensive research for other possible applications.