Fractal and entropy analysis of traditional and modernist building facades in street-level view : the case of Sweden’s growing cities

Abstract: This study presents a quantitative analysis of traditional and modernist building facades in urban environments, focusing on the assessment of their complexity and coherence. Fractal and entropy analysis techniques were employed to objectively evaluate the differences between the two architectural styles within the preference matrix framework. The study aimed to determine variations in fractal dimensions and information entropy, describe the nature of these variations, and discuss their implications for the preference matrix. Street-level view images capturing traditional and modernist architectural styles in Swedish cities were utilized in this study. The images underwent a process of tracing to extract detailed lines representing the building facades. Fractal analysis was applied to measure the complexity of the topology represented by these lines. Additionally, the images were mapped according to building surface, enabling the calculation of information entropy to assess the coherence and diversity of the surface distribution. Significant differences in fractal dimensions were observed between traditional and modernist styles. Traditional architecture exhibited higher fractal dimensions, indicating a more intricate and complex topology characterized by detailed elements. In contrast, modernist architecture displayed lower fractal dimensions, reflecting a less complex arrangement of lines and edges. Regarding information entropy, no significant differences were found between the two styles, suggesting comparable levels of coherence and diversity in the distribution of building surfaces. However, a positive relationship was noted, indicating higher entropy and diversity in the traditional style.