A Multi-Method Framework for Assessing Visual Complexity in Historic Street Façades Through Fractal Analysis, User Perception, AHP, and TOPSIS

This study investigates the visual complexity of two opposing historic street façades on Sadrettin Konevi Street in Erzurum using an integrated framework that combines fractal analysis, user perception, expert evaluation, and TOPSIS-based decision-making. Fractal analysis was first performed using the box-counting method to calculate the façade fractal dimension (FD) values. In the second stage, perceived visual complexity was evaluated through a survey involving 100 architects and architecture-related professionals. In the third stage, visual complexity criteria identified from the literature were refined using the Delphi technique, reducing them to six key street-scale criteria. These criteria were then weighted using the Analytic Hierarchy Process (AHP) based on expert pairwise comparisons, and expert-based evaluation scores of the street façades were calculated accordingly. Finally, TOPSIS was used to integrate findings from fractal analysis, user perception, and expert evaluation into a unified comparative framework. The results demonstrated strong agreement among the three assessment approaches. The façade with the higher fractal dimension (FD) value (1.7574) was also perceived as more visually complex by most participants (67%) and achieved the highest expert-based weighted score. Rather than providing a universally validated model, the proposed framework is intended as a proof-of-concept that illustrates how computational, perceptual, and expert-based approaches can be integrated to assess visual complexity. Because the framework was demonstrated using only two opposing historic street façades, the findings should be interpreted as preliminary and case-specific rather than universally generalizable.