Abstract

Background and purpose
The townscape combines traditional and modern elements shaped across different periods and styles. Some components evoke memories and a sense of belonging, while others hinder the recognition of the city's texture, failing to engage the senses. The theory of complexity seeks to reveal hidden orders within identifying elements, suggesting that spatial relationships follow specific mathematical formulas rather than random arrangements. Though complex, the resulting shape, form, and geometry contain a hidden order that imbues meaning, contributing to the identity and sense of belonging within a space. This research aims to connect physical complexity theory with townscape theories to interpret the complexity of physically identity-laden townscapes, particularly those with historical significance.
Methodology
This study employs a simultaneous descriptive-analytical and quantitative-qualitative approach. It comprises two main sections as the first delves into theoretical foundations related to fractals and their application in townscapes, examining historical context. The second part involves selecting and photographing townscapes in the historical context of Kermanshah city to measure their physical complexity. To calculate the fractal dimension, each photo is categorized into three scales as far, middle, and close distances. Fractal dimensions are calculated using "ImageJ" software for 14 images from seven historical townscapes, including elements added to the townscapes in different periods.
Findings and discussion
Calculating fractal dimensions for selected townscapes within the historical context of Kermanshah at varying distances revealed interesting patterns. It was observed that older townscapes featuring buildings and historical elements exhibit higher complexity compared to newer townscapes. When examining the fractal dimension at a middle distance, it became evident that historical townscapes, characterized by a strong physical identity, showcase increased physical complexity, which is accompanied by either a constant or slight decrease in complexity. This trend is reiterated in the near distance, demonstrating an escalation in physical complexity as one approaches the townscape with a more pronounced physical identity. In addition to changes in the fractal dimension, it is noteworthy that images at a far distance encompass more elements and components compared to the other two distances. Consequently, one might expect a decrease in the fractal dimension as details diminish in the overall image. However, this outcome was observed only in newer townscapes.
Conclusion
The results indicate that townscapes of Kermanshah with a stronger historical identity exhibit higher physical complexity than those lacking historical identity. Additionally, there is a direct correlation between fractal dimension (physical complexity) and subjective knowledge and meaning associated with the townscape. The evaluation of complexity from three different scales reveals that physical complexity is more consistent in historical urban townscapes compared to newer ones. Over time, townscapes become richer and more physically complex, provided newer elements contribute to the continuity of physical-visual content instead of disrupting it. In townscapes with a more complex urban identity, the similarity between old and new elements surpasses differentiation, emphasizing unity and continuity overabundance and transformation. Calculating these complexities is a valuable tool for monitoring damage to historical city sights and proposing solutions for preserving identity, continuity, and connection between the present and the future.