Fractal Analysis of the Asma al-Ḥusna Mo'aqqali Inscription at the Pir Bakran Shrine, Isfahan

Introduction: The Asma al-Husna inscription at the Pir Bakran Shrine is a notable example of Islamic art from the Ilkhanid period, as a manifestation of the divine names and a masterpiece of Islamic calligraphy. In terms of scale and word count, it is among the largest Mo'aqqali inscriptions in the history of architectural ornamentation in Iran. Its existence signifies the glorification and sanctification of God through art. This study applies fractal analysis to examining the complex and repetitive patterns in the inscription. The research seeks to answer the main question: How can the Asma al-Husna inscription at the Pir Bakran shrine be analyzed based on fractal geometry? In this regard, answering two subsidiary questions is essential: How is self-similarity manifested in the structure of the inscription? How can the fractal dimension of the inscription be calculated?Research Method: This research is fundamental in its aim and descriptive-analytical in its methodology. Data collection was conducted through fieldwork and documentary research. Data analysis and fractal dimension calculation were performed using the Fractalyse software through simulation methods and the extension of filled and empty spaces, considered as a spatial fractal.Findings: The structure of the inscription displays self-similarity across multiple layers, including the initial checkerboard pattern, the calligraphic baseline, the geometric design, and its components. The fractal dimension of the inscription was calculated to be ۲.۱۲ (decimal). The repetition of divine names within intricate patterns reflects divine order and the concept of infinity. Furthermore, fractal dimension calculations of the Mo'aqqali scripts in the Asma al-Husna inscription, compared with those of the opposing inscription (Salawat Kabira), revealed identical density, distribution of filled and empty spaces, and fractal breaks in both inscriptions. The arrangement of words in both inscriptions appears to be meticulously calculated.Conclusion: Based on fractal analysis, the degree of conformity of the inscription’s geometric structure with non-Euclidean fractal geometry (the geometry of nature) is determined, quantifying the complexity, roughness, and porosity of the inscription. The inscription exhibits self-similarity in its structure and arrangement of words, as well as a fractional dimension of ۲.۱۲, indicating adherence to non-Euclidean fractal geometry. Moreover, the high complexity of the script (۱.۷۶۲), in harmony with the opposite inscription, attracts and engages the viewer’s effort to read the inscription.

کلیدواژه ها:

Pir Bakran Shrine ، Asma al-Husna Inscription ، Mo'aqqali script ، Fractal geometry ، Self-Similarity ، Fractional Dimension