Hexagonal Fractals: Topological Indices, Fractal Dimensions, Structure-property Modeling and its Applications

Background: Hexagonal fractals are intricate geometric patterns that exhibit self-similarity. They are characterized by their repetitive hexagonal shapes at different scales. Due to their unique properties and potential applications, hexagonal fractals have been stud-ied in various fields, including mathematics, physics, and chemistry. Objective: The primary aim of this research is to provide a comprehensive analysis of hex-agonal fractals, focusing on their topological indices, fractal dimensions, and their applica-tions in structure-property modeling. We aim to calculate topological indices to quantify the structural complexity and connectivity of hexagonal fractals. Additionally, we will determine fractal dimensions to characterize their self-similarity and scaling behaviour. Finally, we will explore the relationship between topological indices, fractal dimensions, and relevant prop-erties through structure-property modeling. Methods: A systematic approach was employed to investigate hexagonal fractals. Various topological indices were computed using established mathematical techniques. Fractal di-mensions were determined. Structure-property modeling was conducted by establishing re-lationships between the calculated topological indices and fractal dimensions with experi-mentally measured properties. Results: The research yielded significant findings regarding hexagonal fractals. A variety of topological indices were calculated, revealing the intricate connectivity and structural com-plexity of these fractals. Fractal dimensions were determined, confirming their self-similar nature and scaling behaviour. Structure-property modeling demonstrated strong correlations between the topological indices and fractal dimensions with properties such as conductivity, mechanical strength, and chemical reactivity. Conclusion: This research provides valuable insights into the topological characteristics, fractal dimensions, and potential applications of hexagonal fractals. The findings contribute to a deeper understanding of these complex structures and their relevance in various scien-tific domains. The developed structure-property modeling approaches offer a valuable tool for predicting and controlling the properties of materials based on their fractal structure. Fu-ture research may explore additional applications and delve into the underlying mechanisms governing the relationship between fractal structure and properties.