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.