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Hexagonal Fractals: Topological Indices, Fractal Dimensions, Structure-property Modeling and its Applications
Gayathri K B1, Roy Santiago1, Govardhan S2
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India.
Background:
Hexagonal fractals are intricate geometric patterns that exhibit selfsimilarity. They are characterized by their repetitive hexagonal shapes at different scales. Due to their unique properties and potential applications, hexagonal fractals have been studied in various fields, including mathematics, physics, and chemistry.
Objectives:
The primary aim of this research is to provide a comprehensive analysis of hexagonal fractals, focusing on their topological indices, fractal dimensions, and their applications in structureproperty 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 properties through structure-property modeling.
Methods:
A systematic approach was employed to investigate hexagonal fractals. Various topological indices were computed using established mathematical techniques. Fractal dimensions were determined. Structure-property modeling was conducted by establishing relationships between the calculated topological indices and fractal dimensions with experimentally measured properties.
Results:
The research yielded significant findings regarding hexagonal fractals. A variety of topological indices were calculated, revealing the intricate connectivity and structural complexity 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 scientific domains. The developed structure-property modeling approaches offer a valuable tool for predicting and controlling the properties of materials based on their fractal structure. Future research may explore additional applications and delve into the underlying mechanisms governing the relationship between fractal structure and properties.
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