K B Gayathri, Santiago Roy, S Govardhan
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India.
Rajalakshmi Institute of Technology, Chennai, 600124, India.
Curr Org Synth. 2025 Feb 3. doi: 10.2174/0115701794361800250116051003.
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.
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.
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.
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.
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.
六边形分形是呈现自相似性的复杂几何图案。它们的特征是在不同尺度上具有重复的六边形形状。由于其独特的性质和潜在应用，六边形分形已在包括数学、物理和化学在内的各个领域得到研究。
本研究的主要目的是对六边形分形进行全面分析，重点关注其拓扑指数、分形维数及其在结构 - 性质建模中的应用。我们旨在计算拓扑指数以量化六边形分形的结构复杂性和连通性。此外，我们将确定分形维数以表征其自相似性和标度行为。最后，我们将通过结构 - 性质建模探索拓扑指数、分形维数与相关性质之间的关系。
采用系统方法研究六边形分形。使用既定数学技术计算各种拓扑指数。确定分形维数。通过建立计算出的拓扑指数和分形维数与实验测量性质之间的关系来进行结构 - 性质建模。
该研究得出了关于六边形分形的重要发现。计算了各种拓扑指数，揭示了这些分形复杂的连通性和结构复杂性。确定了分形维数，证实了它们的自相似性质和标度行为。结构 - 性质建模表明拓扑指数和分形维数与诸如电导率、机械强度和化学反应性等性质之间存在强相关性。
本研究为六边形分形的拓扑特征、分形维数和潜在应用提供了有价值的见解。这些发现有助于更深入地理解这些复杂结构及其在各个科学领域中的相关性。所开发的结构 - 性质建模方法为基于材料的分形结构预测和控制其性质提供了有价值的工具。未来的研究可以探索更多应用，并深入研究控制分形结构与性质之间关系的潜在机制。
