{"title":"Hexagonal Fractals: Topological Indices, Fractal Dimensions, Structure-Property Modeling and its Applications.","authors":"Gayathri K B, Roy Santiago, Govardhan S","doi":"10.2174/0115701794361800250116051003","DOIUrl":null,"url":null,"abstract":"<p><strong>Background: </strong>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.</p><p><strong>Objective: </strong>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.</p><p><strong>Methods: </strong>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.</p><p><strong>Results: </strong>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.</p><p><strong>Conclusion: </strong>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.</p>","PeriodicalId":11101,"journal":{"name":"Current organic synthesis","volume":" ","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Current organic synthesis","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.2174/0115701794361800250116051003","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, ORGANIC","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Current Organic Synthesis publishes in-depth reviews, original research articles and letter/short communications on all areas of synthetic organic chemistry i.e. asymmetric synthesis, organometallic chemistry, novel synthetic approaches to complex organic molecules, carbohydrates, polymers, protein chemistry, DNA chemistry, supramolecular chemistry, molecular recognition and new synthetic methods in organic chemistry. The frontier reviews provide the current state of knowledge in these fields and are written by experts who are internationally known for their eminent research contributions. The journal is essential reading to all synthetic organic chemists. Current Organic Synthesis should prove to be of great interest to synthetic chemists in academia and industry who wish to keep abreast with recent developments in key fields of organic synthesis.
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