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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.
Current Organic Synthesis
|February 4, 2025
Summary
Hexagonal fractals exhibit self-similarity and complex connectivity. Their topological indices and fractal dimensions strongly correlate with material properties like conductivity and strength.
Area of Science:
- Mathematics
- Materials Science
- Physics
Background:
- Hexagonal fractals are geometric patterns with self-similar, repetitive hexagonal structures.
- Their unique properties drive research across mathematics, physics, and chemistry.
Purpose of the Study:
- Analyze hexagonal fractals, focusing on topological indices and fractal dimensions.
- Model structure-property relationships for these complex geometric forms.
Main Methods:
- Computed various topological indices using mathematical techniques.
- Determined fractal dimensions to characterize scaling behavior.
- Established structure-property models linking indices and dimensions to material properties.
Main Results:
- Calculated topological indices revealed intricate connectivity and complexity.
- Fractal dimensions confirmed self-similarity and scaling.
- Structure-property modeling showed strong correlations with conductivity, mechanical strength, and reactivity.
Conclusions:
- The study offers insights into hexagonal fractals' topological characteristics and fractal dimensions.
- Developed models predict material properties based on fractal structure.
- Findings enhance understanding of complex structures in scientific domains.
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