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| Formato: | Recurso digital |
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| Publicado: |
Zenodo
2025
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| Materias: | |
| Acceso en línea: | https://doi.org/10.5281/zenodo.15791929 |
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- <p> Self-organization is a fundamental process in nature where ordered structures<br> emerge from disordered components without external direction. This paper exam<br>ines the phenomenon of self-organizing crystal patterns across dimensional scales, fo<br>cusing particularly on two-dimensional graphene formations and three-dimensional<br> snowflakes. By analyzing the thermodynamic and kinetic factors that drive pattern<br> formation, we identify remarkable similarities in the underlying mechanisms despite<br> dimensional differences. The research reveals that pattern diversity in both systems<br> is governed by similar principles of edge kinetics, surface diffusion, and environmen<br>tal conditions. Quantitative analysis shows that graphene dendritic crystals exhibit<br> fractal dimensions averaging 1.76, comparable to classical Diffusion-Limited Aggre<br>gation models, while dendritic snowflakes follow similar mathematical principles in<br> three dimensions. These findings suggest universal principles of self-organization<br> that transcend dimensionality and specific materials, with significant implications<br> for designing novel materials with controllable morphologies and properties.</p>