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❄️ From snowflakes to graphene: self-organizing crystals reveal universal laws of nature. My new paper explores how edge kinetics, surface diffusion & fractal growth connect 2D & 3D worlds. 📄 t.co/YLyKoMxHFM #materials #graphene #crystals #fractalgeometry #nanotech #science

ZenodoSelf-Organizing Crystal Patterns: From Snowflakes to Graphene Self-organization is a fundamental process in nature where ordered structures emerge from disordered components without external direction. This paper examines the phenomenon of self-organizing crystal patterns across dimensional scales, focusing particularly on two-dimensional graphene formations and three-dimensional snowflakes. By analyzing the thermodynamic and kinetic factors that drive pattern formation, we identify remarkable similarities in the underlying mechanisms despite dimensional differences. The research reveals that pattern diversity in both systems is governed by similar principles of edge kinetics, surface diffusion, and environmental conditions. Quantitative analysis shows that graphene dendritic crystals exhibit fractal dimensions averaging 1.76, comparable to classical Diffusion-Limited Aggregation models, while dendritic snowflakes follow similar mathematical principles in three dimensions. These findings suggest universal principles of self-organization that transcend dimensionality and specific materials, with significant implications for designing novel materials with controllable morphologies and properties.