AUTHOR=Al Saadi Jafar , Badr Layla 

TITLE=Fractal dimension, lacunarity, and Shannon entropy of self-assembled macroscopic copper dendrites

JOURNAL=Frontiers in Physics

VOLUME=Volume 12 - 2024

YEAR=2024

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1278781

DOI=10.3389/fphy.2024.1278781

ISSN=2296-424X

ABSTRACT=Macroscopic copper dendrites are self-assembled in a porous hydrogel without the application of an external potential. The copper dendrites possess fractal characteristics. The impact of the medium thickness, the initial concentration of copper (II) ions, and the solvent polarity on the evolving copper dendrites are addressed by investigating the fractal dimension, lacunarity, and Shannon Entropy of the structures. The analysis gives a quantitative description of the copper dendritic morphology and its connection to the mechanism of the self-assembly. The fractal dimension of the dendrites falls in a 1.75 -1.85 range. High self-similar complex systems show low lacunarity and high Shannon Entropy reflecting the low density of gaps and the high level of detail.