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

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 (SE) of the structures. The analysis gives a quantitative description of the copper dendritic morphology and its connection to the mechanism of self-assembly. The fractal dimension of the dendrites falls in the range of 1.75-1.85. High self-similar complex systems show low lacunarity and high Shannon entropy, reflecting the low density of gaps and the high level of detail.