Revealing Morphological Complexity in Silver Aggregates Through Multifractal Analysis

This paper investigates the morphological complexity of self-organized silver aggregates formed via the reduction of silver ions in a gelatin medium. A comprehensive multifractal analysis showed that the aggregates exhibit complex scaling behavior beyond simple mono-fractality. The reverse sigmoidal dependence of the generalized fractal dimension Dq on the moment order q confirms the aggregates’ multifractal nature, and the variation in Renyi entropy Hq with both q and the size scale ε underscores the system’s inherent chaotic dynamics. The left-sided f(α) multifractal spectra indicate the dominance of peripheral growth of the silver aggregates by the diffusion of Ag+ ions towards the growing electrode. The observed capacity dimension Db range aligns with the diffusion-limited aggregation process, reflecting the interplay between concentration gradient and ionic repulsion. The correlation between lacunarity and the correlation dimension D2 is approached only at the smallest scales.