Self-Similarity of Diffusion-Limited Aggregates and Electrodeposition Clusters

Abstract

We report experimental evidence indicating that two-dimensional zinc electrodeposition clusters in the limit of small ionic concentration and small voltage are self-similar with generalized dimensions ${D}_{q}=1.66\ifmmode\pm\else\textpm\fi{}0.08$. Small-mass clusters obtained in a numerical simulation of diffusion-limited aggregation in a strip geometry are also found to be self-similar, with ${D}_{q}=1.60\ifmmode\pm\else\textpm\fi{}0.02$. These results suggest that electrodeposition and diffusion-limited clusters have a similar geometrical structure.