Fractal Structures of Zinc Metal Leaves Grown by Electrodeposition

Abstract

Zinc metal leaves are grown two-dimensionally by electrodeposition. The structures clearly remind us of the random patterns simulated by computer according to the Witten-Sander diffusion-limited-aggregation model. The scale invariance is tested by computing the density-density correlation function for the digitized patterns of the photographs. The Hausdorff dimension averaged over many examples is $D=1.66\ifmmode\pm\else\textpm\fi{}0.03$, which is in excellent agreement with that of the two-dimensional diffusion-limited-aggregation model ($D\ensuremath{\cong}\frac{5}{3}$).