MODEL OF RAMIFICATION IN ELECTRODEPOSITED FRACTALS

Abstract

The macroscopic branching and shape of a metal, electrodeposited in quasi-two dimensions, can be represented by a Lindenmayer System of multiple iterated function systems. The motif of a central branch that continues and two side branches is shown to allow modeling of the observed shapes. The dilation (or contraction) in length, and the angle of a branch with respect to the central stem are the only parameters needed to create realistic simulations of such ramified deposits. Values for these quantities together with standard deviations measured from a number of electrodeposited copper fractals have been used to generate simulations. Measurement of the parameters of the motif, the average linear dilation factor from one generation to the next, and the angles between branches, show a 5% relative standard deviation of these factors across one growth. The values of these parameters can also indicate the transition from an open fractal form to the more directed dendritic form. The results are compared with other approaches to describing these systems.