A Classroom Demonstration of Electrodeposited Fractal Patterns

Abstract

Because of the increasing interest in teaching fractal geometry (1), it is opportune to design practical student experiments where the complexity of real systems can be examined. This is an inexpensive laboratory experiment combining the recommended techniques for teaching fractal geometry in the classroom with the standard procedures for studying electrochemical deposition (ECD) of ramified patterns {2-8) in the regime of low solution concentration and low applied constant driving force. The patterns in this regime are statistically self-similar fractals. The term fractal refers to a shape made of parts similar to the whole in some way.1 "Statistically self-similar" means that the pattern retains its overall shape at limited length scales of observation. Although a crude version of the experiment was outlined in a conference a few years ago (5), an updated version is presented here. The experimental set-up does not consist of sophisticated instrumentation, where computer-based or digitizing techniques (6, 7) may be required to obtain fractal dimension estimates of the patterns. The set-up is suitable for overhead demonstrations, can be adapted to physical science laboratory courses, and is an attractive way to introduce students to fractal growth phenomena and scaling concepts. Experimental ProcedureApparatus A working grid of 1/2 in. x 1/2 in. basic cells is constructed by drawing fine straight lines on a piece of 16 in. x 16 in. white paper. The grid also can be constructed from quadrille paper sheets that conform to these dimensions. Because 1024 (i.e., 32 x 32) basic cells are provided, each cell