Evaluation of the Fractal Dimension of a Crystal :: Chemistry Chemical Papers

Evaluation of the Fractal Dimension of a Crystal Abstract The purpose of this experiment was to determine the effects of voltage and molarity changes on the fractal dimension of a Cu crystal formed by the re-dox reaction between Cu and CuSO4. Using the introductory information obtained from research, the fractal geometry of the Cu crystals was determined for each set of parameters. Through the analysis of data, it was determined that the fractal dimension is directly related to the voltage. The data also shows that the molarity is inversely related to the fractal dimension, but through research this was determined to be an error. Introduction A fractal is a geometric pattern that is repeated indefinitely that it cannot be represented with typical mathematics. Fractals can be seen in nature in the way minerals develop over time, the manner in which trees limbs shoot from the trunk, and the development of the human body (i.e. the lungs)1. These fractals determine a way to attempt to simplify the randomness of the universe via probability and theories regarding diffusion and intermolecular attractions. The way dimensions in typical geometry are the typical 0-D, 1-D, 2-D, and 3-D. However, much matter does not fit these basic categories. A great example is a snowflake. If the negligible depth of a snowflake were ignored, it would be considered a 2-D object. However this is not completely true. A 2-D object can always be described by a finite number of tiles all in the same plane, because the snowflake cannot be described with only planes and also requires lines, it can be assumed it possesses properties of both a 1-D and 2-D object. A snowflake can be loosely approximated as a ~ 1.5-D object. This is fractal dimension of the object. In order to determine a more exact fractal dimension of an object, smaller and smaller pieces are zoomed in upon and used to determine a rough estimate of the amount of pieces that exhibit the same pattern (self-similarity) as the whole object. The relationship between the zoom and self similarity of the object determine the fractal dimension: