Evaluation of the fractal dimension of a crystalAbstractThe purpose of this experiment was to determine the effects of changes in voltage and molarity on the fractal dimension of a Cu crystal formed by the redox reaction between Cu and CuSO4. Using the introductory information obtained from the research, the fractal geometry of Cu crystals was determined for each set of parameters. Through data analysis, it has been determined that fractal dimension is directly related to voltage. The data also shows that molarity is inversely related to fractal dimension, but through research this has been discovered to be an error. Introduction A fractal is a geometric pattern that repeats infinitely and cannot be represented with typical mathematics. Fractals can be observed in nature in the way minerals develop over time, in the way tree branches grow from the trunk, and in the development of the human body (i.e. the lungs)1. These fractals provide a way to try to simplify the randomness of the universe through probability and theories regarding diffusion and intermolecular attractions. The dimensions in typical geometry are typical 0-D, 1-D, 2-D, and 3-D. However, much of the matter does not fit into these basic categories. A great example is a snowflake. If the negligible depth of a snowflake was ignored, it would be considered a 2D object. However this is not entirely true. A 2-D object can always be described by a finite number of tiles all on the same plane, since the snowflake cannot be described only with planes and also requires lines, it can be assumed to possess properties of both a 1-D and of 2 :-D object. A snowflake can be roughly approximated as a ~1.5-D object. This is the fractal dimension of the object. To determine a more exact fractal dimension of an object, increasingly smaller pieces are enlarged and used to determine a rough estimate of the amount of pieces that exhibit the same pattern (self-similarity) as the entire object. The relationship between the zoom and the self-similarity of the object determines the fractal dimension: