Electrodeposition from copper sulfate gives copper metal forming a fractal like pattern.
The apparatus is assembled by drilling a 1 mm (0.040 in = 18 gauge wire = #60 drill size) in the center of the top 6x6 plastic. This is placed on top of the second 6 x 6 sheet containing s loop of copper wire extending to near the edge of the plastic. This copper circle forms both the cathode and the volume containing the copper sulfate solution. A wire must extend outside the plastic cell. Through the 1 mm orifice is injected, by means of a plastic syringe, an amount of copper sulfate solution. The concentration of the copper sulfate is in the range 0.1M to 0.7M. The anode electrode of copper wire is placed into the central filling hole. A battery, or other DC power source, supplying from 5V to 20V is attached to the two electrodes. Electrolysis should occur leaving a pattern of copper deposit. The current and the time of application of current should be measured. After the deposition, the cell is disassembled, washed, carefully dried and the image scanned into a computer file. A carefully cleaned apparatus is assembled again and further experiments performed.
Another experiment is to inject a different volume of copper sulfate solution determining the volume injected and the radius (and amount) of deposition. The fractal dimension of each pattern should be measured.
Questions:
Since the sixties, fractal science has been one of the fastest growing inter-disciplinary sciences available. Since the plan of the CES is to reform education in high schools, fractals and chaos math seem an ideal place to start. Chaos is based on fundamental principles of nature, and is applicable to many fields of science. The initial applications were discovered in meteorology, but recently the fields of geology, biology, and ecology, as well as the field of pure math, have been developing these principles at a rapid pace. The Mandelbrot Set, the most famous of the fractal patterns, has been subsumed into commercial culture, and is immediately recognizable on t-shirts and posters.
Briefly, a fractal dimension is an abbreviated form of fractional dimension. For an example, take a straight, one dimensional line. Remove the middle third. Then remove the middle thirds from the two segments. Continue this process with the remaining segments indefinitely. What will remain is a distinct pattern of lines of varying lengths, arranged in a linear fashion. It is less than a line, but more than a point. It therefore can be thought of as having a dimension somewhere between zero and one.
This experiment involves the electroplating of copper from copper sulfate. The electrodeposition leaves a pattern, presumably fractal in nature which can be analyzed. The fractal dimension can be determined by a computer analysis of a scanned image of the pattern. The usual method of determining the fractal dimension of an object is simply to divide the image into a number of boxes of equal size, and determining the number of boxes which contain pieces of the image. The natural log of the number of boxes containing information is then plotted against the natural log of the size of the box. The negative of the slope of the resulting line is the fractal dimension of the image. A computer program will be supplied to do this for any given image.
Questions are raised into the nature of the deposition process-- is the fractal pattern related to the nature of copper, or the nature of the process itself? If a different material is plated, will the pattern still be fractal? Will it be the same fractal? How does the pattern change with time? If the experiment is run for longer periods of time, will the fractal dimensions of the object remain constant as the pattern grows?