Lucia plays the violin in her school orchestra and enjoys ocean sports. She hopes to pursue a career in music or marine biology because "there are endless puzzles to solve about the ocean."
Like trees, fish have growth rings, recorded in their scales. Lucia read about fractal math as applied to tree rings, and thought that fish scale rings might also provide information about the life of the animal. She hypothesized that fish scales would follow a fractal pattern a geometric pattern that repeats over a variety of ranges.
Lucia obtained four species of USDA-inspected fish and obtained micrographs of fish scales using a digital microscope. She then converted these images to grayscale and performed rescaled range analysis on the pixel intensity values of a cutout section of each image. From this she calculated a Hurst coefficient to determine whether long- or short-term fractal correlations occurred in the growth of the scale. A Hurst coefficient of .5 to 1.0 indicates a highly fractal pattern. She found an average of .7 for each fish scale tested; mullet had the strongest positive correlation at .79 and salmon the least at .67. Lucia concluded that rescaled range analysis of fish scales has great potential to help in tracking environmental impacts on fish life.