Abstract
A famous topic in mathematics involves the theoretically infinite nature of geographic coastlines. If one were to measure the perimeter of Great Britain, for example, the smaller the measuring tool, the larger and more accurate the measured perimeter would be. This phenomenon contains similar properties to the mathematical objects known as fractals: shapes with infinitely many self-similar segments. In our research project, we set out to visualize what a fractal coastline would look like and how it would compare to its real-life counterpart. To do this, we first obtained the coordinates of the British coastline. We then wrote code to insert a fractal segment between each coordinate, thereby creating a new set of fractal coordinates. This code worked on any number of coordinates and allowed us to use several different types of fractals with any number of iterations. Once we had our desired fractal coordinates, we uploaded them to the mapping software ArcGIS to see our results. From far away, the natural coastline and the fractal coastline looked smooth and identical, but zooming in revealed more detail. It was much easier to see the places where the fractal coastline differed slightly from the natural coastline, just like how a larger measuring tool overlooks the smaller crevices of geographic coastlines. Not only did we achieve our goal of visualizing a fractal coastline, but this research provided us with several jumping-off points for future investigation, such as comparing the coastlines’ numerical perimeters, areas, and fractal dimensions.