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The purpose of this experiment is to determine the fractal dimension of the Boothbay, Maine coastline.
Math is centered around the concept of dimensions. Points, which are of infinitesimal size, have zero dimension. Straight lines, which can be measured, are one dimensional. Flat shapes such as squares are considered to be two dimensional because they can be measured in two directions. Voluminous shapes such as cubes and spheres are three dimensional because they can be measured in three different directions.
A fractal is something that does not have an integral dimension value. An example of something that exists with a fractional dimension is a coastline. Consider the Atlantic shoreline of the United States. When viewed from outer space, the coastline from north to south seems to be about two to four thousand miles long depending on smoothness. However as you get closer and into higher detail, the coastline would appear to be much more intricate and therefore longer, even though the displacement between the north and south borders has not changed. Due to this varying change in detail, the coastline cannot necessarily be classified as one dimensional, nor two dimensional. It is somewhere in between.
The fractal dimension of the Boothbay, Maine coastline is 1.27.
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The fractional dimension of the Boothbay, Maine coastline is 1.27.
Jordan Levine, Leah Oppenheim, Jonathan Hamill, Jason Atkins, Anand Maharaj, Tony Schneider, Keith Singh -- 2002Chaos Project pages in The Physics Factbook™
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