Fractals & Chaos Assignment for 10/23

In class today, we derived a new method of finding the dimension of a fractal. We observed that if we make a log-log plot of the step sizes and counts of steps that “fit” in a curve, the distribution of points comes out to a roughly linear association, the slope of which is the dimension of the fractal. This plot is called a Richardson plot, named after mathematician and meteorologist Lewis Fry Richardson. His work was largely ignored when it was first published in 1961, but gained notoriety when Benoit Mandelbrot cited it extensively in his seminal paper How Long is the Coast of Britain (feel free to read the paper here!)

We concluded class today by testing this theory to find the dimension of a circle, the results of which can be found here.

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