Mandelbrot me
So for my PMath370 class, Chaos and Fractals, I'm supposed to do a final project which somehow reflects content covered in the course. For my report that I wrote for the course a while back in the term, I wrote on the Mandelbrot set and the Julia sets, and the article that I reported on said that we can assign a rational number to each bulb around the main cardioid of the Mandelbrot set, and if you start at the cusp on the right side of the Mandelbrot set and move around the edge of the main cardioid in the clockwise direction, the order of the bulbs based on their assigned rational numbers is the natural order of the rational numbers between 0 and 1, and that there is a bulb for every rational number between 0 and 1. The article I wrote my report on didn't go into depth about this or explain why or show a proof that it was true, it just gave a few examples, so I was thinking, for my final project, that I could look up the references for where the author of that article got his information about the rational numbers related to the Mandelbrot set, and write an essay as my project actually explaining how we know that to be true and maybe a little bit about why it's true. I'm not sure what sort of mathematics it involves though, it might be beyond the scope of my education so far. We'll see, I guess.
