• Background: You are perhaps familiar with the famous Mandelbrot set - a fractal with incredibly complex structure.
These fractals are interesting to compute, as they can be ‘zoomed in’ infinitely to obtain finer and finer structure. While the dimension of a rectangle and a line in the plane (2 and 1) are obvious, its a remarkable fact that fractals have dimensions somewhere in between.
This is a quantity that you can compute numerically with the right algorithm.
In this project, we write code to create some fractals - for instance, the fractals related to Newton’s method (and learn Newton’s method along the way, although this is merely tangential).
Play around with this type of fractal to get interesting shapes, and visualize the fractal with pyplot.
Then - the computational focus - calculate the ‘dimension’ of the fractal using boxes, and see how far you can get with it given the time constraints and computer power you have.
A basic knowledge of complex numbers and an interest in using the plotting tools of python is necessary.