#This repository contains two tasks.
#Task 1: Mandelbrot Sets The first task is relating to Mandelbrot sets. The function mandelbrot takes in the arguments n, N_max, and threshold, and computes the Mandelbrot fractal with a Mandelbrot iteration on each point. The output is a figure which also saves to a png file. It is titled mandelbrot.png. The figure displays a similar looking graphic to that given in the task. At the bottom of the file, there is a call to the function which allows the reader to change the input parameters to output a different figure.
#Task 2: Markov Chains The second task is relating to Markov Chains. A transition matrix P is generated out of random numbers, as well as probability distribution p which is shown as a vector. The sum of each row in transition matrix is equal to 1, as well as the sum of the elements in the matrix. Using a loop, P.T * p is calculated N times until the p stops changing. Separate from this process, np.linalg.eig is used to compute the eigenvector of P.T corresponding to the largest eigenvalue. This eigenvector, when scaled to a sum of 1, should equal the p found earlier. To show the convergence of p on the eigenvector, the norm difference is graphed using a loop. This graph is shown using many different n and N values, and all of them are outputted when the code is run.