Mandelbrotset

Investigate the area of a Mandelbrotset for the course Stochastic Simulation at University of Amsterdam.

License:

Required Packages:

numpy
matplotlib
random
time
math
scipy

You can easily install these packages by using 'pip install name_package' in your anaconda terminal.

Instructions:

Clone the files and make sure you have all required packages installed. Run simulations.py if you want to see the outcomes of simulations for Random Sampling, LHS and Orthogonal sampling.

Note: It may occur that you have to delete the line 'from mandelbrotset.monte import *' and change it to 'from monte import *'. However, some IDE'S require 'from monte import *' (e.g. visual studio) and other 'from mandelbrotset.monte import *' (e.g. pycharm). In any case, make sure that all files are stated in the same folder. This is important as you will need to use functions stated in monte.py.

Explanations per file

• monte.py
  This file contains all functions for estimating the Mandelbrot area: The brute-force estimate of the mandelbrot area, the random sampling method, the Latin Hypercube sampling (LHS) method and the orthogonal sampling method.

• plot_mandelbrot.py
  When running this file we get the results of figure 2, a visualisation of the mandelbrotset (if we change maxiter on line 14 to 20 we get fig 2a, otherwise with maxiter 100 we get fig 2b)

• simulation.py
  This file contains a set-up for the simulations that are used to determine the values in table 2. It prints the values for every simulation, the total variance, STD and the corresponding confidence intervals.

• plot_samplemethods.py
  For figure 3a, b and c run plot_samplemethods.py. To run faster/prevent overloading your computer the file is split into 3 parts and one is meant to run the code per figure and comment out the rest of the code. This is also mentioned in the file itself.

• Orthogonal.py
  This file is intended to test the orthogonal sampling method, if desired. It enables to print the determined blocks and can give a graph of the specified samples.

• LatinHS.py
  This file is intended to test the LHS method, if desired. Also it has the ability to print a plot to visualise which samples are taken.

• antithetic.py
  This file is intended for the use of antithetic variables. It prints the outcomes for random sampling with antithetic variables as well as the outcomes of all other sampling methods.

• plot_an.py
  When running this file we get figure 4.

• CV.py
  This file was intended for control variates. However, this you can neglect this file.