Monte Carlo estimation of the Mandelbrot Set area

Features

1. Surface Area Estimation

• Utilize Monte Carlo estimation to calculate the surface area of the Mandelbrot set.
• Implement grid, random and Latin Hypercube sampling techniques for thorough exploration.

2. Convergence Investigation

• Explore the convergence of the area estimation as a function of the number of iterations in the Mandelbrot calculation.
• Analyze how the choice of sampling method impacts convergence.

3. GPU and CPU Implementation

• Leverage GPU acceleration for performance gains when available.
• Automatically switch to CPU if GPU is not accessible.

4. 95% Confidence Interval

• Calculate the 95% confidence interval for the area estimation to assess the reliability of the results as a function of the amount of runs.

How to Use

1. Clone the repository:

   git clone https://github.com/JTimmr/Stochastic_Simulation
   cd Stochastic_Simulation
   

2. Install dependencies:

   pip install -r requirements.txt
   

3. Open and run the Jupyter Notebook:

   jupyter notebook main.ipynb
   
   

Important Note

The parameter values provided in the Jupyter Notebook are optimized for GPU programming. If you are running the code on a CPU, be aware that the computation may take a significantly longer time. Consider adjusting the parameters based on your hardware specifications for optimal performance. If CUDA is installed and a GPU is detected, the major part of the code will automatically be executed on the GPU.

This project is licensed under the MIT License - see the LICENSE file for details.