This repository contains a Python implementation of the Lévy Walk simulation, a random walk model with a power-law step length distribution. The code simulates multiple walkers with boundary conditions and visualizes their trajectories for different values of the power-law exponent.

Lévy Walk Simulation

This repository provides a Python implementation of the Lévy Walk simulation, a random walk model where the step lengths are drawn from a power-law distribution. The code simulates multiple walkers with boundary conditions and visualizes their trajectories for different values of the power-law exponent.

Features

• Simulate Lévy Walk for multiple walkers with boundary conditions
• Generate step lengths from a power-law distribution
• Plot the trajectories of walkers for different power-law exponents

Requirements

• Python 3.x
• NumPy
• Matplotlib

Usage

1. Clone the repository:

   git clone https://github.com/your-username/levy-walk-simulation.git

2. Navigate to the project directory:

   cd levy-walk-simulation

3. Run the simulation script:

   python levy_walk.py

   This will generate a figure titled LW.png containing 12 subplots, each showing the trajectories of 3 walkers for a different power-law exponent ranging from 0.5 to 2.5.

Code Overview

The repository contains the following Python file:

• levy_walk.py: This file contains two main functions:
  • levy_walk(n_walkers, n_steps, alpha, x_range, y_range): Simulates the Lévy Walk for multiple walkers with boundary conditions.
  • plot_trajectories(trajectories, alpha, ax): Plots the trajectories of multiple walkers on a given Matplotlib axes.

Contributing

Contributions are welcome! If you find any issues or have suggestions for improvements, please open an issue or submit a pull request.

This repository contains a Python script that simulates the Lévy Walk for multiple walkers with boundary conditions. The script generates and plots the trajectories of the walkers for different values of the power-law exponent. Feel free to customize the content of the README file according to your specific requirements.