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

Clone the repository:

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

Navigate to the project directory:
```
cd levy-walk-simulation
```
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.