Python Physics: 1D Random Walks and Animated Histograms

3 min read 16 days ago
Published on May 06, 2025 This response is partially generated with the help of AI. It may contain inaccuracies.

Introduction

This tutorial will guide you through creating a 1D random walk simulation using Python and Web VPython. You will learn how to animate the random walk and generate a histogram to visualize the final positions after multiple iterations. This is a great way to understand random processes and their statistical implications.

Step 1: Setting Up Your Environment

To get started, ensure you have access to a suitable environment for running Web VPython. You can use Trinket or any other platform that supports VPython.

  1. Visit the Trinket website or your chosen platform.
  2. Create a new Python project.
  3. Make sure you have the VPython library available. If using Trinket, it’s already integrated.

Step 2: Implementing the Random Walk

Next, you’ll write the code for the 1D random walk. The basic idea is to move an object either left or right at each step.

  1. Define the number of steps and repetitions:
    steps = 100
    repetitions = 500
    
  2. Set up the initial position:
    position = 0
    
  3. Create a loop for the random walk:
    for i in range(steps)
  4. step = random.choice([-1, 1]) # Choose to move left or right position += step # Update the position

Step 3: Animating the Walk

To visualize the random walk, you’ll animate the movement of an object in the 1D space.

  1. Create a visual object:
    from vpython import sphere, vector
    ball = sphere(pos=vector(position, 0, 0), radius=0.1)
    
  2. Update the position of the ball during the walk:
    for i in range(steps)
  3. rate(10) # Control the speed of the animation step = random.choice([-1, 1]) position += step ball.pos.x = position

Step 4: Creating the Histogram

After running the random walk multiple times, you can display a histogram of the final positions.

  1. Use a list to store final positions:
    final_positions = []
    
  2. Repeat the random walk for the defined number of repetitions and collect the results:
    for j in range(repetitions)
  3. position = 0

    for i in range(steps)

    step = random.choice([-1, 1]) position += step final_positions.append(position)
  4. Import the necessary library for plotting and create the histogram:
    from vpython import histogram
    histogram(data=final_positions, bins=20)  # Adjust bins as necessary
    

Conclusion

In this tutorial, you learned how to implement a 1D random walk using Python and Web VPython, animate the walk, and create a histogram of the final positions. This example illustrates basic principles of randomness and probability.

Next steps could include experimenting with different step sizes, increasing the dimensions of the walk, or further analyzing the resultant distributions. Happy coding!