Python Physics: 1D Random Walks and Animated Histograms
Table of Contents
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.
- Visit the Trinket website or your chosen platform.
- Create a new Python project.
- 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.
- Define the number of steps and repetitions:
steps = 100 repetitions = 500
- Set up the initial position:
position = 0
- Create a loop for the random walk:
for i in range(steps)
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.
- Create a visual object:
from vpython import sphere, vector ball = sphere(pos=vector(position, 0, 0), radius=0.1)
- Update the position of the ball during the walk:
for i in range(steps)
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.
- Use a list to store final positions:
final_positions = []
- Repeat the random walk for the defined number of repetitions and collect the results:
for j in range(repetitions)
- Import the necessary library for plotting and create the histogram:
from vpython import histogram histogram(data=final_positions, bins=20) # Adjust bins as necessary
position = 0
for i in range(steps)
step = random.choice([-1, 1])
position += step
final_positions.append(position)
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!