Average of 100 random walkers with 1000 steps

Question

I was asked to write the code of 100 random walkers, each with 1000 steps. then plot the steps of the average of the 100 walkers. I was able to plot all the walkers in one plot, but couldn't find a way to plot the average. any help will be appreciated. thank you.

here is my code:

import numpy as np
import matplotlib.pyplot as plt
import random

# 1
N = 100
for j in range(N):
    def randomwalk1D(n):
        x, t = 0, 0
        # Generate the time points [1, 2, 3, ... , n]
        time = np.arange(n + 1)
        position = [x]
        directions = [1, -1]
        for i in range(n):
            # Randomly select either +1 or -1
            step = np.random.choice(directions)
            
            # Move the object up or down
            if step == 1:
                x += 1
            elif step == -1:
                x -= 1
            # Keep track of the positions
            position.append(x)
        return time, position
    rw = randomwalk1D(1000)
    plt.plot(rw[0], rw[1], 'r-', label="rw")
plt.show()

Answer 1

Modify your code like this:

import numpy as np
import matplotlib.pyplot as plt
import random

# 1
N = 100
walkers = []  # HERE
for j in range(N):
    def randomwalk1D(n):
        x, t = 0, 0
        # Generate the time points [1, 2, 3, ... , n]
        time = np.arange(n + 1)
        position = [x]
        directions = [1, -1]
        for i in range(n):
            # Randomly select either +1 or -1
            step = np.random.choice(directions)
            
            # Move the object up or down
            if step == 1:
                x += 1
            elif step == -1:
                x -= 1
            # Keep track of the positions
            position.append(x)
        return time, position
    rw = randomwalk1D(1000)
    walkers.append(rw)
    plt.plot(rw[0], rw[1], 'r-', label="rw")
walkers = np.array(walkers)  # HERE
plt.plot(walkers[0][0], walkers[:, 1].mean(axis=0), 'b-', label="mean")  # HERE
plt.show()

Update

How can I calculate the root mean square of this array?

# Remove the time dimension, extract the position
arr = walkers[:, 1]

# Compute the Root Mean Square
rms = np.sqrt(np.mean(arr**2, axis=1))