Random walk generator

The below python code can be used to generate random walk process as aid to explain various phenomenas with random walk.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import animation

def random_walk(input):
    r = np.random.uniform(0, 1, 1)
    if r <= 0.33:
        z = 1
    elif r > 0.33 and r <= 0.66:
        z = 0
    else:
        z = -1
    return input + z

def animate(i):
    global rw_array, z, T
    for _ in range(10):  # Increase steps per frame for faster simulation
        z = random_walk(z)
        rw_array.append(z)
    
    # Update the data
    line.set_data(np.arange(len(rw_array)), np.array(rw_array))
    
    # Dynamically adjust y-limits
    ymin, ymax = min(rw_array), max(rw_array)
    ax.set_ylim(ymin - 10, ymax + 10)  # Add padding for better visualization

    # Dynamically adjust x-limits if needed
    if len(rw_array) >= T:
        T = T * 2
        ax.set_xlim(0, T)

    return line,

def init():
    line.set_data([], [])
    return line,

T = 100
rw_array = []
z = 0

fig = plt.figure('-r')
ax = fig.add_subplot(1, 1, 1)
plt.xlim(0, T)
plt.xlabel('t')
plt.title('Simple Random Walk with Dynamic Y-Limits')
line, = ax.plot([], [], lw=2)

# Faster animation with more steps and reduced interval
anim = animation.FuncAnimation(
    fig, animate, init_func=init, frames=500, interval=10, blit=True
)

# Save the animation as a GIF
anim.save('dynamic_y_limits_random_walk.gif', writer='pillow', fps=30)
plt.show()