Random_walk_4_direction.py

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


def random_walk(n, a):
    x = 0
    y = 0
    for i in range(n):
        angle = random.uniform(0, 2*np.pi)
        sin = np.sin(angle)
        cos = np.cos(angle)
        x += a*cos
        y += a*sin
    return (x, y)


number_of_walks = 3000
length = 50
step_length = 1

walk_size_array = np.zeros((1, length))
average_distance_array = np.zeros((1, length))
sqrt_walk_size_array = np.zeros((1, length))

for walk_length in range(1, length):
    sum_distance = 0

    for i in range(number_of_walks):
       (x, y) = random_walk(walk_length, step_length) 
       distance = np.sqrt(x*x + y*y)
       sum_distance += distance
    average_distance = float(sum_distance) / number_of_walks
    walk_size_array[0, walk_length] = walk_length
    average_distance_array[0, walk_length] = float(average_distance)
    sqrt_walk_size_array[0, walk_length] = np.sqrt(walk_length)
   
    print("walk size = ", walk_length, " average distance = ", average_distance)

plt.figure()
walk = plt.scatter(walk_size_array, average_distance_array)
sqrt_walk = plt.scatter(walk_size_array, sqrt_walk_size_array)
plt.xlabel("Walk size")
plt.ylabel("Average distance")
plt.show()