%matplotlib inline

from math import sqrt
import numpy as np
import matplotlib.pyplot as plt


def RandomWalk(N,d):
    walk = np.cumsum(2*np.random.binomial(1,.5,N)-1)
    return walk

plt.plot(np.arange(100),RandomWalk(100,1))
plt.show()

endpoints = []
for k in range(5):
    particularWalk = RandomWalk(100,1)
    endpoints.append(particularWalk[-1])
    plt.plot(np.arange(100),particularWalk)
    
    
plt.show()

endpoints = []
for k in range(20):
    particularWalk = RandomWalk(100,1)
    endpoints.append(particularWalk[-1])
    plt.plot(np.arange(100),particularWalk)
    
    
plt.show()

endpoints = []
for k in range(180):
    particularWalk = RandomWalk(100,1)
    endpoints.append(particularWalk[-1])
    plt.plot(np.arange(100),particularWalk)
    
    
plt.show()