import random

import numpy as np

import matplotlib.pyplot as plt

import math

def randpath(tt):

b=[]

bb=[]

b.append(0)

bb.append(0)

b2=[]

for i in range(tt):

c=random.random()

bb.append(i+1)

if c<=0.5:

b.append(b[-1]+1)

else:

b.append(b[-1]-1)

for j in range(len(b)):

b2.append(b[j])

return b,bb,b2

a,b,c=randpath(1000)

a1,b1,c1=randpath(1000)

for k in range(len(b)):

plt.scatter([b[k],],[c[k],],10,color='blue')

plt.scatter([b1[k],],[c1[k],],10,color='red')

plt.xlim(0,1000)

plt.xlabel('time/step number')

plt.ylabel('X')

plt.title('random walk in one dimension')

plt.show()

"""

c111=[0]*101

for i in range(2000):

a1,b1,c1=randpath(100)

for j in range(len(a1)):

c111[j]=c111[j]+c1[j]/2000.0

for k in range(len(b1)):

plt.scatter([b1[k],],[c111[k],],5,color='orange',label='the average for 2000')

c22=[]

c11=[0]*101

for i in range(20000):

a1,b1,c1=randpath(100)

for j in range(len(a1)):

c11[j]=c11[j]+c1[j]/20000.0

for k in range(len(b1)):

plt.scatter([b1[k],],[c11[k],],5,color='green',label='the average for 20000')

plt.scatter([b1[k],],[a1[k],], 3, color ='orange')

z1=np.polyfit(b1, c11,1)

for i in range(len(b1)):

c22.append(z1[0]*b1[i]+z1[1])

plt.plot(b1,c22,color='red')

plt.xlim(0,100)

plt.ylim(0,100)

plt.xlabel('time/step number')

plt.ylabel('the average square distance')

plt.title('the random walk in one dimesion')

print z1

plt.legend(loc='upper right',frameon=True)

plt.show()

"""