A Random Walk In #Python

Walk around n blocks. At each block, decide whether to turn east, west, north or south. At the end of the n blocks, compute how the distance reached from the origin.

Repeat t times. Compute the % of walks that ended 4 blocks away from the origin.In [61]:

walks,blocks = 0,0
walks=int(input("no of walks "))
blocks=int(input("blocks per walks "))

no of walks 10000
blocks per walks 50

In [68]:

import random

maxdistance = 4
listless = []

for w in range(walks):
    
    #print()
    #print ("Try " + str(w+1))
    
    distance, percentless, countless = 0,0,0
    wherenow = [0,0]
    
    for b in range(blocks):
    
        trynow=random.randint(0,4)
        if trynow == 0: #go east
            wherenow[0] += 1
        elif trynow == 1: #go north
            wherenow[1] += 1
        elif trynow == 2: #go west
            wherenow[0] += -1
        else: #south
            wherenow[1] += -1

        distance = wherenow[0]**2 + wherenow[1]**2
        if distance<(maxdistance**2): 
            countless += 1
            
        percentless =  (countless/(b+1)*100)

        #print("Block " + str(b) + " Choice " + str(trynow) + " Current post (" + str(wherenow[0]) + "," + str(wherenow[1]) + ") Distance " + str(distance) + " Less than " + str(maxdistance) + " is " + str(countless) + " percent " + str(percentless))

    listless.append(percentless)

In [67]:

print()
print(listless)

[36.0, 14.000000000000002, 14.000000000000002, 34.0, 54.0, 36.0, 12.0, 44.0, 22.0, 10.0, 12.0, 30.0, 12.0, 14.000000000000002, 42.0, 18.0, 26.0, 10.0, 14.000000000000002, 22.0, 8.0, 10.0, 12.0, 20.0, 40.0, 38.0, 12.0, 30.0, 22.0, 66.0, 72.0, 16.0, 14.000000000000002, 22.0, 57.99999999999999, 30.0, 40.0, 26.0, 48.0, 10.0, 40.0, 36.0, 8.0, 12.0, 26.0, 56.00000000000001, 36.0, 38.0, 62.0, 72.0, 24.0, 32.0, 24.0, 50.0, 18.0, 12.0, 42.0, 12.0, 16.0, 48.0, 74.0, 44.0, 34.0, 80.0, 38.0, 36.0, 42.0, 16.0, 14.000000000000002, 10.0, 36.0, 10.0, 24.0, 40.0, 96.0, 24.0, 92.0, 14.000000000000002, 22.0, 28.000000000000004, 57.99999999999999, 22.0, 12.0, 22.0, 14.000000000000002, 36.0, 28.000000000000004, 10.0, 20.0, 90.0, 30.0, 38.0, 12.0, 18.0, 16.0, 24.0, 26.0, 36.0, 22.0, 50.0, 28.000000000000004, 34.0, 34.0, 24.0, 18.0, 16.0, 56.00000000000001, 42.0, 26.0, 28.000000000000004, 76.0, 14.000000000000002, 40.0, 28.000000000000004, 60.0, 14.000000000000002, 18.0, 16.0, 32.0, 14.000000000000002, 16.0, 8.0, 38.0, 100.0, 50.0, 38.0, 40.0, 64.0, 12.0, 6.0, 50.0, 40.0, 57.99999999999999, 14.000000000000002, 22.0, 64.0, 57.99999999999999, 16.0, 14.000000000000002, 30.0, 10.0, 40.0, 98.0, 26.0, 16.0, 34.0, 40.0, 42.0, 18.0, 40.0, 10.0, 32.0, 18.0, 10.0, 50.0, 72.0, 34.0, 34.0, 6.0, 22.0, 28.000000000000004, 20.0, 54.0, 68.0, 16.0, 10.0, 18.0, 66.0, 56.00000000000001, 54.0, 54.0, 34.0, 48.0, 60.0, 50.0, 18.0, 72.0, 70.0, 36.0, 48.0, 46.0, 14.000000000000002, 64.0, 12.0, 22.0, 22.0, 26.0, 46.0, 46.0, 10.0, 12.0, 38.0, 46.0, 24.0, 12.0, 30.0, 48.0, 28.000000000000004, 52.0, 30.0, 18.0, 26.0, 16.0, 30.0, 18.0, 82.0, 76.0, 96.0, 14.000000000000002, 12.0, 14.000000000000002, 30.0, 40.0, 16.0, 16.0, 28.000000000000004, 40.0, 50.0, 54.0, 18.0, 32.0, 6.0, 30.0, 10.0, 10.0, 22.0, 26.0, 14.000000000000002, 22.0, 82.0, 88.0, 12.0, 22.0, 6.0, 14.000000000000002, 60.0, 46.0, 96.0, 36.0, 52.0, 24.0, 18.0, 38.0, 20.0, 18.0, 16.0, 18.0, 8.0, 14.000000000000002, 6.0, 10.0, 52.0, 18.0, 78.0, 16.0, 56.00000000000001, 32.0, 8.0, 44.0, 42.0, 14.000000000000002, 20.0, 52.0, 38.0, 54.0, 14.000000000000002, 38.0, 52.0, 32.0, 92.0, 14.000000000000002, 14.000000000000002, 10.0, 30.0, 86.0, 54.0, 22.0, 30.0, 18.0, 36.0, 12.0, 12.0, 48.0, 12.0, 68.0, 12.0, 38.0, 34.0, 14.000000000000002, 30.0, 18.0, 32.0, 42.0, 16.0, 40.0, 70.0, 28.000000000000004, 64.0, 26.0, 78.0, 32.0, 26.0, 44.0, 12.0, 36.0, 78.0, 12.0, 52.0, 44.0, 32.0, 12.0, 56.00000000000001, 52.0, 38.0, 24.0, 10.0, 32.0, 42.0, 28.000000000000004, 66.0, 84.0, 32.0, 14.000000000000002, 52.0, 36.0, 34.0, 8.0, 34.0, 80.0, 20.0, 36.0, 82.0, 62.0, 16.0, 42.0, 26.0, 14.000000000000002, 66.0, 38.0, 46.0, 12.0, 62.0, 78.0, 42.0, 12.0, 28.000000000000004, 18.0, 76.0, 42.0, 38.0, 60.0, 34.0, 20.0, 10.0, 42.0, 8.0, 22.0, 32.0, 36.0, 68.0, 34.0, 74.0, 18.0, 22.0, 40.0, 10.0, 16.0, 90.0, 26.0, 24.0, 30.0, 22.0, 30.0, 46.0, 20.0, 30.0, 18.0, 50.0, 16.0, 30.0, 38.0, 16.0, 10.0, 14.000000000000002, 20.0, 40.0, 16.0, 6.0, 40.0, 36.0, 26.0, 32.0, 64.0, 20.0, 76.0, 12.0, 14.000000000000002, 6.0, 12.0, 12.0, 38.0, 14.000000000000002, 24.0, 40.0, 36.0, 18.0, 40.0, 36.0, 20.0, 22.0, 18.0, 57.99999999999999, 32.0, 70.0, 44.0, 12.0, 42.0, 36.0, 32.0, 14.000000000000002, 24.0, 100.0, 68.0, 30.0, 42.0, 32.0, 28.000000000000004, 38.0, 48.0, 34.0, 32.0, 42.0, 24.0, 8.0, 6.0, 26.0, 46.0, 70.0, 28.000000000000004, 10.0, 18.0, 34.0, 22.0, 36.0, 18.0, 12.0, 18.0, 8.0, 16.0, 10.0, 22.0, 57.99999999999999, 20.0, 46.0, 40.0, 100.0, 16.0, 44.0, 76.0, 24.0, 62.0, 34.0, 38.0, 32.0, 26.0, 22.0, 12.0, 36.0, 26.0, 46.0, 10.0, 14.000000000000002, 6.0, 24.0, 48.0, 36.0, 30.0, 40.0, 26.0, 18.0, 50.0, 38.0, 38.0, 8.0, 6.0, 10.0, 46.0, 60.0, 34.0, 92.0, 42.0, 74.0, 56.00000000000001, 46.0, 52.0, 24.0, 14.000000000000002, 38.0, 42.0, 12.0, 28.000000000000004, 18.0, 46.0, 16.0, 16.0, 78.0, 57.99999999999999, 48.0, 22.0, 12.0, 36.0, 38.0, 70.0, 52.0, 32.0, 14.000000000000002, 64.0, 42.0, 62.0, 10.0, 80.0, 28.000000000000004, 24.0, 62.0, 70.0, 14.000000000000002, 22.0, 22.0, 78.0, 22.0, 22.0, 22.0, 24.0, 32.0, 8.0, 12.0, 16.0, 48.0, 82.0, 40.0, 42.0, 72.0, 34.0, 18.0, 12.0, 24.0, 16.0, 6.0, 26.0, 28.000000000000004, 56.00000000000001, 6.0, 22.0, 96.0, 26.0, 56.00000000000001, 28.000000000000004, 8.0, 22.0, 98.0, 66.0, 18.0, 14.000000000000002, 64.0, 14.000000000000002, 14.000000000000002, 18.0, 48.0, 78.0, 26.0, 60.0, 16.0, 48.0, 74.0, 28.000000000000004, 16.0, 62.0, 48.0, 57.99999999999999, 24.0, 14.000000000000002, 32.0, 26.0, 26.0, 30.0, 24.0, 34.0, 14.000000000000002, 10.0, 36.0, 48.0, 42.0, 28.000000000000004, 32.0, 8.0, 10.0, 22.0, 24.0, 16.0, 52.0, 32.0, 50.0, 16.0, 42.0, 46.0, 20.0, 30.0, 30.0, 36.0, 18.0, 42.0, 26.0, 16.0, 16.0, 16.0, 12.0, 38.0, 22.0, 16.0, 76.0, 34.0, 22.0, 22.0, 56.00000000000001, 24.0, 40.0, 26.0, 44.0, 6.0, 6.0, 94.0, 70.0, 18.0, 62.0, 57.99999999999999, 54.0, 32.0, 8.0, 20.0, 52.0, 18.0, 14.000000000000002, 24.0, 30.0, 16.0, 36.0, 18.0, 18.0, 62.0, 42.0, 66.0, 36.0, 14.000000000000002, 10.0, 20.0, 20.0, 34.0, 48.0, 44.0, 32.0, 44.0, 66.0, 26.0, 66.0, 26.0, 16.0, 10.0, 46.0, 86.0, 8.0, 72.0, 18.0, 60.0, 28.000000000000004, 10.0, 46.0, 50.0, 24.0, 36.0, 28.000000000000004, 24.0, 14.000000000000002, 14.000000000000002, 100.0, 66.0, 46.0, 72.0, 12.0, 28.000000000000004, 28.000000000000004, 36.0, 36.0, 12.0, 28.000000000000004, 18.0, 22.0, 24.0, 10.0, 88.0, 48.0, 20.0, 50.0, 46.0, 34.0, 34.0, 16.0, 40.0, 56.00000000000001, 62.0, 22.0, 28.000000000000004, 18.0, 22.0, 30.0, 16.0, 12.0, 10.0, 40.0, 20.0, 44.0, 72.0, 14.000000000000002, 26.0, 78.0, 30.0, 32.0, 14.000000000000002, 22.0, 24.0, 26.0, 74.0, 30.0, 22.0, 22.0, 46.0, 14.000000000000002, 57.99999999999999, 60.0, 48.0, 14.000000000000002, 34.0, 74.0, 26.0, 30.0, 50.0, 30.0, 18.0, 32.0, 46.0, 26.0, 32.0, 12.0, 57.99999999999999, 32.0, 10.0, 56.00000000000001, 38.0, 22.0, 50.0, 52.0, 14.000000000000002, 57.99999999999999, 26.0, 22.0, 28.000000000000004, 52.0, 42.0, 20.0, 14.000000000000002, 60.0, 30.0, 12.0, 12.0, 26.0, 44.0, 26.0, 76.0, 54.0, 48.0, 8.0, 26.0, 66.0, 20.0, 66.0, 12.0, 12.0, 16.0, 6.0, 56.00000000000001, 28.000000000000004, 42.0, 40.0, 8.0, 48.0, 10.0, 36.0, 34.0, 64.0, 10.0, 76.0, 20.0, 20.0, 16.0, 92.0, 46.0, 22.0, 32.0, 94.0, 50.0, 44.0, 84.0, 24.0, 16.0, 70.0, 40.0, 8.0, 16.0, 28.000000000000004, 22.0, 48.0, 44.0, 18.0, 30.0, 30.0, 66.0, 38.0, 26.0, 64.0, 8.0, 14.000000000000002, 72.0, 24.0, 32.0, 24.0, 8.0, 56.00000000000001, 44.0, 74.0, 24.0, 80.0, 66.0, 44.0, 8.0, 32.0, 16.0, 8.0, 32.0, 38.0, 32.0, 28.000000000000004, 22.0, 40.0, 48.0, 16.0, 76.0, 40.0, 18.0, 38.0, 30.0, 8.0, 20.0, 18.0, 20.0, 60.0, 50.0, 18.0, 28.000000000000004, 30.0, 24.0, 20.0, 14.000000000000002, 70.0, 18.0, 26.0, 36.0, 32.0, 42.0, 34.0, 10.0, 28.000000000000004, 30.0, 18.0, 78.0, 26.0, 86.0, 30.0, 28.000000000000004, 38.0, 18.0, 56.00000000000001, 20.0, 98.0, 82.0, 30.0, 38.0, 20.0, 22.0, 22.0, 14.000000000000002, 40.0, 20.0, 36.0, 28.000000000000004, 32.0, 32.0, 20.0, 38.0, 50.0, 8.0, 34.0, 18.0, 22.0, 34.0, 18.0, 84.0, 26.0, 8.0, 44.0, 56.00000000000001, 24.0, 26.0, 10.0, 14.000000000000002, 14.000000000000002, 30.0, 22.0, 26.0, 62.0, 22.0, 84.0, 18.0, 34.0, 46.0, 24.0, 10.0, 10.0, 56.00000000000001, 28.000000000000004, 12.0, 62.0, 38.0, 57.99999999999999, 22.0, 16.0, 82.0, 10.0, 72.0, 30.0, 72.0, 38.0, 24.0, 62.0, 30.0, 22.0, 16.0, 52.0, 36.0, 50.0, 46.0, 52.0, 72.0, 18.0, 96.0, 10.0, 20.0, 12.0, 22.0, 80.0, 20.0, 24.0, 88.0, 38.0, 74.0, 32.0, 22.0, 68.0, 38.0, 26.0, 24.0, 8.0, 26.0, 8.0, 14.000000000000002, 32.0, 22.0, 28.000000000000004, 88.0, 28.000000000000004, 10.0, 34.0, 50.0, 54.0, 52.0, 40.0, 98.0, 16.0, 40.0, 38.0, 38.0, 8.0, 32.0, 16.0, 14.000000000000002, 38.0, 12.0, 20.0, 38.0, 52.0, 12.0, 16.0, 57.99999999999999, 26.0, 52.0, 18.0, 30.0, 36.0, 26.0, 16.0, 24.0, 14.000000000000002, 26.0, 22.0, 26.0, 44.0, 10.0, 44.0, 20.0, 54.0, 18.0, 96.0, 22.0, 36.0, 28.000000000000004, 18.0, 46.0, 56.00000000000001, 98.0, 28.000000000000004, 57.99999999999999, 46.0, 48.0, 22.0, 52.0, 10.0, 26.0, 32.0, 64.0, 6.0, 22.0, 36.0, 74.0, 72.0, 34.0, 38.0, 12.0, 46.0, 20.0, 26.0, 80.0, 30.0, 52.0, 14.000000000000002, 30.0, 28.000000000000004, 10.0, 16.0, 34.0, 34.0, 26.0, 12.0, 60.0, 16.0, 18.0, 8.0, 46.0, 6.0, 52.0, 8.0, 20.0, 26.0, 30.0, 62.0, 86.0, 22.0, 32.0, 72.0, 76.0, 14.000000000000002, 20.0, 16.0, 20.0, 26.0, 20.0, 44.0, 18.0, 12.0, 20.0, 50.0, 62.0, 54.0, 30.0, 14.000000000000002, 26.0, 18.0, 24.0, 46.0, 60.0, 44.0, 28.000000000000004, 24.0, 20.0, 46.0, 16.0, 50.0, 46.0, 38.0, 24.0, 60.0, 12.0, 28.000000000000004, 12.0, 44.0, 48.0, 30.0, 56.00000000000001, 18.0, 24.0, 22.0, 56.00000000000001, 36.0, 12.0, 14.000000000000002, 46.0, 12.0, 46.0, 16.0, 70.0, 38.0, 10.0, 12.0, 52.0, 12.0, 14.000000000000002, 8.0, 18.0, 6.0, 10.0, 10.0, 56.00000000000001, 40.0, 46.0, 32.0, 20.0, 62.0, 44.0, 57.99999999999999, 24.0, 26.0, 8.0, 18.0, 6.0, 18.0, 8.0, 36.0, 78.0, 10.0, 26.0, 72.0, 46.0, 28.000000000000004, 24.0, 38.0, 10.0, 18.0, 24.0, 18.0, 46.0, 22.0, 60.0, 8.0, 24.0, 52.0, 36.0, 66.0, 62.0, 40.0, 42.0, 42.0, 26.0, 16.0, 96.0, 76.0, 42.0, 10.0, 16.0, 64.0, 30.0, 44.0, 38.0, 70.0, 18.0, 14.000000000000002, 34.0, 32.0, 36.0, 20.0, 8.0, 68.0, 42.0, 14.000000000000002, 36.0, 98.0, 98.0, 10.0, 22.0, 74.0, 10.0, 57.99999999999999, 28.000000000000004, 20.0, 30.0, 70.0, 86.0, 26.0, 34.0, 60.0, 8.0, 28.000000000000004, 74.0, 72.0, 30.0, 44.0, 28.000000000000004, 50.0, 12.0, 12.0, 72.0, 26.0, 34.0, 22.0, 18.0, 66.0, 20.0, 18.0, 68.0, 14.000000000000002, 28.000000000000004, 100.0, 64.0, 44.0, 10.0, 26.0, 98.0, 8.0, 8.0, 57.99999999999999, 38.0, 22.0, 12.0, 42.0, 46.0, 36.0, 46.0, 16.0, 54.0, 12.0, 10.0, 30.0, 14.000000000000002, 22.0, 16.0, 54.0, 66.0, 34.0, 14.000000000000002, 64.0, 56.00000000000001, 52.0, 22.0, 22.0, 62.0, 12.0, 16.0, 16.0, 34.0, 30.0, 38.0, 62.0, 50.0, 18.0, 70.0, 26.0, 70.0, 68.0, 98.0, 20.0, 28.000000000000004, 20.0, 32.0, 26.0, 20.0, 34.0, 57.99999999999999, 34.0, 46.0, 52.0, 50.0, 34.0, 30.0, 60.0, 28.000000000000004, 14.000000000000002, 8.0, 42.0, 64.0, 26.0, 64.0, 40.0, 22.0, 60.0, 46.0, 78.0, 30.0, 26.0, 28.000000000000004, 10.0, 26.0, 24.0, 22.0, 50.0, 88.0, 26.0, 36.0, 22.0, 26.0, 18.0, 22.0, 62.0, 34.0, 88.0, 18.0, 30.0, 52.0, 12.0, 32.0, 46.0, 30.0, 12.0, 24.0, 26.0, 20.0, 38.0, 14.000000000000002, 52.0, 16.0, 100.0, 30.0, 6.0, 64.0, 46.0, 60.0, 18.0, 26.0, 12.0, 24.0, 26.0, 12.0, 72.0, 8.0, 8.0, 80.0, 44.0, 84.0, 16.0, 24.0, 14.000000000000002, 10.0, 10.0, 14.000000000000002, 26.0, 20.0, 20.0, 28.000000000000004, 28.000000000000004, 30.0, 10.0, 94.0, 10.0, 14.000000000000002, 42.0, 48.0, 30.0, 40.0, 66.0, 68.0, 66.0, 57.99999999999999, 38.0, 18.0, 18.0, 22.0, 70.0, 34.0, 54.0, 96.0, 18.0, 46.0, 42.0, 14.000000000000002, 98.0, 8.0, 36.0, 16.0, 16.0, 28.000000000000004, 50.0, 26.0, 28.000000000000004, 44.0, 62.0, 14.000000000000002, 44.0, 10.0, 8.0, 74.0, 24.0, 32.0, 20.0, 26.0, 30.0, 16.0, 26.0, 26.0, 57.99999999999999, 20.0, 26.0, 72.0, 100.0, 22.0, 22.0, 44.0, 22.0, 50.0, 18.0, 12.0, 14.000000000000002, 40.0, 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In [ ]: