I am trying to perform a two-dimensional random walk for a particle, but I am not getting the desired result. The plot produced is a linear plot, which obviously should not have been. Similar code for a one-dimensional gives the desired result. Can someone please suggest where am I making any mistakes? Thanks.

import numpy
import random
HEAD = 1
TAIL = 2

a = numpy.zeros((2, 50))
b = a.transpose()
ns = 50                        # no of steps

for step in range(ns):
    for _ in range(ns):
        coin = random.randint(1,2)
        if coin == HEAD:
            b[step,0]+=1  # one unit length to the right
        elif coin == TAIL:
            b[step,1]-=1   # one unit length to the left
  • $\begingroup$ What plot are you referring to? $\endgroup$
    – nicoguaro
    Jun 9, 2021 at 16:35
  • 1
    $\begingroup$ Your code says "If it's HEAD, go on to the right, else is its TAIL, go one down." As a consequence, you only ever move to the right or down, but never to the left or up. This is not the logic you wanted to implement, I suspect. $\endgroup$ Jun 9, 2021 at 16:44
  • $\begingroup$ I still could not get you, sorry, what part of my code, do you want me to change? Thanks $\endgroup$ Jun 9, 2021 at 16:58

1 Answer 1


You are only moving in one direction for each axis.

coin_x = random.randint(1,2)

# Move on x axis
if coin_x == HEAD:
elif coin_x == TAIL:

# Move on y axis
coin_y = random.randint(1,2)
if coin_y == HEAD:
elif coin_y == TAIL:


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