Strange behaviour of random-walk in Python

Question

I have a Python dictionary of two-dimensional points, like points = {1:[0,1],2: [0,0],3: [0,-1]}. With each iteration I'm choosing a random point from a dictionary and change it's coordinates (applying random-walk) with the following function:

def changecoor(X):
  import random
  return [X[0] + random.choice((-1,1)),X[1] + random.choice((-1,1))]

Every five iterations, I'm adding a new point to the dictionary. The code is as follows:

points = {1: [0,0]} # creating the first element
for i in range(2000):
  mychoice = random.choice(list(points.keys())) # choosing a random element from the dict
  points[mychoice] = changecoor(points[mychoice]) # applying a function to the chosen element
  if i % 5 == 0:
    points[len(points) + 1] = [0,0]  # Adding new element every 5 loops

Now, if I plot my elements on a graph, I expect the element [0,0] to be somewhere in the middle, but it isn't. The second coordinate is evenly distributed around 0, but I don't have a single point which has the first coordinate negative.

This is an example of what I get:

Answer 1

Your code is correct, but your plotting of the results is not correct.

Using your code

import random

def changecoor(X):
    return [X[0] + random.choice((-1,1)),X[1] + random.choice((-1,1))]

points = {1: [0,0]} # creating the first element
for i in range(2000):
    mychoice = random.choice(list(points.keys())) # choosing a random element from the dict
    points[mychoice] = changecoor(points[mychoice]) # applying a function to the chosen element
    if i % 5 == 0:
        points[len(points) + 1] = [0,0]  # Adding new element every 5 loops

If we take just the values() of the points dictionary and put that into a dataframe like

import pandas as pd

df = pd.DataFrame(points.values(), columns=['x','y'])

Then we do a scatterplot of the x,y values for each point we get a graph of the expected distribution around 0 that you are expecting