Random Walk in Python

1. Introduction

This is an article about random walk in python. It’s a process that explains the path which is made of random steps in sequence. A simple example is on the integers number line. Integers start from 0 and each step is either -1 or +1 with a probability of 50%. The complex examples are molecules moving in a gas, stock price fluctuations, and the search path of prey by a carnivorous animal.

2. Random Walk

2.1 Prerequisites

Python 3.6.8 is required on windows or any operating system. Pycharm is needed for python programming.

2.2 Download

Python 3.6.8 can be downloaded from the website. Pycharm is available at this link.

2.3 Required Libraries

2.3.1 Python Setup

To install python, the download package or executable needs to be executed.

2.4 IDE

2.4.1 Pycharm Setup

Pycharm package or installable needs to be executed to install Pycharm.

2.5 Launching IDE

2.5.1 Pycharm

Launch the Pycharm and start creating a pure python project named HelloWorld. The screen shows the project creation.

Python vs Java - Pycharm Create project
Pycharm Create project

The project settings are set on the next screen as shown below.

Python vs Java - Pycharm Project Settings
Pycharm Project Settings

Pycharm welcome screen comes up and shows the progress as indicated below.

Pycharm Project View

You can create a and execute the python file by selecting the Run menu.

Pycharm Hello World

The output message “Hello World” is printed when the python file is Run.

Pycharm Python Execution

2.6 One Dimensional Random Walk

Let us start with a one-dimensional walk. The steps are taken in only two directions. It can be right or left on the x-axis. It can also be up or down on the y-axis. The code below shows how to implement the one-dimensional random walk.

One Dimensional Random Walk

import numpy as nump
import matplotlib.pyplot as plot
def SingleDimensionRandomWalk(n): 
   x = 0
   y = 0
   xposition = [0]
   yposition = [0] 

   for i in range (1,n+1):
       step = nump.random.uniform(0,1)

       if step  0.5:  
           x += 1
           y += -1 

   return [xposition,yposition]

OneDRandomWalk = SingleDimensionRandomWalk(2345) 
plot.plot(OneDRandomWalk[0],OneDRandomWalk[1],'r-', label = "RandomWalk1D") 
plot.title("One Dimensional Random Walks")

You can execute the above code with the command below:

Execution Command


The output is the plot which is shown below:

Single Dimensional Random Walk

2.7 Two-Dimensional Random walk

Now let us see the implementation of a two-dimensional walk. Two-dimensional can be North, South, West, and East directions on the x and y-axis. The implementation is shown below in the code snippet. Two Dimensional Random Walk

import numpy as nump 
import pylab as pythonlab
import random as pyran
n = 2345 
x = nump.zeros(n) 
y = nump.zeros(n) 
for i in range(1, n): 
    step = pyran.choice(steps) 
    if step == "EAST": 
        x[i] = x[i - 1] + 1
        y[i] = y[i - 1] 
    elif step == "WEST": 
        x[i] = x[i - 1] - 1
        y[i] = y[i - 1] 
    elif step == "NORTH": 
        x[i] = x[i - 1] 
        y[i] = y[i - 1] + 1
        x[i] = x[i - 1] 
        y[i] = y[i - 1] - 1
pythonlab.title("Two Dimensional Random Walk")
pythonlab.plot(x, y)

You can execute the above code with the command below:

Execution Command


The output is the plot which is shown below:

Two-Dimensional Random Walk

3. Download the Source Code

You can download the full source code of this example here: Random Walk in Python

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Bhagvan Kommadi

Bhagvan Kommadi is the Founder of Architect Corner & has around 20 years’ experience in the industry, ranging from large scale enterprise development to helping incubate software product start-ups. He has done Masters in Industrial Systems Engineering at Georgia Institute of Technology (1997) and Bachelors in Aerospace Engineering from Indian Institute of Technology, Madras (1993). He is member of IFX forum,Oracle JCP and participant in Java Community Process. He founded Quantica Computacao, the first quantum computing startup in India. Markets and Markets have positioned Quantica Computacao in ‘Emerging Companies’ section of Quantum Computing quadrants. Bhagvan has engineered and developed simulators and tools in the area of quantum technology using IBM Q, Microsoft Q# and Google QScript. He has reviewed the Manning book titled : "Machine Learning with TensorFlow”. He is also the author of Packt Publishing book - "Hands-On Data Structures and Algorithms with Go".He is member of IFX forum,Oracle JCP and participant in Java Community Process. He is member of the MIT Technology Review Global Panel.
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