Enough boring theory. Let’s take a break to get some coding knowledge. So, to code the random walk, we basically need some libraries in python, some for math and some others for curve fitting.
Required Libraries
 matplotlib This is an external library to help you plot a curve. To install this library, enter the following code in your cmd.
pip install matplotlib
This would be enough to get you through the installation.
 Numpy It is also an external Python library that helps you work with arrays and matrices. To install the library, enter the following code in cmd.
pip install numpy
 random This is a builtin python library that we will use to generate random points.
Onedimensional random walk . An elementary example of a random walk is a random walk over a string of integers, which starts at 0 and is shifted by +1 or? 1 with equal probability.
So let’s try to implement 1D random walk in python.
Output:
Higher dimensions In higher dimensions, many randomly passed points have interesting geometric properties. In fact, a discrete fractal is obtained, that is, a set that demonstrates stochastic selfsimilarity on a large scale. On a small scale, you can observe "irregularities" arising from the net on which the walk is performed. Lawler’s two books mentioned below are good sources on this topic. The trajectory of a random walk — it is a set of visited points, treated as a set that does not account for when the walk has reached a point. In one dimension, the trajectory — it’s just all the points between the minimum height and the maximum height that the walk has reached (on average, both orders of magnitude? N).
Let’s try to create a random walk in 2D.


Output:
Applications
 In computer networks, random Traversals can simulate the number of transmission packets buffered on the server.
 In population genetics, random walks describe the statistical properties of genetic drift.
 In image segmentation, random walks are used to define labels (i.e. E. "Object" or "background") associated with each pixel.
 In brain research, random walks and enhanced random walks are used to simulate neuronal firing cascades in the brain.
 Random walks have also been used to sample huge online graphs such as online social media.
Links
1. Wikipedia — A random walk
2. Stackoverflow — Random Walk 1D
3. matplotlib documentation
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