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Jupyter with Numpy – Random Walks Simulation

This article includes:

  • Introduction to Random Walks
  • Creating a simple simulation
  • Benefits of learning the concept of Random Walks
  • Creating another simple simulation in Jupyter Notebook
  • Creating an intermediate-level simulation of Random Walks

What is Random Walks Simulation?

Suppose you have a coin. Each time you flip it and get head, you walk forward. If you get tails, you walk backward. You do this several times and you end up with so many patterns on the ground. The final location may be far from where you started or close to it. All movements depend on the probability that either tail or head gives you. The series of steps that you have taken can be called sequences which are taken randomly.

In mathematics, a random walk is a simple model that describes how a system behaves when it randomly changes over time. It is used in many applications such as behaviors of the stock market, animal migrations, etc.

Create a Simple Simulation

In Pure Python:

import random

position = 0
steps = 100

for i in range(steps):
    step = random.choice([-1, 1])
    position += step
    print(f'Step {i + 1}: {position}')

What this code basically does is start the steps at position 0. The target number of steps is 100 and the movement is based on the probability of the random choice which is either -1 or 1.

When I run the code, it gave me:

In MS Excel, the data gathered can be represented as a graph as shown below.

As clearly indicated in the graph, we can see how the positions change. These positions are influenced randomly with either -1 or 1.

Some Benefits of Understanding the Concept of Random Walks

  • Helps model complex systems: Many systems are influenced by random events such as the stock market, particle motion, and animal migration. By creating models of these events, we can gain insights into the behavior of these systems and how it changes over time.
  • Provides insights into probability theory: An important concept of probability theory, it can aid us in understanding other probability concepts, such as the Central Limit Theorem and Markov chains.
  • Useful in finance: Random walks can help in the understanding of the behaviors or patterns of stock markets.
  • Improves algorithm development: It can help developers to create more efficient algorithms.
  • Helps predict outcomes: We can predict the likelihood of certain outcomes and make informed decisions based on the results of Random Walks simulation.
  • Enhances statistical analysis: Often used in statistical analysis to model and analyze complex data, Random Walks can help statisticians use these models more effectively and make more accurate predictions.

Creating another simple simulation in Jupyter Notebook

See my code in my GitHub repo here.

Creating an intermediate-level simulation of Random Walks

For this simulation, I added the mean and standard deviation to see the spread of data.

See my code in my GitHub repo here.

Conclusion

Random Walks is a powerful tool that models the behavior of a system based on the random events that influenced it. There are many real-world applications of Random walks including the development of algorithms, animal behavior, stock market movements, and particle motions.

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