Keywords
Markov Chains, Interactive Demo, Page Rank

Technologies
Mathematica, Wolfram

This project develops an interactive Mathematica notebook designed to improve understanding of Markov chains through visualisation and experimentation. While the theory of Markov chains has been well established, concepts such as convergence, reversibility, and long-term behaviour are often difficult to grasp from the textbook material alone. The objective was to create a tool that allows users to explore these ideas dynamically and build intuition by going through the markov chain process and understanding what happens at each step. The notebook introduces key concepts including transition matrices, graph representations, Spectral Gap, Mixing time and stationary distributions, before examining classical models such as PageRank, random walks, the Bernoulli–Laplace model, Card shuffling and the Ehrenfest urn. These examples are used to investigate important properties including ergodicity, reversibility, spectral gap, and mixing time. The project demonstrates that interactive visualisation can significantly enhance understanding of stochastic processes by linking theoretical results with observable behaviour