Markov Chains explained visually

Abstraction: Interactive visual introduction to Markov chains, transition matrices, and state spaces

Key points:

• Markov chain: a system that hops between states with fixed transition probabilities; future state depends only on current state (memoryless property)
• Transition matrix encodes all probabilities: rows = current state, columns = next state; each row must sum to 1
• State space size n yields n^2 cells in the transition matrix — grows quadratically
• Weather modeling example: 0.9 self-transition probability captures "stickiness" that naive 50/50 daily randomness misses
• PageRank (Google's search ranking) is a real-world Markov chain over web pages
• Applied by meteorologists, ecologists, financial engineers, and computer scientists for simulation

Connections: Markov Chains · Stochastic Processes · Transition Matrices

Source: http://setosa.io/ev/markov-chains/