NUMB3RS - Season 2 - "Harvest" - Markov Chain Links
Introduction to State Transitions
A Markov chain consists of a set of states and the probabilities of transitioning from one state to another. Suppose the weather in a town transitions daily between two states: Rain () and No Rain (). If it rains today, the probability of rain tomorrow is , and no rain is . If it does not rain today, the probability of rain tomorrow is , and no rain is .
This can be represented by a transition matrix :
Where Row 1 represents 'Rain Today', Row 2 represents 'No Rain Today', Column 1 represents 'Rain Tomorrow', and Column 2 represents 'No Rain Tomorrow'.
3-State Transition Flow Simulator
Watch state distributions adjust over time. Use standard presets or simulate one-step forward transitions to find how values converge to steady state probabilities.
State Node Diagram
Current Distribution
Clicking Transition multiple times applies the transition rules sequentially. Notice how the values progressively converge to ~45% Sunny, ~34% Cloudy, and ~21% Rainy regardless of your starting values!
Step State Evolution Log
| Step | Sunny (S) | Cloudy (C) | Rainy (R) | Matrix Representation |
|---|---|---|---|---|
| T = 0 | 100% | 0% | 0% | [ 1.000, 0.000, 0.000 ] |