Each dot is one passenger. Every hour, each passenger rolls the dice using the column of P for where they are now. The bars show the exact probability vector xk = P xk−1; the dot counts show one random crowd following it.
Transition matrix P · columns = from, rows = to
Starting vector x₀
Probability over time
State vectors xk
| Hour | Pool | Buffet | Theater |
|---|
Dotted underline = the random starting state taken from the book. Shaded = the current state (what the chain “remembers”). Red = the character just drawn.
Same book, same length, bigger memory each rung. This is Shannon’s 1948 experiment.
Press the button to generate one sample at each order.
Inside the transition matrix
Full matrix P (k = 1 letters) · column = current letter, row = next