Power Method: A Markov Chain Finds Its Eigenvector

A Markov chain on three states moves probability between them. A probability vector has three entries that add up to one, so it lives on this triangle, with one corner for each state.

One step multiplies by the transition matrix: p transpose times P. Each row of P adds up to one, so the result is again a probability vector, a new point on the triangle.

The rest of the narration is in the book's Companion.