#aperiodicity

A first-order Markov chain on the states A, T, G, C has the transitions $A \to A$, $A \to T$, $T \to T$, $T \to G$, $G \to G$, $G \to C$, $C \to C$ and $C \to A$, each with probability $1/2$. This chain is ergodic.