The Kimura 3-parameter (K3P) Model is a Markov model of base substitution. It assumes the root distribution vectors describe all bases occurring uniformly in the ancestral sequence. It allows different probabilities of the base changes A-G, A-C and A-T. This is the most general group based model on group $(\mathbb{Z}/2\mathbb{Z})^2$.

The transition matrix has the form $$\begin{pmatrix} \alpha&\gamma&\beta&\delta\\ \gamma&\alpha&\delta&\beta\\ \beta&\delta&\alpha&\gamma\\ \delta&\beta&\gamma&\alpha \end{pmatrix}$$