Modification of the interact at http://interact.sagemath.org/node/39

Markov Chains

@interact
def _(A=matrix(RDF,3,3,[8,2,0,1,7,2,1,3,6])/10,x_init=("$\pi^{(0)}$",vector([.2,.5,.3]))):
    x_init = vector(x_init)
    data = [x_init * (A^i) for i in range(20)]
    pi = zip(*data)
    p = line(enumerate(pi[0]),color='red',legend_label='$\pi_1$',thickness=3)
    p += line(enumerate(pi[1]),color='blue',legend_label='$\pi_2$',thickness=3)
    p += line(enumerate(pi[2]),color='green',legend_label='$\pi_3$',thickness=3)
    p.ymax(1)
    show(p)