twinDragon.sagews

A = matrix([[1,1],[-1,1]])
D = [vector([0,0]), vector([1,0])]

@interact
def f(A = matrix([[1,1],[-1,1]]), D = '[[0,0],[1,0]]', k=(3..17)):
    print "Det = ", A.det()
    D = matrix(eval(D)).rows()
    def Dn(k):
        ans = []
        for d in Tuples(D, k):
            s = sum(A^(-n)*d[n] for n in range(k))
            ans.append(s)
        return ans

    G = points([v.list() for v in Dn(k)])

    show(G, frame=True, axes=False)

Interact: please open in CoCalc