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We need much more input to help seriously, like the size of the matrix, a concrete example of A, an example of plot you want.

Waiting for more details, here is a sample of what you can easily get:

sage: A = matrix([[2,1],[1,1]])
sage: A
[2 1]
[1 1]
sage: C = matrix([[2],[3]])
sage: C
[2]
[3]
sage: A * C
[7]
[5]
sage: L = []
sage: L = [C]
sage: for i in range(10):
....:     C = A*C
....:     L.append(C)
sage: L
[
[2]  [7]  [19]  [50]  [131]  [343]  [898]  [2351]  [6155]  [16114]
[3], [5], [12], [31], [ 81], [212], [555], [1453], [3804], [ 9959],

[42187]
[26073]
]


We need much more input to help seriously, like the size of the matrix, a concrete example of A, an example of plot picture you want.want to obtain.

Waiting for more details, here is a sample of what you can easily get:

sage: A = matrix([[2,1],[1,1]])
sage: A
[2 1]
[1 1]
sage: C = matrix([[2],[3]])
sage: C
[2]
[3]
sage: A * C
[7]
[5]
sage: L = []
sage: L = [C]
sage: for i in range(10):
....:     C = A*C
....:     L.append(C)
sage: L
[
[2]  [7]  [19]  [50]  [131]  [343]  [898]  [2351]  [6155]  [16114]
[3], [5], [12], [31], [ 81], [212], [555], [1453], [3804], [ 9959],

[42187]
[26073]
]