###### tags: `other`

import numpy as np

mat = np.array([[0,0.5,0.5,0],[0.6,0,0.4,0],[0.7,0.3,0,0],[0,0,0,1]])

print('Initial steps: \n', mat, '\n')
print('After 3 steps: \n', np.linalg.matrix_power(mat,3), '\n')
print('After 10 steps: \n', np.linalg.matrix_power(mat,10), '\n')
print('After 30 steps: \n', np.linalg.matrix_power(mat,30), '\n')
print('After 100 steps: \n', np.linalg.matrix_power(mat,100), '\n')
print('After 300 steps: \n', np.linalg.matrix_power(mat,300), '\n')

Initial steps:
 [[0.  0.5 0.5 0. ]
 [0.6 0.  0.4 0. ]
 [0.7 0.3 0.  0. ]
 [0.  0.  0.  1. ]]

After 3 steps:
 [[0.23  0.385 0.385 0.   ]
 [0.462 0.23  0.308 0.   ]
 [0.539 0.231 0.23  0.   ]
 [0.    0.    0.    1.   ]]

After 10 steps:
 [[0.40201735 0.28714809 0.31083456 0.        ]
 [0.39195065 0.29305958 0.31498977 0.        ]
 [0.38779545 0.2954585  0.31674605 0.        ]
 [0.         0.         0.         1.        ]]

After 30 steps:
 [[0.39461986 0.29147922 0.31390092 0.        ]
 [0.39461846 0.29148004 0.3139015  0.        ]
 [0.39461789 0.29148038 0.31390174 0.        ]
 [0.         0.         0.         1.        ]]

After 100 steps:
 [[0.39461883 0.29147982 0.31390135 0.        ]
 [0.39461883 0.29147982 0.31390135 0.        ]
 [0.39461883 0.29147982 0.31390135 0.        ]
 [0.         0.         0.         1.        ]]

After 300 steps:
 [[0.39461883 0.29147982 0.31390135 0.        ]
 [0.39461883 0.29147982 0.31390135 0.        ]
 [0.39461883 0.29147982 0.31390135 0.        ]
 [0.         0.         0.         1.        ]]