Clues: [contextual images]
Instructions: Name That Actor
_ _ _ _ _ _ A _ _ _ _
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The title is a hint for 'matrix' (a simulation). This implies that the given hints are a matrix multiplication.
Performing the matrix multiplication with the filled cells as 1 and empty as 0 gives this result for the first set:
0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0
Which shows an 'R'. Repeating this process for the other matrix multiplications gives the hint 'Rivendell', a city in Lord of the Rings (which again is hinted by the title).
The master of Rivendell is Elrond. The corresponding actor, and final answer to the puzzle, is Hugo Weaving.
(credits to cap for fixing this last bit).
Additionally, Hugo Weaving played Agent Smith in the Matrix, in which he multiplied like a computer virus. Thus we use matrix multiplication!