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Question one asked "How many of these neighborhood configurations are there?"
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That means "how many entries are there in this list?"
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And we can figure that out the same way we figured out
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that there were eight entries in the elementary cellular automata.
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We can say that there is two possibilities for each of these seven cells
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they each can be either black or white and so there is two to the seventh
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possible neighborhood coonfigurations which is equal to 128.
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So there is 128 entries in this list and c was the correct answer.
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Question two asked "How many different cellular automata rule tables are there?"
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Well, that asks how many ways can we fill in these update states for the center cells,
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and since there is 128 possibilities, and each time there's two possibilities black or white
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we get two times two times two 128 times which is two raised to the 128th power,
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a ridiculously large number.