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Let's assume that the bits in the Moore neighborhood are numbere as follows:

$$\begin{array}{lll} a_4 & a_3 & a_2 & a_{11}\\ a_5 & {\large a_0} & a_1 & a_{10} \\ a_6 & a_7 & a_8 & a_9 \end{array}$$

and let $x$, which belongs to the set of positive integers, denote time. For Conway’s Game of Life, how to draw a circuit that calculates $а_0(x + 1)$ in terms of $а_0(x), \ldots , а_8(x)$.

Thanks much in advance!!!!

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You might want to post this on stack overflow. Not that it isn't on topic here, you just might get a better response there. –  Sam DeHority Feb 7 '13 at 19:29
    
what is $b_0$?? –  example Feb 7 '13 at 19:35
    
Sorry) That was typing error))) –  user60465 Feb 7 '13 at 20:40
    
What does "circuit" mean? –  Chris Eagle Feb 7 '13 at 22:33
1  
Also posted to MO, mathoverflow.net/questions/121169/… where I expect it to be closed, fast. –  Gerry Myerson Feb 8 '13 at 10:37

1 Answer 1

up vote 3 down vote accepted

Here is a logic circuit to calculate the next state. I uses a lot of XOR and AND gates, a few OR gates and a couple of NOT gates. It basically sums the number of surrounding cells $S = a1+a2+a3+a4+a5+a6+a7+a8$ and then produces a $1$ if $S=3$ or $S+a0=3$.

Calculating the value of a0(t+1) from a0..a8 using logic gates

I haven't tested it, so there is probably a mistake somewhere.

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Thanks much!!!!! –  user60465 Feb 9 '13 at 9:12

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