# circuit in Conway’s Game of Life

1,753

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 $S+a0=3$.

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

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### user60465

Updated on August 01, 2022

• user60465 5 months

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!!!!

• guest196883 almost 10 years
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.
• example almost 10 years
what is $b_0$??
• user60465 almost 10 years
Sorry) That was typing error)))
• Chris Eagle almost 10 years
What does "circuit" mean?
• Gerry Myerson almost 10 years
Also posted to MO, mathoverflow.net/questions/121169/… where I expect it to be closed, fast.
• MJD almost 10 years
What are $a_9, a_{10}, a_{11}$ for?
• Ropstah almost 5 years
@ChrisEagle - isn't a circuit a particular type of graph or network? - math.stackexchange.com/a/1598203/157195