circuit in Conway’s Game of Life

Question

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!!!!

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. — guest196883, Feb 07 '13 at 19:29
Also posted to MO, http://mathoverflow.net/questions/121169/circuit-in-conways-game-of-life where I expect it to be closed, fast. — Gerry Myerson, Feb 08 '13 at 10:37
@ChrisEagle - isn't a circuit a particular type of graph or network? - https://math.stackexchange.com/a/1598203/157195 — Ropstah, Jan 06 '18 at 12:02

score 4 · Accepted Answer · answered Feb 08 '13 at 22:26

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.

circuit in Conway’s Game of Life

1 Answers1