circuit in Conway’s Game of Life


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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Updated on August 01, 2022


  • user60465
    user60465 over 1 year

    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
      guest196883 over 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
      example over 10 years
      what is $b_0$??
    • user60465
      user60465 over 10 years
      Sorry) That was typing error)))
    • Chris Eagle
      Chris Eagle over 10 years
      What does "circuit" mean?
    • Gerry Myerson
      Gerry Myerson over 10 years
      Also posted to MO,… where I expect it to be closed, fast.
    • MJD
      MJD over 10 years
      What are $a_9, a_{10}, a_{11}$ for?
    • Ropstah
      Ropstah almost 6 years
      @ChrisEagle - isn't a circuit a particular type of graph or network? -