circuit in Conway’s Game of Life

logic cellular-automata

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 $S+a0=3$.

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.

1,753

user60465

Updated on August 01, 2022

Comments

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