Utilizing Excel's turing capabilities to create Conway's 'Game of Life'

Patrick2788 

I too had a one-step success, followed by failure.  I started by just exploring a single step of the process and came up with

Stepλ
"Calculates outturn for a single cell"
= LET(
    count, SUM(OFFSET(cell, -1, -1, 3, 3)) - cell,
    IF(cell, SUM(SIGN(count = {2, 3})), SIGN(count = 3))
  )

For the entire board

= MAP(start, Stepλ)

worked fine but

= REDUCE(start, SEQUENCE(2), LAMBDA(board,k, MAP(board, Stepλ)))

failed because OFFSET is a range operator and, at step 2, I was offering it an array.  Back to the drawing board!  I would probably stick with REDUCE but it is back to the start with OFFSET.

At the moment I see myself as going with MAKEARRAY in order to generate indices and 

= SUM(INDEX(start,r+δr,c+δc)) - INDEX(start,r,c)

δr = {1;0;-1}
δc = {1,0,-1}

Still some edge conditions to sort, though.